# MINLPLib

### A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

#### Home // Instances // Documentation // Download // Statistics

This page lists for every application of MINLPLib instances the associated instances.

**Agriculture:**

**Alkylation:**

**Argentina utility plant:**

**Asset Management:**

**Autocorrelated Sequences:**

- autocorr_bern20-03

degree-four model for low autocorrelated binary sequences This instance arises in theoretical physics. Determining a ground state in the so-called Bernasconi model amounts to minimizing a degree-four energy function over variables taking values in {+1,-1}. Here, the energy function is expressed in 0/1 variables. The model contains symmetries, leading to multiple optimum solutions. - autocorr_bern20-05

degree-four model for low autocorrelated binary sequences This instance arises in theoretical physics. Determining a ground state in the so-called Bernasconi model amounts to minimizing a degree-four energy function over variables taking values in {+1,-1}. Here, the energy function is expressed in 0/1 variables. The model contains symmetries, leading to multiple optimum solutions. - autocorr_bern20-10

degree-four model for low autocorrelated binary sequences This instance arises in theoretical physics. Determining a ground state in the so-called Bernasconi model amounts to minimizing a degree-four energy function over variables taking values in {+1,-1}. Here, the energy function is expressed in 0/1 variables. The model contains symmetries, leading to multiple optimum solutions. - autocorr_bern20-15

- autocorr_bern25-03

- autocorr_bern25-06

- autocorr_bern25-13

- autocorr_bern25-19

- autocorr_bern25-25

- autocorr_bern30-04

- autocorr_bern30-08

- autocorr_bern30-15

- autocorr_bern30-23

- autocorr_bern30-30

- autocorr_bern35-04

- autocorr_bern35-09

- autocorr_bern35-18

- autocorr_bern35-26

- autocorr_bern35-35

- autocorr_bern40-05

- autocorr_bern40-10

- autocorr_bern40-20

- autocorr_bern40-30

- autocorr_bern40-40

- autocorr_bern45-05

- autocorr_bern45-11

- autocorr_bern45-23

- autocorr_bern45-34

- autocorr_bern45-45

- autocorr_bern50-06

- autocorr_bern50-13

- autocorr_bern50-25

- autocorr_bern50-38

- autocorr_bern50-50

- autocorr_bern55-06

- autocorr_bern55-14

- autocorr_bern55-28

- autocorr_bern55-41

- autocorr_bern55-55

- autocorr_bern60-08

- autocorr_bern60-15

- autocorr_bern60-30

- autocorr_bern60-45

- autocorr_bern60-60

**Batch processing:**

- batch
- batchdes
- contvar
- enpro48pb

enpro48 with added bounds to avoid evaluation errors - enpro56pb

enpro56 with added bounds to avoid evaluation errors - ravempb

ravem with added bounds to avoid evaluation errors

**Belgian chocolate problem:**

**Breeding:**

- pedigree_ex1058

Optimize selection of a fixed-size breeding population under a relatedness constraint - pedigree_ex485

Optimize selection of a fixed-size breeding population under a relatedness constraint - pedigree_ex485_2

Optimize selection of a fixed-size breeding population under a relatedness constraint - pedigree_sim2000

Optimize selection of a fixed-size breeding population under a relatedness constraint - pedigree_sim400

Optimize selection of a fixed-size breeding population under a relatedness constraint - pedigree_sp_top4_250

Optimize selection of a fixed-size breeding population under a relatedness constraint - pedigree_sp_top4_300

Optimize selection of a fixed-size breeding population under a relatedness constraint - pedigree_sp_top4_350tr

Optimize selection of a fixed-size breeding population under a relatedness constraint - pedigree_sp_top5_200

Optimize selection of a fixed-size breeding population under a relatedness constraint - pedigree_sp_top5_250

Optimize selection of a fixed-size breeding population under a relatedness constraint

**Cascading Tanks:**

**Catalyst Mixing:**

**Catalytic Cracking of Gas Oil:**

**Chain Optimization:**

**Chemical Equilibrium:**

**Coil Compression String Design:**

**Coloring:**

- color_lab2_4x0

A generalization of the vertex coloring problem that models the assignment of test variants of a written exam to the desks of a classroom in such a way that desks that are close-by receive different variants. - color_lab3_3x0

A generalization of the vertex coloring problem that models the assignment of test variants of a written exam to the desks of a classroom in such a way that desks that are close-by receive different variants. - color_lab3_4x0

A generalization of the vertex coloring problem that models the assignment of test variants of a written exam to the desks of a classroom in such a way that desks that are close-by receive different variants. - color_lab6b_4x20

**Computational geometry:**

- gabriel01

The question to answer is to find the minimum value of k such that the k-Gabriel graph of any set of points in the plane is Hamiltonian. A known upper bound on k is 10. Infeasibility of this instance would give some indication for lower bounds on k. - gabriel02

The question to answer is to find the minimum value of k such that the k-Gabriel graph of any set of points in the plane is Hamiltonian. A known upper bound on k is 10. Infeasibility of this instance would give some indication for lower bounds on k. - gabriel04

The question to answer is to find the minimum value of k such that the k-Gabriel graph of any set of points in the plane is Hamiltonian. A known upper bound on k is 10. Infeasibility of this instance would give some indication for lower bounds on k. - gabriel05

- gabriel06

- gabriel07

- gabriel08

- gabriel09

- gabriel10

**Constraint Satisfaction:**

- maxcsp-ehi-85-297-12

Binary Max-CSP (find a complete instantiation of variables which maximizes the number of satisfied constraints) instance with table constraint from CSP 2008 Competition. - maxcsp-ehi-85-297-36

Binary Max-CSP (find a complete instantiation of variables which maximizes the number of satisfied constraints) instance with table constraint from CSP 2008 Competition. - maxcsp-ehi-85-297-71

Binary Max-CSP (find a complete instantiation of variables which maximizes the number of satisfied constraints) instance with table constraint from CSP 2008 Competition. - maxcsp-ehi-90-315-70

- maxcsp-geo50-20-d4-75-36

- maxcsp-langford-3-11

**Contingency Planning:**

**Cross-dock Door Assignment:**

**Crude Oil Scheduling:**

- crudeoil_lee1_05

Generated by running Scheduler.gms with LeeCrudeOil1 and for 5 slots - crudeoil_lee1_06

Generated by running Scheduler.gms with LeeCrudeOil1 and for 6 slots - crudeoil_lee1_07

Generated by running Scheduler.gms with LeeCrudeOil1 and for 7 slots - crudeoil_lee1_08

Generated by running Scheduler.gms with LeeCrudeOil1 and for 8 slots - crudeoil_lee1_09

Generated by running Scheduler.gms with LeeCrudeOil1 and for 9 slots - crudeoil_lee1_10

Generated by running Scheduler.gms with LeeCrudeOil1 and for 10 slots - crudeoil_lee2_05

Generated by running Scheduler.gms with LeeCrudeOil2 and for 5 slots - crudeoil_lee2_06

Generated by running Scheduler.gms with LeeCrudeOil2 and for 6 slots - crudeoil_lee2_07

Generated by running Scheduler.gms with LeeCrudeOil2 and for 7 slots - crudeoil_lee2_08

Generated by running Scheduler.gms with LeeCrudeOil2 and for 8 slots - crudeoil_lee2_09

Generated by running Scheduler.gms with LeeCrudeOil2 and for 9 slots - crudeoil_lee2_10

Generated by running Scheduler.gms with LeeCrudeOil2 and for 10 slots - crudeoil_lee3_05

Generated by running Scheduler.gms with LeeCrudeOil3 and for 5 slots - crudeoil_lee3_06

Generated by running Scheduler.gms with LeeCrudeOil3 and for 6 slots - crudeoil_lee3_07

Generated by running Scheduler.gms with LeeCrudeOil3 and for 7 slots - crudeoil_lee3_08

Generated by running Scheduler.gms with LeeCrudeOil3 and for 8 slots - crudeoil_lee3_09

Generated by running Scheduler.gms with LeeCrudeOil3 and for 9 slots - crudeoil_lee3_10

Generated by running Scheduler.gms with LeeCrudeOil3 and for 10 slots - crudeoil_lee4_05

Generated by running Scheduler.gms with LeeCrudeOil4 and for 5 slots - crudeoil_lee4_06

Generated by running Scheduler.gms with LeeCrudeOil4 and for 6 slots - crudeoil_lee4_07

Generated by running Scheduler.gms with LeeCrudeOil4 and for 7 slots - crudeoil_lee4_08

Generated by running Scheduler.gms with LeeCrudeOil4 and for 8 slots - crudeoil_lee4_09

Generated by running Scheduler.gms with LeeCrudeOil4 and for 9 slots - crudeoil_lee4_10

Generated by running Scheduler.gms with LeeCrudeOil4 and for 10 slots - crudeoil_li01
- crudeoil_li02
- crudeoil_li03
- crudeoil_li05
- crudeoil_li06
- crudeoil_li11
- crudeoil_li21

**Cutting Stock:**

**Cyclic multiproduct scheduling on parallel lines:**

**Cyclic Scheduling of Continuous Parallel Units:**

- csched1
- csched1a

Corrected version of csched1. The printed version of the paper had some data inconsistencies. The objective of the models also has been reformulated. - csched2
- csched2a

Corrected version of csched2. The printed version of the paper had some data inconsistencies. The objective of the models also has been reformulated.

**Density modification based on single-crystal X-ray diffraction data:**

**Design of Just-in-Time Flowshops:**

- jit1

This just-in-time flowshop problem involves P products and S stages. Each stage contains identical equipment performing the same type of operation on different products. The objective is to minimize the total equipment related cost.

**Deterministic Security Constrained Unit Commitment:**

**Edge-crossing minimization in bipartite graphs:**

- edgecross10-010

edge-crossing minimization in bipartite graphs modeled as a quadratic linear ordering problem This instance is for the edge crossing minimization problem in a bipartite graph G. G has to be drawn in the plane so that the nodes of its two shores are placed on two parallel horizontal lines. The task is to minimize the number of edge crossings by permuting the order of nodes on each layer, assuming that all edges are drawn as straight lines. The problem can be modeled as a quadratic objective over linear ordering variables. - edgecross10-020

edge-crossing minimization in bipartite graphs modeled as a quadratic linear ordering problem This instance is for the edge crossing minimization problem in a bipartite graph G. G has to be drawn in the plane so that the nodes of its two shores are placed on two parallel horizontal lines. The task is to minimize the number of edge crossings by permuting the order of nodes on each layer, assuming that all edges are drawn as straight lines. The problem can be modeled as a quadratic objective over linear ordering variables. - edgecross10-030

edge-crossing minimization in bipartite graphs modeled as a quadratic linear ordering problem This instance is for the edge crossing minimization problem in a bipartite graph G. G has to be drawn in the plane so that the nodes of its two shores are placed on two parallel horizontal lines. The task is to minimize the number of edge crossings by permuting the order of nodes on each layer, assuming that all edges are drawn as straight lines. The problem can be modeled as a quadratic objective over linear ordering variables. - edgecross10-040

- edgecross10-050

- edgecross10-060

- edgecross10-070

- edgecross10-080

- edgecross10-090

- edgecross14-019

- edgecross14-039

- edgecross14-058

- edgecross14-078

- edgecross14-098

- edgecross14-117

- edgecross14-137

- edgecross14-156

- edgecross14-176

- edgecross20-040

- edgecross20-080

- edgecross22-048

- edgecross22-096

- edgecross24-057

- edgecross24-115

**Elastic-plastic torsion:**

**Electricity generation:**

**Electricity Networks:**

- powerflow0009p

Optimal Power Flow problem modeled using trigonometric functions (polar coordinates) - powerflow0009r

Optimal Power Flow problem modeled using quadratic functions (rectangular coordinates) - powerflow0014p

Optimal Power Flow problem modeled using trigonometric functions (polar coordinates) - powerflow0014r

Optimal Power Flow problem modeled using quadratic functions (rectangular coordinates) - powerflow0030p

Optimal Power Flow problem modeled using trigonometric functions (polar coordinates) - powerflow0030r

Optimal Power Flow problem modeled using quadratic functions (rectangular coordinates) - powerflow0039p

Optimal Power Flow problem modeled using trigonometric functions (polar coordinates) - powerflow0039r

Optimal Power Flow problem modeled using quadratic functions (rectangular coordinates) - powerflow0057p

Optimal Power Flow problem modeled using trigonometric functions (polar coordinates) - powerflow0057r

Optimal Power Flow problem modeled using quadratic functions (rectangular coordinates) - powerflow0118p

Optimal Power Flow problem modeled using trigonometric functions (polar coordinates) - powerflow0118r

Optimal Power Flow problem modeled using quadratic functions (rectangular coordinates) - powerflow0300p

Optimal Power Flow problem modeled using trigonometric functions (polar coordinates) - powerflow0300r

Optimal Power Flow problem modeled using quadratic functions (rectangular coordinates) - powerflow2383wpp

Optimal Power Flow problem modeled using trigonometric functions (polar coordinates) - powerflow2383wpr

Optimal Power Flow problem modeled using quadratic functions (rectangular coordinates) - powerflow2736spp

Optimal Power Flow problem modeled using trigonometric functions (polar coordinates) - powerflow2736spr

Optimal Power Flow problem modeled using quadratic functions (rectangular coordinates) - transswitch0009p

Optimal Transmission Switching problem modeled using trigonometric functions (polar coordinates) - transswitch0009r

Optimal Transmission Switching problem modeled using quadratic functions (rectangular coordinates) - transswitch0014p

Optimal Transmission Switching problem modeled using trigonometric functions (polar coordinates) - transswitch0014r

Optimal Transmission Switching problem modeled using quadratic functions (rectangular coordinates) - transswitch0030p

Optimal Transmission Switching problem modeled using trigonometric functions (polar coordinates) - transswitch0030r

Optimal Transmission Switching problem modeled using quadratic functions (rectangular coordinates) - transswitch0039p

Optimal Transmission Switching problem modeled using trigonometric functions (polar coordinates) - transswitch0039r

Optimal Transmission Switching problem modeled using quadratic functions (rectangular coordinates) - transswitch0057p

Optimal Transmission Switching problem modeled using trigonometric functions (polar coordinates) - transswitch0057r

Optimal Transmission Switching problem modeled using quadratic functions (rectangular coordinates) - transswitch0118p

Optimal Transmission Switching problem modeled using trigonometric functions (polar coordinates) - transswitch0118r

Optimal Transmission Switching problem modeled using quadratic functions (rectangular coordinates) - transswitch0300p

Optimal Transmission Switching problem modeled using trigonometric functions (polar coordinates) - transswitch0300r

Optimal Transmission Switching problem modeled using quadratic functions (rectangular coordinates) - transswitch2383wpp

Optimal Transmission Switching problem modeled using trigonometric functions (polar coordinates) - transswitch2383wpr

Optimal Transmission Switching problem modeled using quadratic functions (rectangular coordinates) - transswitch2736spp

Optimal Transmission Switching problem modeled using trigonometric functions (polar coordinates) - transswitch2736spr

Optimal Transmission Switching problem modeled using quadratic functions (rectangular coordinates)

**Electricity Storage:**

- gams02

A GAMS client model forwarded by M. Bussieck 12th Feb 2015 and replaced by an updated version on 26th March 2015.

**Electrons on a Sphere:**

**Energy:**

**Facility Location:**

- emfl050_3_3

Given a set of 50 existing facilities, we compute the coordinates of 9 new facilities on a rectangular grid subject to minimizing the weighted sum of the euclidian distances between facilities. - emfl050_5_5

Given a set of 50 existing facilities, we compute the coordinates of 25 new facilities on a rectangular grid subject to minimizing the weighted sum of the euclidian distances between facilities. - emfl100_3_3

Given a set of 100 existing facilities, we compute the coordinates of 9 new facilities on a rectangular grid subject to minimizing the weighted sum of the euclidian distances between facilities. - emfl100_5_5

Given a set of 100 existing facilities, we compute the coordinates of 25 new facilities on a rectangular grid subject to minimizing the weighted sum of the euclidian distances between facilities. - sfacloc1_2_80

Probabilistic Facility Location and Assignment with Random Demand (given by 5000 scenarios), where 2 facilities can be opened anywhere in the Euclidean plane (distances are measured with the Manhattan (or L1) metric), the facilities are capacitated and each customer may be served by more than one facility. The objective is to minimize an upper-bound on the weighted total-distance (i.e., the sum of the product of the demand of each customer times the distance to the facility serving that customer) such that this bound is satisfied with a reliability level of 0.80. - sfacloc1_2_90

Probabilistic Facility Location and Assignment with Random Demand (given by 5000 scenarios), where 2 facilities can be opened anywhere in the Euclidean plane (distances are measured with the Manhattan (or L1) metric), the facilities are capacitated and each customer may be served by more than one facility. The objective is to minimize an upper-bound on the weighted total-distance (i.e., the sum of the product of the demand of each customer times the distance to the facility serving that customer) such that this bound is satisfied with a reliability level of 0.90. - sfacloc1_2_95

Probabilistic Facility Location and Assignment with Random Demand (given by 5000 scenarios), where 2 facilities can be opened anywhere in the Euclidean plane (distances are measured with the Manhattan (or L1) metric), the facilities are capacitated and each customer may be served by more than one facility. The objective is to minimize an upper-bound on the weighted total-distance (i.e., the sum of the product of the demand of each customer times the distance to the facility serving that customer) such that this bound is satisfied with a reliability level of 0.95. - sfacloc1_3_80

Probabilistic Facility Location and Assignment with Random Demand (given by 5000 scenarios), where 3 facilities can be opened anywhere in the Euclidean plane (distances are measured with the Manhattan (or L1) metric), the facilities are capacitated and each customer may be served by more than one facility. The objective is to minimize an upper-bound on the weighted total-distance (i.e., the sum of the product of the demand of each customer times the distance to the facility serving that customer) such that this bound is satisfied with a reliability level of 0.80. - sfacloc1_3_90

Probabilistic Facility Location and Assignment with Random Demand (given by 5000 scenarios), where 3 facilities can be opened anywhere in the Euclidean plane (distances are measured with the Manhattan (or L1) metric), the facilities are capacitated and each customer may be served by more than one facility. The objective is to minimize an upper-bound on the weighted total-distance (i.e., the sum of the product of the demand of each customer times the distance to the facility serving that customer) such that this bound is satisfied with a reliability level of 0.90. - sfacloc1_3_95

Probabilistic Facility Location and Assignment with Random Demand (given by 5000 scenarios), where 3 facilities can be opened anywhere in the Euclidean plane (distances are measured with the Manhattan (or L1) metric), the facilities are capacitated and each customer may be served by more than one facility. The objective is to minimize an upper-bound on the weighted total-distance (i.e., the sum of the product of the demand of each customer times the distance to the facility serving that customer) such that this bound is satisfied with a reliability level of 0.95. - sfacloc1_4_80

Probabilistic Facility Location and Assignment with Random Demand (given by 5000 scenarios), where 4 facilities can be opened anywhere in the Euclidean plane (distances are measured with the Manhattan (or L1) metric), the facilities are capacitated and each customer may be served by more than one facility. The objective is to minimize an upper-bound on the weighted total-distance (i.e., the sum of the product of the demand of each customer times the distance to the facility serving that customer) such that this bound is satisfied with a reliability level of 0.80. - sfacloc1_4_90

Probabilistic Facility Location and Assignment with Random Demand (given by 5000 scenarios), where 4 facilities can be opened anywhere in the Euclidean plane (distances are measured with the Manhattan (or L1) metric), the facilities are capacitated and each customer may be served by more than one facility. The objective is to minimize an upper-bound on the weighted total-distance (i.e., the sum of the product of the demand of each customer times the distance to the facility serving that customer) such that this bound is satisfied with a reliability level of 0.90. - sfacloc1_4_95

Probabilistic Facility Location and Assignment with Random Demand (given by 5000 scenarios), where 4 facilities can be opened anywhere in the Euclidean plane (distances are measured with the Manhattan (or L1) metric), the facilities are capacitated and each customer may be served by more than one facility. The objective is to minimize an upper-bound on the weighted total-distance (i.e., the sum of the product of the demand of each customer times the distance to the facility serving that customer) such that this bound is satisfied with a reliability level of 0.95. - sfacloc2_2_80

Probabilistic Facility Location and Assignment with Random Demand (given by 5000 scenarios), where 2 facilities can be opened anywhere in the Euclidean plane (distances are measured with the Manhattan (or L1) metric), the facilities are capacitated and each customer is served by a single facility. The objective is to minimize an upper-bound on the weighted total-distance (i.e., the sum of the product of the demand of each customer times the distance to the facility serving that customer) such that this bound is satisfied with a reliability level of 0.80. - sfacloc2_2_90

Probabilistic Facility Location and Assignment with Random Demand (given by 5000 scenarios), where 2 facilities can be opened anywhere in the Euclidean plane (distances are measured with the Manhattan (or L1) metric), the facilities are capacitated and each customer is served by a single facility. The objective is to minimize an upper-bound on the weighted total-distance (i.e., the sum of the product of the demand of each customer times the distance to the facility serving that customer) such that this bound is satisfied with a reliability level of 0.90. - sfacloc2_2_95

Probabilistic Facility Location and Assignment with Random Demand (given by 5000 scenarios), where 2 facilities can be opened anywhere in the Euclidean plane (distances are measured with the Manhattan (or L1) metric), the facilities are capacitated and each customer is served by a single facility. The objective is to minimize an upper-bound on the weighted total-distance (i.e., the sum of the product of the demand of each customer times the distance to the facility serving that customer) such that this bound is satisfied with a reliability level of 0.95. - sfacloc2_3_80

Probabilistic Facility Location and Assignment with Random Demand (given by 5000 scenarios), where 3 facilities can be opened anywhere in the Euclidean plane (distances are measured with the Manhattan (or L1) metric), the facilities are capacitated and each customer is served by a single facility. The objective is to minimize an upper-bound on the weighted total-distance (i.e., the sum of the product of the demand of each customer times the distance to the facility serving that customer) such that this bound is satisfied with a reliability level of 0.80. - sfacloc2_3_90

Probabilistic Facility Location and Assignment with Random Demand (given by 5000 scenarios), where 3 facilities can be opened anywhere in the Euclidean plane (distances are measured with the Manhattan (or L1) metric), the facilities are capacitated and each customer is served by a single facility. The objective is to minimize an upper-bound on the weighted total-distance (i.e., the sum of the product of the demand of each customer times the distance to the facility serving that customer) such that this bound is satisfied with a reliability level of 0.90. - sfacloc2_3_95

Probabilistic Facility Location and Assignment with Random Demand (given by 5000 scenarios), where 3 facilities can be opened anywhere in the Euclidean plane (distances are measured with the Manhattan (or L1) metric), the facilities are capacitated and each customer is served by a single facility. The objective is to minimize an upper-bound on the weighted total-distance (i.e., the sum of the product of the demand of each customer times the distance to the facility serving that customer) such that this bound is satisfied with a reliability level of 0.95. - sfacloc2_4_80

Probabilistic Facility Location and Assignment with Random Demand (given by 5000 scenarios), where 4 facilities can be opened anywhere in the Euclidean plane (distances are measured with the Manhattan (or L1) metric), the facilities are capacitated and each customer is served by a single facility. The objective is to minimize an upper-bound on the weighted total-distance (i.e., the sum of the product of the demand of each customer times the distance to the facility serving that customer) such that this bound is satisfied with a reliability level of 0.80. - sfacloc2_4_90

Probabilistic Facility Location and Assignment with Random Demand (given by 5000 scenarios), where 4 facilities can be opened anywhere in the Euclidean plane (distances are measured with the Manhattan (or L1) metric), the facilities are capacitated and each customer is served by a single facility. The objective is to minimize an upper-bound on the weighted total-distance (i.e., the sum of the product of the demand of each customer times the distance to the facility serving that customer) such that this bound is satisfied with a reliability level of 0.90. - sfacloc2_4_95

Probabilistic Facility Location and Assignment with Random Demand (given by 5000 scenarios), where 4 facilities can be opened anywhere in the Euclidean plane (distances are measured with the Manhattan (or L1) metric), the facilities are capacitated and each customer is served by a single facility. The objective is to minimize an upper-bound on the weighted total-distance (i.e., the sum of the product of the demand of each customer times the distance to the facility serving that customer) such that this bound is satisfied with a reliability level of 0.95. - squfl010-025

Separable quadratic uncapacitated facility location problem. A set of customers, each having unit demand, has to be satisfied by open facilities. The objective is to minimize the sum of the fixed cost for operating facilities and the shipping cost which is proportional to the square of the quantity delivered to each customer. - squfl010-025persp

Separable quadratic uncapacitated facility location problem. A set of customers, each having unit demand, has to be satisfied by open facilities. The objective is to minimize the sum of the fixed cost for operating facilities and the shipping cost which is proportional to the square of the quantity delivered to each customer. Perspective reformulation of squfl010-025. - squfl010-040

Separable quadratic uncapacitated facility location problem. A set of customers, each having unit demand, has to be satisfied by open facilities. The objective is to minimize the sum of the fixed cost for operating facilities and the shipping cost which is proportional to the square of the quantity delivered to each customer. - squfl010-040persp

Separable quadratic uncapacitated facility location problem. A set of customers, each having unit demand, has to be satisfied by open facilities. The objective is to minimize the sum of the fixed cost for operating facilities and the shipping cost which is proportional to the square of the quantity delivered to each customer. Perspective reformulation of squfl010-040. - squfl010-080

Separable quadratic uncapacitated facility location problem. A set of customers, each having unit demand, has to be satisfied by open facilities. The objective is to minimize the sum of the fixed cost for operating facilities and the shipping cost which is proportional to the square of the quantity delivered to each customer. - squfl010-080persp

Separable quadratic uncapacitated facility location problem. A set of customers, each having unit demand, has to be satisfied by open facilities. The objective is to minimize the sum of the fixed cost for operating facilities and the shipping cost which is proportional to the square of the quantity delivered to each customer. Perspective reformulation of squfl010-080. - squfl015-060

- squfl015-060persp

Separable quadratic uncapacitated facility location problem. A set of customers, each having unit demand, has to be satisfied by open facilities. The objective is to minimize the sum of the fixed cost for operating facilities and the shipping cost which is proportional to the square of the quantity delivered to each customer. Perspective reformulation of squfl015-060. - squfl015-080

- squfl015-080persp

Separable quadratic uncapacitated facility location problem. A set of customers, each having unit demand, has to be satisfied by open facilities. The objective is to minimize the sum of the fixed cost for operating facilities and the shipping cost which is proportional to the square of the quantity delivered to each customer. Perspective reformulation of squfl015-080. - squfl020-040

- squfl020-040persp

Separable quadratic uncapacitated facility location problem. A set of customers, each having unit demand, has to be satisfied by open facilities. The objective is to minimize the sum of the fixed cost for operating facilities and the shipping cost which is proportional to the square of the quantity delivered to each customer. Perspective reformulation of squfl020-040. - squfl020-050

- squfl020-050persp

Separable quadratic uncapacitated facility location problem. A set of customers, each having unit demand, has to be satisfied by open facilities. The objective is to minimize the sum of the fixed cost for operating facilities and the shipping cost which is proportional to the square of the quantity delivered to each customer. Perspective reformulation of squfl020-050. - squfl020-150

- squfl020-150persp

Separable quadratic uncapacitated facility location problem. A set of customers, each having unit demand, has to be satisfied by open facilities. The objective is to minimize the sum of the fixed cost for operating facilities and the shipping cost which is proportional to the square of the quantity delivered to each customer. Perspective reformulation of squfl020-150. - squfl025-025

- squfl025-025persp

Separable quadratic uncapacitated facility location problem. A set of customers, each having unit demand, has to be satisfied by open facilities. The objective is to minimize the sum of the fixed cost for operating facilities and the shipping cost which is proportional to the square of the quantity delivered to each customer. Perspective reformulation of squfl025-025. - squfl025-030

- squfl025-030persp

Separable quadratic uncapacitated facility location problem. A set of customers, each having unit demand, has to be satisfied by open facilities. The objective is to minimize the sum of the fixed cost for operating facilities and the shipping cost which is proportional to the square of the quantity delivered to each customer. Perspective reformulation of squfl025-030. - squfl025-040

- squfl025-040persp

Separable quadratic uncapacitated facility location problem. A set of customers, each having unit demand, has to be satisfied by open facilities. The objective is to minimize the sum of the fixed cost for operating facilities and the shipping cost which is proportional to the square of the quantity delivered to each customer. Perspective reformulation of squfl025-040. - squfl030-100

- squfl030-100persp

Separable quadratic uncapacitated facility location problem. A set of customers, each having unit demand, has to be satisfied by open facilities. The objective is to minimize the sum of the fixed cost for operating facilities and the shipping cost which is proportional to the square of the quantity delivered to each customer. Perspective reformulation of squfl030-100. - squfl030-150

- squfl030-150persp

Separable quadratic uncapacitated facility location problem. A set of customers, each having unit demand, has to be satisfied by open facilities. The objective is to minimize the sum of the fixed cost for operating facilities and the shipping cost which is proportional to the square of the quantity delivered to each customer. Perspective reformulation of squfl030-150. - squfl040-080

- squfl040-080persp

Separable quadratic uncapacitated facility location problem. A set of customers, each having unit demand, has to be satisfied by open facilities. The objective is to minimize the sum of the fixed cost for operating facilities and the shipping cost which is proportional to the square of the quantity delivered to each customer. Perspective reformulation of squfl040-080.

**Farming:**

**Feed Mix:**

**Feed Plate Location:**

**feed plate location:**

**Financial Optimization:**

**Flow in a Channel:**

**four membrane pipe modules in feed-and-bleed coupling:**

**Frequency Assignment:**

- celar6-sub0

A radio-link frequency assignment problem formulated as a cost-function network, aka weighted constraint satisfaction problem.

**Gas Trade:**

**Gas Transmission:**

- gasnet_al1

The problem considered is a complex industrial problem concerning the operation of an industrial gas pipeline network. Given the network information consisting of a set of plants, cold boxes, compressors, pipeline network sections and customer demands in every section, we wish to decide which compressors and cold boxes to operate and their operation levels in order to minimize the total cost of satisfying customer demands. - gasnet_al2

The problem considered is a complex industrial problem concerning the operation of an industrial gas pipeline network. Given the network information consisting of a set of plants, cold boxes, compressors, pipeline network sections and customer demands in every section, we wish to decide which compressors and cold boxes to operate and their operation levels in order to minimize the total cost of satisfying customer demands. - gasnet_al3

The problem considered is a complex industrial problem concerning the operation of an industrial gas pipeline network. Given the network information consisting of a set of plants, cold boxes, compressors, pipeline network sections and customer demands in every section, we wish to decide which compressors and cold boxes to operate and their operation levels in order to minimize the total cost of satisfying customer demands. - gasnet_al4

- gasnet_al5

- gastrans

The problem of distributing gas through a network of pipelines is formulated as a cost minimization subject to nonlinear flow-pressure relations, material balances, and pressure bounds. The Belgian gas network is used as an example. - gastrans040

Given gas flow and pressure specifications at entries and exits of a realistic gas network, the problem is to find a feasible network flow or to prove that none exists. The data is based on a real-world network from the gas transport company Open Grid Europe GmbH. - gastrans135

Given gas flow and pressure specifications at entries and exits of a realistic gas network, the problem is to find a feasible network flow or to prove that none exists. The data is based on a real-world network from the gas transport company Open Grid Europe GmbH. The network consists of 135 nodes, 141 pipes, and 29 compressor stations. - gastrans582_cold13

Given gas flow and pressure specifications at entries and exits of a realistic gas network, the problem is to find a feasible network flow or to prove that none exists. The data is based on a real-world network from the gas transport company Open Grid Europe GmbH. The network consists of 582 nodes, 278 pipes, 5 compressor stations, 23 control valve stations, 8 resistors, 26 valves, and 269 "short pipes". - gastrans582_cold13_95

Given gas flow and pressure specifications at entries and exits of a realistic gas network, the problem is to find a feasible network flow or to prove that none exists. The data is based on a real-world network from the gas transport company Open Grid Europe GmbH. The network consists of 582 nodes, 278 pipes, 5 compressor stations, 23 control valve stations, 8 resistors, 26 valves, and 269 "short pipes". Compared to instance gastrans582_cold13, in this instance the nominations have been scaled to 95% of the flow amount, i.e., the supplied (discharged) amount of gas at every entry (exit) has been scaled by 0.95. - gastrans582_cold17

Given gas flow and pressure specifications at entries and exits of a realistic gas network, the problem is to find a feasible network flow or to prove that none exists. The data is based on a real-world network from the gas transport company Open Grid Europe GmbH. The network consists of 582 nodes, 278 pipes, 5 compressor stations, 23 control valve stations, 8 resistors, 26 valves, and 269 "short pipes". - gastrans582_cold17_95

Given gas flow and pressure specifications at entries and exits of a realistic gas network, the problem is to find a feasible network flow or to prove that none exists. The data is based on a real-world network from the gas transport company Open Grid Europe GmbH. The network consists of 582 nodes, 278 pipes, 5 compressor stations, 23 control valve stations, 8 resistors, 26 valves, and 269 "short pipes". Compared to instance gastrans582_cold17, in this instance the nominations have been scaled to 95% of the flow amount, i.e., the supplied (discharged) amount of gas at every entry (exit) has been scaled by 0.95. - gastrans582_cool12

Given gas flow and pressure specifications at entries and exits of a realistic gas network, the problem is to find a feasible network flow or to prove that none exists. The data is based on a real-world network from the gas transport company Open Grid Europe GmbH. The network consists of 582 nodes, 278 pipes, 5 compressor stations, 23 control valve stations, 8 resistors, 26 valves, and 269 "short pipes". - gastrans582_cool12_95

Given gas flow and pressure specifications at entries and exits of a realistic gas network, the problem is to find a feasible network flow or to prove that none exists. The data is based on a real-world network from the gas transport company Open Grid Europe GmbH. The network consists of 582 nodes, 278 pipes, 5 compressor stations, 23 control valve stations, 8 resistors, 26 valves, and 269 "short pipes". Compared to instance gastrans582_cool12, in this instance the nominations have been scaled to 95% of the flow amount, i.e., the supplied (discharged) amount of gas at every entry (exit) has been scaled by 0.95. - gastrans582_cool14

- gastrans582_cool14_95

Given gas flow and pressure specifications at entries and exits of a realistic gas network, the problem is to find a feasible network flow or to prove that none exists. The data is based on a real-world network from the gas transport company Open Grid Europe GmbH. The network consists of 582 nodes, 278 pipes, 5 compressor stations, 23 control valve stations, 8 resistors, 26 valves, and 269 "short pipes". Compared to instance gastrans582_cool14, in this instance the nominations have been scaled to 95% of the flow amount, i.e., the supplied (discharged) amount of gas at every entry (exit) has been scaled by 0.95. - gastrans582_freezing27

- gastrans582_freezing27_95

Given gas flow and pressure specifications at entries and exits of a realistic gas network, the problem is to find a feasible network flow or to prove that none exists. The data is based on a real-world network from the gas transport company Open Grid Europe GmbH. The network consists of 582 nodes, 278 pipes, 5 compressor stations, 23 control valve stations, 8 resistors, 26 valves, and 269 "short pipes". Compared to instance gastrans582_freezing27, in this instance the nominations have been scaled to 95% of the flow amount, i.e., the supplied (discharged) amount of gas at every entry (exit) has been scaled by 0.95. - gastrans582_freezing30

- gastrans582_freezing30_95

Given gas flow and pressure specifications at entries and exits of a realistic gas network, the problem is to find a feasible network flow or to prove that none exists. The data is based on a real-world network from the gas transport company Open Grid Europe GmbH. The network consists of 582 nodes, 278 pipes, 5 compressor stations, 23 control valve stations, 8 resistors, 26 valves, and 269 "short pipes". Compared to instance gastrans582_freezing30, in this instance the nominations have been scaled to 95% of the flow amount, i.e., the supplied (discharged) amount of gas at every entry (exit) has been scaled by 0.95. - gastrans582_mild10

- gastrans582_mild10_95

Given gas flow and pressure specifications at entries and exits of a realistic gas network, the problem is to find a feasible network flow or to prove that none exists. The data is based on a real-world network from the gas transport company Open Grid Europe GmbH. The network consists of 582 nodes, 278 pipes, 5 compressor stations, 23 control valve stations, 8 resistors, 26 valves, and 269 "short pipes". Compared to instance gastrans582_mild10, in this instance the nominations have been scaled to 95% of the flow amount, i.e., the supplied (discharged) amount of gas at every entry (exit) has been scaled by 0.95. - gastrans582_mild11

- gastrans582_mild11_95

Given gas flow and pressure specifications at entries and exits of a realistic gas network, the problem is to find a feasible network flow or to prove that none exists. The data is based on a real-world network from the gas transport company Open Grid Europe GmbH. The network consists of 582 nodes, 278 pipes, 5 compressor stations, 23 control valve stations, 8 resistors, 26 valves, and 269 "short pipes". Compared to instance gastrans582_mild11, in this instance the nominations have been scaled to 95% of the flow amount, i.e., the supplied (discharged) amount of gas at every entry (exit) has been scaled by 0.95. - gastrans582_warm15

- gastrans582_warm15_95

Given gas flow and pressure specifications at entries and exits of a realistic gas network, the problem is to find a feasible network flow or to prove that none exists. The data is based on a real-world network from the gas transport company Open Grid Europe GmbH. The network consists of 582 nodes, 278 pipes, 5 compressor stations, 23 control valve stations, 8 resistors, 26 valves, and 269 "short pipes". Compared to instance gastrans582_warm15, in this instance the nominations have been scaled to 95% of the flow amount, i.e., the supplied (discharged) amount of gas at every entry (exit) has been scaled by 0.95. - gastrans582_warm31

- gastrans582_warm31_95

Given gas flow and pressure specifications at entries and exits of a realistic gas network, the problem is to find a feasible network flow or to prove that none exists. The data is based on a real-world network from the gas transport company Open Grid Europe GmbH. The network consists of 582 nodes, 278 pipes, 5 compressor stations, 23 control valve stations, 8 resistors, 26 valves, and 269 "short pipes". Compared to instance gastrans582_warm31, in this instance the nominations have been scaled to 95% of the flow amount, i.e., the supplied (discharged) amount of gas at every entry (exit) has been scaled by 0.95. - gastransnlp

The problem of distributing gas through a network of pipelines is formulated as a cost minimization subject to nonlinear flow-pressure relations, material balances, and pressure bounds. The Belgian gas network is used as an example.

**Gas Transmission Network Design:**

**Gear Train Design:**

**General Equilibrium:**

**Geometry:**

- ball_mk2_10

A simple MINLP with a feasible set described by a ball. The basic model over which these variations are made is: min sum_i=1^n x_i s.t. sum_i=1^n (x_i - 0.5)^2 <= (n-1)/4 x integer between -1 and 1. Obvisouly, this problem is infeasible and has no solution. It can be shown that any outer-approximation based method will need 2^n linear inequalities to show infeasibility, see reference. In this instance, the ball is slightly moved to contain the point 0. - ball_mk2_30

A simple MINLP with a feasible set described by a ball. The basic model over which these variations are made is: min sum_i=1^n x_i s.t. sum_i=1^n (x_i - 0.5)^2 <= (n-1)/4 x integer between -1 and 1. Obvisouly, this problem is infeasible and has no solution. It can be shown that any outer-approximation based method will need 2^n linear inequalities to show infeasibility, see reference. In this instance, the ball is slightly moved to contain the point 0. - ball_mk3_10

A simple MINLP with a feasible set described by a ball. The basic model over which these variations are made is: min sum_i=1^n x_i s.t. sum_i=1^n (x_i - 0.5)^2 <= (n-1)/4 x integer between -1 and 1. Obvisouly, this problem is infeasible and has no solution. It can be shown that any outer-approximation based method will need 2^n linear inequalities to show infeasibility, see reference. In this instance, the ball is an empty ellipse, but the quadratic form is still diagonal. - ball_mk3_20

A simple MINLP with a feasible set described by a ball. The basic model over which these variations are made is: min sum_i=1^n x_i s.t. sum_i=1^n (x_i - 0.5)^2 <= (n-1)/4 x integer between -1 and 1. Obvisouly, this problem is infeasible and has no solution. It can be shown that any outer-approximation based method will need 2^n linear inequalities to show infeasibility, see reference. In this instance, the ball is an empty ellipse, but the quadratic form is still diagonal. - ball_mk3_30

A simple MINLP with a feasible set described by a ball. The basic model over which these variations are made is: min sum_i=1^n x_i s.t. sum_i=1^n (x_i - 0.5)^2 <= (n-1)/4 x integer between -1 and 1. Obvisouly, this problem is infeasible and has no solution. It can be shown that any outer-approximation based method will need 2^n linear inequalities to show infeasibility, see reference. In this instance, the ball is an empty ellipse, but the quadratic form is still diagonal. - ball_mk4_05

A simple MINLP with a feasible set described by a ball. The basic model over which these variations are made is: min sum_i=1^n x_i s.t. sum_i=1^n (x_i - 0.5)^2 <= (n-1)/4 x integer between -1 and 1. Obvisouly, this problem is infeasible and has no solution. It can be shown that any outer-approximation based method will need 2^n linear inequalities to show infeasibility, see reference. In this instance, the ball is an empty ellipse and the quadratic form is not diagonal. - ball_mk4_10

A simple MINLP with a feasible set described by a ball. The basic model over which these variations are made is: min sum_i=1^n x_i s.t. sum_i=1^n (x_i - 0.5)^2 <= (n-1)/4 x integer between -1 and 1. Obvisouly, this problem is infeasible and has no solution. It can be shown that any outer-approximation based method will need 2^n linear inequalities to show infeasibility, see reference. In this instance, the ball is an empty ellipse and the quadratic form is not diagonal. - ball_mk4_15

A simple MINLP with a feasible set described by a ball. The basic model over which these variations are made is: min sum_i=1^n x_i s.t. sum_i=1^n (x_i - 0.5)^2 <= (n-1)/4 x integer between -1 and 1. Obvisouly, this problem is infeasible and has no solution. It can be shown that any outer-approximation based method will need 2^n linear inequalities to show infeasibility, see reference. In this instance, the ball is an empty ellipse and the quadratic form is not diagonal. - circle
- himmel16
- house
- kall_circles_c6a

A set of circles are to be cut from rectangular design plates to be produced, or from a set of stocked rectangles of known geometric dimensions. The objective is to minimize the area of the design rectangles. The design plates are subject to lower and upper bounds of their widths and lengths. The objects are free of any orientation restrictions. - kall_circles_c6b

A set of circles are to be cut from rectangular design plates to be produced, or from a set of stocked rectangles of known geometric dimensions. The objective is to minimize the area of the design rectangles. The design plates are subject to lower and upper bounds of their widths and lengths. The objects are free of any orientation restrictions. - kall_circles_c6c

A set of circles are to be cut from rectangular design plates to be produced, or from a set of stocked rectangles of known geometric dimensions. The objective is to minimize the area of the design rectangles. The design plates are subject to lower and upper bounds of their widths and lengths. The objects are free of any orientation restrictions. - kall_circles_c7a

- kall_circles_c8a

- kall_circlespolygons_c1p11

A set of circles and convex polygons are to be cut from rectangular design plates to be produced, or from a set of stocked rectangles of known geometric dimensions. The objective is to minimize the area of the design rectangles. The design plates are subject to lower and upper bounds of their widths and lengths. The objects are free of any orientation restrictions. - kall_circlespolygons_c1p12

A set of circles and convex polygons are to be cut from rectangular design plates to be produced, or from a set of stocked rectangles of known geometric dimensions. The objective is to minimize the area of the design rectangles. The design plates are subject to lower and upper bounds of their widths and lengths. The objects are free of any orientation restrictions. - kall_circlespolygons_c1p13

A set of circles and convex polygons are to be cut from rectangular design plates to be produced, or from a set of stocked rectangles of known geometric dimensions. The objective is to minimize the area of the design rectangles. The design plates are subject to lower and upper bounds of their widths and lengths. The objects are free of any orientation restrictions. - kall_circlespolygons_c1p5a

- kall_circlespolygons_c1p5b

- kall_circlespolygons_c1p6a

- kall_circlesrectangles_c1r11

A set of circles and rectangles are to be cut from rectangular design plates to be produced, or from a set of stocked rectangles of known geometric dimensions. The objective is to minimize the area of the design rectangles. The design plates are subject to lower and upper bounds of their widths and lengths. The objects are free of any orientation restrictions. - kall_circlesrectangles_c1r12

A set of circles and rectangles are to be cut from rectangular design plates to be produced, or from a set of stocked rectangles of known geometric dimensions. The objective is to minimize the area of the design rectangles. The design plates are subject to lower and upper bounds of their widths and lengths. The objects are free of any orientation restrictions. - kall_circlesrectangles_c1r13

A set of circles and rectangles are to be cut from rectangular design plates to be produced, or from a set of stocked rectangles of known geometric dimensions. The objective is to minimize the area of the design rectangles. The design plates are subject to lower and upper bounds of their widths and lengths. The objects are free of any orientation restrictions. - kall_circlesrectangles_c6r1

- kall_circlesrectangles_c6r29

- kall_circlesrectangles_c6r39

- kall_congruentcircles_c31

- kall_congruentcircles_c32

- kall_congruentcircles_c41

- kall_congruentcircles_c42

- kall_congruentcircles_c51

- kall_congruentcircles_c52

- kall_congruentcircles_c61

- kall_congruentcircles_c62

- kall_congruentcircles_c63

- kall_congruentcircles_c71

- kall_congruentcircles_c72

- kall_diffcircles_10

- kall_diffcircles_5a

- kall_diffcircles_5b

- kall_diffcircles_6

- kall_diffcircles_7

- kall_diffcircles_8

- kall_diffcircles_9

- kall_ellipsoids_tc02b

A set of tri-axial ellipsoids, with given semi-axes, is to be packed into a rectangular box; its widths, lengths and height are subject to lower and upper bounds. We want to minimize the volume of this box and seek an overlap-free placement of the ellipsoids which can take any orientation. - kall_ellipsoids_tc03c

A set of tri-axial ellipsoids, with given semi-axes, is to be packed into a rectangular box; its widths, lengths and height are subject to lower and upper bounds. We want to minimize the volume of this box and seek an overlap-free placement of the ellipsoids which can take any orientation. - kall_ellipsoids_tc05a

A set of tri-axial ellipsoids, with given semi-axes, is to be packed into a rectangular box; its widths, lengths and height are subject to lower and upper bounds. We want to minimize the volume of this box and seek an overlap-free placement of the ellipsoids which can take any orientation. - maxmin
- ngone

Find a polygon with 100 sides of maximal area, under the constraint that no two of its vertices are further apart than 1. - orth_d3m6

computation of the minimal orthogonality measure of a 3x6 matrix with orthonormal rows - orth_d3m6_pl

computation of the minimal orthogonality measure of a 3x6 matrix with orthonormal rows; formulation based on parametrization via Plücker coordinates - orth_d4m6_pl

computation of the minimal orthogonality measure of a 4x6 matrix with orthonormal rows; formulation based on parametrization via Plücker coordinates - pointpack02

Find the maximum radius of 2 non-overlapping circles that all lie in the unix-box. - pointpack04

Find the maximum radius of 4 non-overlapping circles that all lie in the unix-box. - pointpack06

Find the maximum radius of 6 non-overlapping circles that all lie in the unix-box. - pointpack08

Find the maximum radius of 8 non-overlapping circles that all lie in the unix-box. - pointpack10

Find the maximum radius of 10 non-overlapping circles that all lie in the unix-box. - pointpack12

Find the maximum radius of 12 non-overlapping circles that all lie in the unix-box. - pointpack14

Find the maximum radius of 14 non-overlapping circles that all lie in the unix-box. - polygon100
- polygon25
- polygon50
- polygon75
- ringpack_10_1

This is an application from the tube industry, which is called Recursive Circle Packing Problem. The original task is to minimize the total number of rectangles to pack a given set of rings. Unfortunately, this variant is way too difficult for current global solvers (even for examples with 4-5 rings). An easier variant is to minimize free space in a given set of rectangles. This instance is for the variant with 10 rings and 1 rectangle. - ringpack_10_2

This is an application from the tube industry, which is called Recursive Circle Packing Problem. The original task is to minimize the total number of rectangles to pack a given set of rings. Unfortunately, this variant is way too difficult for current global solvers (even for examples with 4-5 rings). An easier variant is to minimize free space in a given set of rectangles. This instance is for the variant with 10 rings and 2 rectangles. - ringpack_20_1

This is an application from the tube industry, which is called Recursive Circle Packing Problem. The original task is to minimize the total number of rectangles to pack a given set of rings. Unfortunately, this variant is way too difficult for current global solvers (even for examples with 4-5 rings). An easier variant is to minimize free space in a given set of rectangles. This instance is for the variant with 20 rings and 1 rectangle. - ringpack_20_2

This is an application from the tube industry, which is called Recursive Circle Packing Problem. The original task is to minimize the total number of rectangles to pack a given set of rings. Unfortunately, this variant is way too difficult for current global solvers (even for examples with 4-5 rings). An easier variant is to minimize free space in a given set of rectangles. This instance is for the variant with 20 rings and 2 rectangles. - ringpack_20_3

This is an application from the tube industry, which is called Recursive Circle Packing Problem. The original task is to minimize the total number of rectangles to pack a given set of rings. Unfortunately, this variant is way too difficult for current global solvers (even for examples with 4-5 rings). An easier variant is to minimize free space in a given set of rectangles. This instance is for the variant with 20 rings and 3 rectangles. - ringpack_30_1

This is an application from the tube industry, which is called Recursive Circle Packing Problem. The original task is to minimize the total number of rectangles to pack a given set of rings. Unfortunately, this variant is way too difficult for current global solvers (even for examples with 4-5 rings). An easier variant is to minimize free space in a given set of rectangles. This instance is for the variant with 30 rings and 1 rectangle. - ringpack_30_2

This is an application from the tube industry, which is called Recursive Circle Packing Problem. The original task is to minimize the total number of rectangles to pack a given set of rings. Unfortunately, this variant is way too difficult for current global solvers (even for examples with 4-5 rings). An easier variant is to minimize free space in a given set of rectangles. This instance is for the variant with 30 rings and 2 rectangles. - tricp

Triangular Graph Circle Packing

**Graph Partitioning:**

- graphpart_2g-0044-1601

This is a quadratic model for the graph partitioning problem. The graphs are taken from the publication of Ghaddar et al. We used 3 parts of the partition to generate the quadratic instances. The model assigns each node to one of the three parts. Hence, the model is symmetric, which should probably be used in a solution algorithm. - graphpart_2g-0055-0062

This is a quadratic model for the graph partitioning problem. The graphs are taken from the publication of Ghaddar et al. We used 3 parts of the partition to generate the quadratic instances. The model assigns each node to one of the three parts. Hence, the model is symmetric, which should probably be used in a solution algorithm. - graphpart_2g-0066-0066

This is a quadratic model for the graph partitioning problem. The graphs are taken from the publication of Ghaddar et al. We used 3 parts of the partition to generate the quadratic instances. The model assigns each node to one of the three parts. Hence, the model is symmetric, which should probably be used in a solution algorithm. - graphpart_2g-0077-0077

- graphpart_2g-0088-0088

- graphpart_2g-0099-9211

- graphpart_2g-1010-0824

- graphpart_2pm-0044-0044

- graphpart_2pm-0055-0055

- graphpart_2pm-0066-0066

- graphpart_2pm-0077-0777

- graphpart_2pm-0088-0888

- graphpart_2pm-0099-0999

- graphpart_3g-0234-0234

- graphpart_3g-0244-0244

- graphpart_3g-0333-0333

- graphpart_3g-0334-0334

- graphpart_3g-0344-0344

- graphpart_3g-0444-0444

- graphpart_3pm-0234-0234

- graphpart_3pm-0244-0244

- graphpart_3pm-0333-0333

- graphpart_3pm-0334-0334

- graphpart_3pm-0344-0344

- graphpart_3pm-0444-0444

- graphpart_clique-20

- graphpart_clique-30

- graphpart_clique-40

- graphpart_clique-50

- graphpart_clique-60

- graphpart_clique-70

- sonet17v4

A variant of the graph partitioning problem where the weight of a cluster in the partition depends on the edges incident to its nodes. This instance has its origin in SONET/SDH optical networks. - sonet18v6

A variant of the graph partitioning problem where the weight of a cluster in the partition depends on the edges incident to its nodes. This instance has its origin in SONET/SDH optical networks. - sonet19v5

A variant of the graph partitioning problem where the weight of a cluster in the partition depends on the edges incident to its nodes. This instance has its origin in SONET/SDH optical networks. - sonet20v6

- sonet21v6

- sonet22v4

- sonet22v5

- sonet23v4

- sonet23v6

- sonet24v2

- sonet24v5

- sonet25v5

- sonet25v6

- sonetgr17

**Hang Glider:**

**Hanging Chain:**

**Heat Exchanger Network:**

- heatexch_gen1
- heatexch_gen2
- heatexch_gen3
- heatexch_spec1
- heatexch_spec2
- heatexch_spec3
- heatexch_trigen

Sustainable Integration of Trigeneration Systems with Heat Exchanger Networks

**Heat Integrated Distillation Sequences:**

**Hybrid Dynamic Systems:**

- hybriddynamic_fixed

Fixed Finite Elements - hybriddynamic_fixedcc

Fixed Finite Elements - hybriddynamic_var

Variable Finite Elements - hybriddynamic_varcc

Variable Finite Elements

**Hydro Energy System Scheduling:**

**Hydrodealkylation of Toluene:**

**Hydrostatic Thrust Bearing Design:**

**Isometrization:**

**Job Scheduling:**

**Journal Bearing:**

**Kissing Number Problem:**

- kissing2

Determining whether 100 unit spheres can be arranged to be adjacent to a central unit sphere in R^8. This is possible if there is a feasible solution with objective value 0. - knp3-12

Determining whether 12 3-dimensional spheres of radius 1 can be adjacent to a central sphere of radius 1. This is possible, iff the optimal value of this instance is >= 1. - knp4-24

Determining whether 24 5-dimensional spheres of radius 1 can be adjacent to a central sphere of radius 1. This is possible, iff the optimal value of this instance is >= 1. - knp5-40

Determining whether 40 5-dimensional spheres of radius 1 can be adjacent to a central sphere of radius 1. This is possible, iff the optimal value of this instance is >= 1. - knp5-41

Determining whether 41 5-dimensional spheres of radius 1 can be adjacent to a central sphere of radius 1. This is possible, iff the optimal value of this instance is >= 1. - knp5-42

Determining whether 42 5-dimensional spheres of radius 1 can be adjacent to a central sphere of radius 1. This is possible, iff the optimal value of this instance is >= 1. - knp5-43

Determining whether 43 5-dimensional spheres of radius 1 can be adjacent to a central sphere of radius 1. This is possible, iff the optimal value of this instance is >= 1. - knp5-44

Determining whether 44 5-dimensional spheres of radius 1 can be adjacent to a central sphere of radius 1. This is possible, iff the optimal value of this instance is >= 1.

**Launch Vehicle Design:**

**Layout:**

- clay0203h

Non overlapping rectangular units must be placed within the confines of certain designated areas such that the cost of connecting these units is minimized. - clay0203m

Non overlapping rectangular units must be placed within the confines of certain designated areas such that the cost of connecting these units is minimized. - clay0204h

Non overlapping rectangular units must be placed within the confines of certain designated areas such that the cost of connecting these units is minimized. - clay0204m

- clay0205h

- clay0205m

- clay0303h

- clay0303m

- clay0304h

- clay0304m

- clay0305h

- clay0305m

- faclay20h

single-row facility layout problem modeled as a quadratic linear ordering problem An instance of the single-row facility layout problem is formally defined by n one-dimensional facilities with given positive lengths and pairwise non-negative weights. The objective is to arrange the facilities so as to minimize the total weighted sum of the center-to-center distances between all pairs of facilities. This problem can be modeled as a quadratic objective over linear ordering variables. - faclay25

single-row facility layout problem modeled as a quadratic linear ordering problem An instance of the single-row facility layout problem is formally defined by n one-dimensional facilities with given positive lengths and pairwise non-negative weights. The objective is to arrange the facilities so as to minimize the total weighted sum of the center-to-center distances between all pairs of facilities. This problem can be modeled as a quadratic objective over linear ordering variables. - faclay30

single-row facility layout problem modeled as a quadratic linear ordering problem An instance of the single-row facility layout problem is formally defined by n one-dimensional facilities with given positive lengths and pairwise non-negative weights. The objective is to arrange the facilities so as to minimize the total weighted sum of the center-to-center distances between all pairs of facilities. This problem can be modeled as a quadratic objective over linear ordering variables. - faclay30h

- faclay33

- faclay35

- faclay60

- faclay70

- faclay75

- faclay80

- flay02h

Determine the optimal length and width of a number of rectangular patches of land with fixed area, such that the perimeter of the set of patches is minimized. - flay02m

Determine the optimal length and width of a number of rectangular patches of land with fixed area, such that the perimeter of the set of patches is minimized. - flay03h

Determine the optimal length and width of a number of rectangular patches of land with fixed area, such that the perimeter of the set of patches is minimized. - flay03m

- flay04h

- flay04m

- flay05h

- flay05m

- flay06h

- flay06m

- fo7

Facility Layout - fo7_2

Facility Layout - fo7_ar25_1

Optimization of block layout design problems with unequal areas - fo7_ar2_1

Optimization of block layout design problems with unequal areas - fo7_ar3_1

Optimization of block layout design problems with unequal areas - fo7_ar4_1

Optimization of block layout design problems with unequal areas - fo7_ar5_1

Optimization of block layout design problems with unequal areas - fo8

Facility Layout - fo8_ar25_1

Optimization of block layout design problems with unequal areas - fo8_ar2_1

Optimization of block layout design problems with unequal areas - fo8_ar3_1

Optimization of block layout design problems with unequal areas - fo8_ar4_1

Optimization of block layout design problems with unequal areas - fo8_ar5_1

Optimization of block layout design problems with unequal areas - fo9

Facility Layout - fo9_ar25_1

Optimization of block layout design problems with unequal areas - fo9_ar2_1

Optimization of block layout design problems with unequal areas - fo9_ar3_1

Optimization of block layout design problems with unequal areas - fo9_ar4_1

Optimization of block layout design problems with unequal areas - fo9_ar5_1

Optimization of block layout design problems with unequal areas - m3

Facility Layout - m6

Facility Layout - m7

Facility Layout - m7_ar25_1

Optimization of block layout design problems with unequal areas - m7_ar2_1

Optimization of block layout design problems with unequal areas - m7_ar3_1

Optimization of block layout design problems with unequal areas - m7_ar4_1

Optimization of block layout design problems with unequal areas - m7_ar5_1

Optimization of block layout design problems with unequal areas - no7_ar25_1

Optimization of block layout design problems with unequal areas - no7_ar2_1

Optimization of block layout design problems with unequal areas - no7_ar3_1

Optimization of block layout design problems with unequal areas - no7_ar4_1

Optimization of block layout design problems with unequal areas - no7_ar5_1

Optimization of block layout design problems with unequal areas - o7

Facility Layout - o7_2

Facility Layout - o7_ar25_1

Optimization of block layout design problems with unequal areas - o7_ar2_1

Optimization of block layout design problems with unequal areas - o7_ar3_1

Optimization of block layout design problems with unequal areas - o7_ar4_1

Optimization of block layout design problems with unequal areas - o7_ar5_1

Optimization of block layout design problems with unequal areas - o8_ar4_1

Optimization of block layout design problems with unequal areas - o9_ar4_1

Optimization of block layout design problems with unequal areas - slay04h

Determine the optimal placement of a set of units with fixed width and length such that the Euclidean distance between their center point and a predefined "safety point" is minimized. - slay04m

Determine the optimal placement of a set of units with fixed width and length such that the Euclidean distance between their center point and a predefined "safety point" is minimized. - slay05h

Determine the optimal placement of a set of units with fixed width and length such that the Euclidean distance between their center point and a predefined "safety point" is minimized. - slay05m

- slay06h

- slay06m

- slay07h

- slay07m

- slay08h

- slay08m

- slay09h

- slay09m

- slay10h

- slay10m

**Linear Phase Lowpass Filter Design:**

- fdesign10

This model finds the filter weights for a finite impulse response (FIR) filter using the minimax linear phase lowpass filter design from Lobo et. al (Section 3.3). - fdesign25

This model finds the filter weights for a finite impulse response (FIR) filter using the minimax linear phase lowpass filter design from Lobo et. al (Section 3.3). - fdesign50

This model finds the filter weights for a finite impulse response (FIR) filter using the minimax linear phase lowpass filter design from Lobo et. al (Section 3.3).

**Linear Quadratic Control:**

**Location Item Planning:**

**Marine Population Dynamics:**

**Market Equilibrium:**

**Matrix Eigenvalues:**

- eigena2

Given a symmetric matrix A, find an orthogonal matrix Q and diagonal matrix D such that A Q(T) = Q(T) D.

**Max Cut:**

- ising2_5-300_5555

A one-dimensional ising chain instance from an application in statistical physics. - toroidal2g20_5555

A 2-dimensional toroidal grid graph with gaussian distributed weights from an application in statistical physics. - toroidal3g7_6666

A 3-dimensional toroidal grid graph with gaussian distributed weights from an application in statistical physics.

**Metabolic Networks:**

**Methanol to Hydrocarbons:**

**Minimal Surface:**

**Minimizing Total Average Cycle Stock:**

**Molecular Design:**

**Multi-commodity capacity facility location-allocation:**

**Multi-Product Batch Plant Design:**

- batch0812
- batch0812_nc

Nonconvex variant of batch0812 - batch_nc

Nonconvex variant of batch - batchs101006m

Determine volume of equipment, number of units to operate in parallel, and locations of intermediate storage tanks. - batchs121208m

Determine volume of equipment, number of units to operate in parallel, and locations of intermediate storage tanks. - batchs151208m

Determine volume of equipment, number of units to operate in parallel, and locations of intermediate storage tanks. - batchs201210m

**Multiperiod Blend Scheduling:**

**Multiproduct CSTR:**

**Natural Gas Production:**

- gasprod_sarawak01

Li et al. reformulated the natural gas production model of Selot et al. from a general MINLP to MIQCQP. The modeling files corresponding to these problems have been scaled in accordance with the design of Li et al. The 3 test cases are effectively the same problem with a different number of uncertain scenarios. - gasprod_sarawak16

Li et al. reformulated the natural gas production model of Selot et al. from a general MINLP to MIQCQP. The modeling files corresponding to these problems have been scaled in accordance with the design of Li et al. The 3 test cases are effectively the same problem with a different number of uncertain scenarios. - gasprod_sarawak81

Li et al. reformulated the natural gas production model of Selot et al. from a general MINLP to MIQCQP. The modeling files corresponding to these problems have been scaled in accordance with the design of Li et al. The 3 test cases are effectively the same problem with a different number of uncertain scenarios.

**Network Design:**

- nd_netgen-2000-2-5-a-a-ns_7

Single-commodity Nonlinear Network Design problem - nd_netgen-2000-3-4-b-a-ns_7

Single-commodity Nonlinear Network Design problem - nd_netgen-3000-1-1-b-b-ns_7

Single-commodity Nonlinear Network Design problem - ndcc12

Multicommodity network design problem with congestion constraints and fixed costs for opening arcs. - ndcc12persp

Multicommodity network design problem with congestion constraints and fixed costs for opening arcs. Perspective reformulation of ndcc12. - ndcc13

Multicommodity network design problem with congestion constraints and fixed costs for opening arcs. - ndcc13persp

Multicommodity network design problem with congestion constraints and fixed costs for opening arcs. Perspective reformulation of ndcc13. - ndcc14

Multicommodity network design problem with congestion constraints and fixed costs for opening arcs. - ndcc14persp

Multicommodity network design problem with congestion constraints and fixed costs for opening arcs. Perspective reformulation of ndcc14. - ndcc15

Multicommodity network design problem with congestion constraints and fixed costs for opening arcs. - ndcc15persp

Multicommodity network design problem with congestion constraints and fixed costs for opening arcs. Perspective reformulation of ndcc15. - ndcc16

Multicommodity network design problem with congestion constraints and fixed costs for opening arcs. - ndcc16persp

Multicommodity network design problem with congestion constraints and fixed costs for opening arcs. Perspective reformulation of ndcc16. - steenbrf

A totally separable nonconvex multi-commodity network problem - telecomsp_metro

Telecommunication Network Design with Shared Protection - telecomsp_njlata

Telecommunication Network Design with Shared Protection - telecomsp_nor_sun

Telecommunication Network Design with Shared Protection - telecomsp_pacbell

Telecommunication Network Design with Shared Protection

**Nuclear Reactor Core Reload Pattern:**

- nuclear104
- nuclear10a
- nuclear10b
- nuclear14
- nuclear14a
- nuclear14b
- nuclear25
- nuclear25a
- nuclear25b
- nuclear49
- nuclear49a
- nuclear49b
- nuclearva
- nuclearvb
- nuclearvc
- nuclearvd
- nuclearve
- nuclearvf

**Optimal Control:**

- cont6-qq

A quadratic-quadratic control problem. Example 6 from Maurer and Mittelmann (2001). - dtoc5

A discrete time optimal control (DTOC) problem with 50000 time periods, 1 control variable, and 1 state variable. Problem 5 in Coleman and Liao (1995) - junkturn

A spacecraft orientation problem as nonlinear optimal control problem by Junkins and Turner. - optcdeg2

Determine the applied force that restores a damped spring-mass system to equilibrium as fast as possible. Example 5.11 in Murtagh and Saunders (1982). - optmass

The problem is that of a particle of unit mass moving on a frictionless plane under the action of a controlling force whose magnitude may not exceed unity. The objective function maximizes the particle's final distance from the origin and minimizes its final speed. - parabol5_2_1

Parabolic Boundary Control Problem with pure Neumann boundary control - parabol5_2_2

Parabolic Boundary Control Problem with quadratic boundary control - parabol5_2_3

Parabolic Boundary Control Problem parabol5_2_1, but with different state constraints - parabol5_2_4

Parabolic Boundary Control Problem with instationary Burgers equation and active control constraints - parabol_p

Parabolic Boundary Control Problem parabol5_2_1, but the Hessian of the Lagrangian is not convex on the full space - trainf

Minimization of the energy spent to move a train from the beginning of a flat track to its end in a given time. The train is slowed down by some drag (assumed to be quadratic in the the velocity). The control variables are the acceleration force and the braking force applied on the train.

**Optimal vehicle allocation for minimizing greenhouse gas emissions:**

**Parameter estimation in quantitative IR spectroscopy:**

**Particle Steering:**

**Periodic Scheduling of Continuous Multiproduct Plants:**

- multiplants_mtg1a
- multiplants_mtg1b
- multiplants_mtg1c
- multiplants_mtg2
- multiplants_mtg5
- multiplants_mtg6
- multiplants_stg1
- multiplants_stg1a
- multiplants_stg1b
- multiplants_stg1c
- multiplants_stg5
- multiplants_stg6

**Pipeline design:**

**Pooling problem:**

- pooling_adhya1pq

PQ formulation of pooling problem. Explicitly added RLT constraints were removed from the original formulation of Alfaki and Haugland. - pooling_adhya1stp

STP formulation of pooling problem. Explicitly added RLT constraints were removed from the original formulation of Alfaki and Haugland. - pooling_adhya1tp

TP formulation of pooling problem. Explicitly added RLT constraints were removed from the original formulation of Alfaki and Haugland. - pooling_adhya2pq

PQ formulation of pooling problem. Explicitly added RLT constraints were removed from the original formulation of Alfaki and Haugland. - pooling_adhya2stp

STP formulation of pooling problem. Explicitly added RLT constraints were removed from the original formulation of Alfaki and Haugland. - pooling_adhya2tp

TP formulation of pooling problem. Explicitly added RLT constraints were removed from the original formulation of Alfaki and Haugland. - pooling_adhya3pq

PQ formulation of pooling problem. Explicitly added RLT constraints were removed from the original formulation of Alfaki and Haugland. - pooling_adhya3stp

STP formulation of pooling problem. Explicitly added RLT constraints were removed from the original formulation of Alfaki and Haugland. - pooling_adhya3tp

TP formulation of pooling problem. Explicitly added RLT constraints were removed from the original formulation of Alfaki and Haugland. - pooling_adhya4pq

- pooling_adhya4stp

- pooling_adhya4tp

- pooling_bental4pq

- pooling_bental4stp

- pooling_bental4tp

- pooling_bental5pq

- pooling_bental5stp

- pooling_bental5tp

- pooling_digabel16
- pooling_digabel18
- pooling_digabel19
- pooling_foulds2pq

- pooling_foulds2stp

- pooling_foulds2tp

- pooling_foulds3pq

- pooling_foulds3stp

- pooling_foulds3tp

- pooling_foulds4pq

- pooling_foulds4stp

- pooling_foulds4tp

- pooling_foulds5pq

- pooling_foulds5stp

- pooling_foulds5tp

- pooling_haverly1pq

- pooling_haverly1stp

- pooling_haverly1tp

- pooling_haverly2pq

- pooling_haverly2stp

- pooling_haverly2tp

- pooling_haverly3pq

- pooling_haverly3stp

- pooling_haverly3tp

- pooling_rt2pq

- pooling_rt2stp

- pooling_rt2tp

- pooling_sppa0pq

- pooling_sppa0stp

- pooling_sppa0tp

- pooling_sppa5pq

- pooling_sppa5stp

- pooling_sppa5tp

- pooling_sppa9pq

- pooling_sppa9stp

- pooling_sppa9tp

- pooling_sppb0pq

- pooling_sppb0stp

- pooling_sppb0tp

- pooling_sppb2pq

- pooling_sppb2stp

- pooling_sppb2tp

- pooling_sppb5pq

- pooling_sppb5stp

- pooling_sppb5tp

- pooling_sppc0pq

- pooling_sppc0stp

- pooling_sppc0tp

- pooling_sppc1pq

- pooling_sppc1stp

- pooling_sppc1tp

- pooling_sppc3pq

- pooling_sppc3stp

- pooling_sppc3tp

**Pooling Problem:**

- crudeoil_pooling_ct1

Scheduling of the unloading crude of incoming marine vessels to a refinery and transfer of the crudes from storage to charging tanks to the crude oil distillation units. Continuous time formulation. Minimization of total costs. - crudeoil_pooling_ct2

Scheduling of the unloading crude of incoming marine vessels to a refinery and transfer of the crudes from storage to charging tanks to the crude oil distillation units. Continuous time formulation. Maximization of gross margin. - crudeoil_pooling_ct3

Scheduling of the unloading crude of incoming marine vessels to a refinery and transfer of the crudes from storage to charging tanks to the crude oil distillation units. Continuous time formulation. Minimization of total costs. - crudeoil_pooling_ct4

Scheduling of the unloading crude of incoming marine vessels to a refinery and transfer of the crudes from storage to charging tanks to the crude oil distillation units. Continuous time formulation. Maximization of gross margin. - crudeoil_pooling_dt1

Scheduling of the unloading crude of incoming marine vessels to a refinery and transfer of the crudes from storage to charging tanks to the crude oil distillation units. Discrete time formulation. Minimization of total costs. - crudeoil_pooling_dt2

Scheduling of the unloading crude of incoming marine vessels to a refinery and transfer of the crudes from storage to charging tanks to the crude oil distillation units. Discrete time formulation. Maximization of gross margin. - crudeoil_pooling_dt3

Scheduling of the unloading crude of incoming marine vessels to a refinery and transfer of the crudes from storage to charging tanks to the crude oil distillation units. Discrete time formulation. Minimization of total costs. - crudeoil_pooling_dt4

Scheduling of the unloading crude of incoming marine vessels to a refinery and transfer of the crudes from storage to charging tanks to the crude oil distillation units. Discrete time formulation. Maximization of gross margin. - genpooling_lee1
- genpooling_lee2
- genpooling_meyer04
- genpooling_meyer10
- genpooling_meyer15
- haverly
- pooling_epa1
- pooling_epa2
- pooling_epa3

**Portfolio Optimization:**

- alan
- meanvar-orl400_05_e_7

Mean-Variance problem with minimum buy-in and cardinality constraints - meanvar-orl400_05_e_8

Mean-Variance problem with minimum buy-in and cardinality constraints - portfol_buyin
- portfol_card
- portfol_classical050_1
- portfol_classical200_2
- portfol_robust050_34
- portfol_robust100_09
- portfol_robust200_03
- portfol_roundlot
- portfol_shortfall050_68
- portfol_shortfall100_04
- portfol_shortfall200_05
- qp2
- qp3
- qp4
- ramsey
- smallinvDAXr1b010-011

Small Investor Mean-Variance Portfolio Optimization This is a natural extension of the standard Markovitz Mean-Variance-Optimization (MVO) model by constraints for small investors. The variables in the standard Markovitz model determine which fraction of the investment is made in the repective assets. When the investment is bounded within a range that is not very much bigger than the prices of the assets, one has to take into account that each asset has a minimum unit of which only integer multiples can be traded, e.g. 1, 0.1, or 0.01. Hence, the optimization problem for the small investor has integer variables in addition to the budget constraints that define lower and upper bounds on the investment. - smallinvDAXr1b020-022

Small Investor Mean-Variance Portfolio Optimization This is a natural extension of the standard Markovitz Mean-Variance-Optimization (MVO) model by constraints for small investors. The variables in the standard Markovitz model determine which fraction of the investment is made in the repective assets. When the investment is bounded within a range that is not very much bigger than the prices of the assets, one has to take into account that each asset has a minimum unit of which only integer multiples can be traded, e.g. 1, 0.1, or 0.01. Hence, the optimization problem for the small investor has integer variables in addition to the budget constraints that define lower and upper bounds on the investment. - smallinvDAXr1b050-055

Small Investor Mean-Variance Portfolio Optimization This is a natural extension of the standard Markovitz Mean-Variance-Optimization (MVO) model by constraints for small investors. The variables in the standard Markovitz model determine which fraction of the investment is made in the repective assets. When the investment is bounded within a range that is not very much bigger than the prices of the assets, one has to take into account that each asset has a minimum unit of which only integer multiples can be traded, e.g. 1, 0.1, or 0.01. Hence, the optimization problem for the small investor has integer variables in addition to the budget constraints that define lower and upper bounds on the investment. - smallinvDAXr1b100-110

- smallinvDAXr1b150-165

- smallinvDAXr1b200-220

- smallinvDAXr2b010-011

- smallinvDAXr2b020-022

- smallinvDAXr2b050-055

- smallinvDAXr2b100-110

- smallinvDAXr2b150-165

- smallinvDAXr2b200-220

- smallinvDAXr3b010-011

- smallinvDAXr3b020-022

- smallinvDAXr3b050-055

- smallinvDAXr3b100-110

- smallinvDAXr3b150-165

- smallinvDAXr3b200-220

- smallinvDAXr4b010-011

- smallinvDAXr4b020-022

- smallinvDAXr4b050-055

- smallinvDAXr4b100-110

- smallinvDAXr4b150-165

- smallinvDAXr4b200-220

- smallinvDAXr5b010-011

- smallinvDAXr5b020-022

- smallinvDAXr5b050-055

- smallinvDAXr5b100-110

- smallinvDAXr5b150-165

- smallinvDAXr5b200-220

- smallinvSNPr1b010-011

Small Investor Mean-Variance Portfolio Optimization This is a natural extension of the standard Markovitz Mean-Variance-Optimization (MVO) model by constraints for small investors. The variables in the standard Markovitz model determine which fraction of the investment is made in the repective assets. When the investment is bounded within a range that is not very much bigger than the prices of the assets, one has to take into account that each asset has a minimum unit of which only integer multiples can be traded, e.g. 1, 0.1, or 0.01. Hence, the optimization problem for the small investor has integer variables in addition to the budget constraints that define lower and upper bounds on the investment. Update (2018-08-07): After a fix to the convexity check routines, it was found that the smallest eigenvalue of the quadratic coefficients matrix in the quadratic constraint is slightly negative (about -2e-7). Though these instances were originally intended to be convex, a loss of precision in the process of creating the original POLIP instance lead to a loss of positive semi-definiteness in the coefficients matrix. - smallinvSNPr1b020-022

Small Investor Mean-Variance Portfolio Optimization This is a natural extension of the standard Markovitz Mean-Variance-Optimization (MVO) model by constraints for small investors. The variables in the standard Markovitz model determine which fraction of the investment is made in the repective assets. When the investment is bounded within a range that is not very much bigger than the prices of the assets, one has to take into account that each asset has a minimum unit of which only integer multiples can be traded, e.g. 1, 0.1, or 0.01. Hence, the optimization problem for the small investor has integer variables in addition to the budget constraints that define lower and upper bounds on the investment. Update (2018-08-07): After a fix to the convexity check routines, it was found that the smallest eigenvalue of the quadratic coefficients matrix in the quadratic constraint is slightly negative (about -2e-7). Though these instances were originally intended to be convex, a loss of precision in the process of creating the original POLIP instance lead to a loss of positive semi-definiteness in the coefficients matrix. - smallinvSNPr1b050-055

Small Investor Mean-Variance Portfolio Optimization This is a natural extension of the standard Markovitz Mean-Variance-Optimization (MVO) model by constraints for small investors. The variables in the standard Markovitz model determine which fraction of the investment is made in the repective assets. When the investment is bounded within a range that is not very much bigger than the prices of the assets, one has to take into account that each asset has a minimum unit of which only integer multiples can be traded, e.g. 1, 0.1, or 0.01. Hence, the optimization problem for the small investor has integer variables in addition to the budget constraints that define lower and upper bounds on the investment. Update (2018-08-07): After a fix to the convexity check routines, it was found that the smallest eigenvalue of the quadratic coefficients matrix in the quadratic constraint is slightly negative (about -2e-7). Though these instances were originally intended to be convex, a loss of precision in the process of creating the original POLIP instance lead to a loss of positive semi-definiteness in the coefficients matrix. - smallinvSNPr1b100-110

- smallinvSNPr1b150-165

- smallinvSNPr1b200-220

- smallinvSNPr2b010-011

- smallinvSNPr2b020-022

- smallinvSNPr2b050-055

- smallinvSNPr2b100-110

- smallinvSNPr2b150-165

- smallinvSNPr2b200-220

- smallinvSNPr3b010-011

- smallinvSNPr3b020-022

- smallinvSNPr3b050-055

- smallinvSNPr3b100-110

- smallinvSNPr3b150-165

- smallinvSNPr3b200-220

- smallinvSNPr4b010-011

- smallinvSNPr4b020-022

- smallinvSNPr4b050-055

- smallinvSNPr4b100-110

- smallinvSNPr4b150-165

- smallinvSNPr4b200-220

- smallinvSNPr5b010-011

- smallinvSNPr5b020-022

- smallinvSNPr5b050-055

- smallinvSNPr5b100-110

- smallinvSNPr5b150-165

- smallinvSNPr5b200-220

- worst

**power plant operation:**

- chp_partload
- chp_shorttermplan1a

Short-term planning of combined heat and power (CHP) systems - chp_shorttermplan1b

Short-term planning of combined heat and power (CHP) systems - chp_shorttermplan2a

Short-term planning of combined heat and power (CHP) systems - chp_shorttermplan2b

Short-term planning of combined heat and power (CHP) systems - chp_shorttermplan2c

Short-term planning of combined heat and power (CHP) systems - chp_shorttermplan2d

Short-term planning of combined heat and power (CHP) systems - super1
- super2
- super3
- super3t

**Process Flowsheets:**

**Process Networks:**

- procurement1large

Optimal Procurement Contract Selection with Price Optimization under Uncertainty for Process Networks - procurement1mot

Optimal Procurement Contract Selection with Price Optimization under Uncertainty for Process Networks - procurement2mot

Optimal Procurement Contract Selection with Price Optimization under Uncertainty for Process Networks Constant-Elasticity Model

**Process selection:**

- ex3pb

ex3 with added bounds to avoid evaluation errors

**Product Portfolio Optimization:**

- kport20

This problem computes minimal cost solutions satisfying the demand of pre-given product portfolios. It determines the number and size of reactors and gives a schedule of how may batches of each product run on each reactor. - kport40

This problem computes minimal cost solutions satisfying the demand of pre-given product portfolios. It determines the number and size of reactors and gives a schedule of how may batches of each product run on each reactor.

**Product positioning in a multiattribute space:**

**Production:**

**pseudo components properties:**

**Pump configuration problem:**

**Quantum Mechanics:**

- quantum

Find energy eigenvalues of the anharmonic oscillator with g=1 in the Gaussian and Post-Gaussian variational methods.

**Radiation therapy:**

**Rail Line Optimization:**

**Retrofit Planning:**

- rsyn0805h

Redesign of existing plants to increase throughput, reduce energy consumption, improve yields, and reduce waste generation. Given limited capital investments to make process improvements and cost estimations over a given time horizon, the problem is to identify the modifications that yield the highest economic improvement which is defined as the income from product sales minus the cost of raw materials, energy, and process modifications. - rsyn0805m

Redesign of existing plants to increase throughput, reduce energy consumption, improve yields, and reduce waste generation. Given limited capital investments to make process improvements and cost estimations over a given time horizon, the problem is to identify the modifications that yield the highest economic improvement which is defined as the income from product sales minus the cost of raw materials, energy, and process modifications. - rsyn0805m02h

Redesign of existing plants to increase throughput, reduce energy consumption, improve yields, and reduce waste generation. Given limited capital investments to make process improvements and cost estimations over a given time horizon, the problem is to identify the modifications that yield the highest economic improvement which is defined as the income from product sales minus the cost of raw materials, energy, and process modifications. - rsyn0805m02m

- rsyn0805m03h

- rsyn0805m03m

- rsyn0805m04h

- rsyn0805m04m

- rsyn0810h

- rsyn0810m

- rsyn0810m02h

- rsyn0810m02m

- rsyn0810m03h

- rsyn0810m03m

- rsyn0810m04h

- rsyn0810m04m

- rsyn0815h

- rsyn0815m

- rsyn0815m02h

- rsyn0815m02m

- rsyn0815m03h

- rsyn0815m03m

- rsyn0815m04h

- rsyn0815m04m

- rsyn0820h

- rsyn0820m

- rsyn0820m02h

- rsyn0820m02m

- rsyn0820m03h

- rsyn0820m03m

- rsyn0820m04h

- rsyn0820m04m

- rsyn0830h

- rsyn0830m

- rsyn0830m02h

- rsyn0830m02m

- rsyn0830m03h

- rsyn0830m03m

- rsyn0830m04h

- rsyn0830m04m

- rsyn0840h

- rsyn0840m

- rsyn0840m02h

- rsyn0840m02m

- rsyn0840m03h

- rsyn0840m03m

- rsyn0840m04h

- rsyn0840m04m

**Robotics:**

**Rockets:**

**Sensor Placement:**

- radar-2000-10-a-6_lat_7

1-D Sensor Placement Problem, whereby a set of n sensors have to be optimally placed to cover a given area while minimizing the fixed deployment cost plus an energy cost that is linear in the surface covered (and therefore quadratic in its radius). - radar-3000-10-a-8_lat_7

1-D Sensor Placement Problem, whereby a set of n sensors have to be optimally placed to cover a given area while minimizing the fixed deployment cost plus an energy cost that is linear in the surface covered (and therefore quadratic in its radius).

**Separation Sequences Based on Distillation:**

**Service System Design:**

- sssd08-04

Stochastic Service System Design. Servers are modeled as M/M/1 queues, and a set of customers must be assigned to the servers which can be operated at different service levels. The objective is to minimize assignment and operating costs. - sssd08-04persp

Stochastic Service System Design. Servers are modeled as M/M/1 queues, and a set of customers must be assigned to the servers which can be operated at different service levels. The objective is to minimize assignment and operating costs. Perspective reformulation of sssd08-04. - sssd12-05

Stochastic Service System Design. Servers are modeled as M/M/1 queues, and a set of customers must be assigned to the servers which can be operated at different service levels. The objective is to minimize assignment and operating costs. - sssd12-05persp

Stochastic Service System Design. Servers are modeled as M/M/1 queues, and a set of customers must be assigned to the servers which can be operated at different service levels. The objective is to minimize assignment and operating costs. Perspective reformulation of sssd12-05. - sssd15-04

Stochastic Service System Design. Servers are modeled as M/M/1 queues, and a set of customers must be assigned to the servers which can be operated at different service levels. The objective is to minimize assignment and operating costs. - sssd15-04persp

Stochastic Service System Design. Servers are modeled as M/M/1 queues, and a set of customers must be assigned to the servers which can be operated at different service levels. The objective is to minimize assignment and operating costs. Perspective reformulation of sssd15-04. - sssd15-06

- sssd15-06persp

Stochastic Service System Design. Servers are modeled as M/M/1 queues, and a set of customers must be assigned to the servers which can be operated at different service levels. The objective is to minimize assignment and operating costs. Perspective reformulation of sssd15-06. - sssd15-08

- sssd15-08persp

Stochastic Service System Design. Servers are modeled as M/M/1 queues, and a set of customers must be assigned to the servers which can be operated at different service levels. The objective is to minimize assignment and operating costs. Perspective reformulation of sssd15-08. - sssd16-07

- sssd16-07persp

Stochastic Service System Design. Servers are modeled as M/M/1 queues, and a set of customers must be assigned to the servers which can be operated at different service levels. The objective is to minimize assignment and operating costs. Perspective reformulation of sssd16-07. - sssd18-06

- sssd18-06persp

Stochastic Service System Design. Servers are modeled as M/M/1 queues, and a set of customers must be assigned to the servers which can be operated at different service levels. The objective is to minimize assignment and operating costs. Perspective reformulation of sssd18-06. - sssd18-08

- sssd18-08persp

Stochastic Service System Design. Servers are modeled as M/M/1 queues, and a set of customers must be assigned to the servers which can be operated at different service levels. The objective is to minimize assignment and operating costs. Perspective reformulation of sssd18-08. - sssd20-04

- sssd20-04persp

Stochastic Service System Design. Servers are modeled as M/M/1 queues, and a set of customers must be assigned to the servers which can be operated at different service levels. The objective is to minimize assignment and operating costs. Perspective reformulation of sssd20-04. - sssd20-08

- sssd20-08persp

Stochastic Service System Design. Servers are modeled as M/M/1 queues, and a set of customers must be assigned to the servers which can be operated at different service levels. The objective is to minimize assignment and operating costs. Perspective reformulation of sssd20-08. - sssd22-08

- sssd22-08persp

Stochastic Service System Design. Servers are modeled as M/M/1 queues, and a set of customers must be assigned to the servers which can be operated at different service levels. The objective is to minimize assignment and operating costs. Perspective reformulation of sssd22-08. - sssd25-04

- sssd25-04persp

Stochastic Service System Design. Servers are modeled as M/M/1 queues, and a set of customers must be assigned to the servers which can be operated at different service levels. The objective is to minimize assignment and operating costs. Perspective reformulation of sssd25-04. - sssd25-08

- sssd25-08persp

Stochastic Service System Design. Servers are modeled as M/M/1 queues, and a set of customers must be assigned to the servers which can be operated at different service levels. The objective is to minimize assignment and operating costs. Perspective reformulation of sssd25-08.

**Shape Optimization:**

**Shortest Path:**

- qspp_0_10_0_1_10_1

Quadratic Shortest Path Problem - qspp_0_11_0_1_10_1

Quadratic Shortest Path Problem - qspp_0_12_0_1_10_1

Quadratic Shortest Path Problem - qspp_0_13_0_1_10_1

Quadratic Shortest Path Problem - qspp_0_14_0_1_10_1

Quadratic Shortest Path Problem - qspp_0_15_0_1_10_1

Quadratic Shortest Path Problem

**Simultaneous Optimization for HEN Synthesis:**

**Social Accounting Matrix Balancing:**

- cesam2cent

Illustrates a cross entropy technique for estimating the cells of a consistent SAM assuming that the initial data are inconsistent and measured with error. - cesam2log

Illustrates a cross entropy technique for estimating the cells of a consistent SAM assuming that the initial data are inconsistent and measured with error. This is a variant of cesam2cent where the centropy() function is written explicitly via basis arithmetic functions (log, ...). - sambal

**Spacecraft Landing:**

**Spatial Competition:**

**Sports Tournament:**

- sporttournament06

This is a quadratic model for the max-cut problem. The instance arises when minimizing so-called breaks in sports tournaments. - sporttournament08

This is a quadratic model for the max-cut problem. The instance arises when minimizing so-called breaks in sports tournaments. - sporttournament10

This is a quadratic model for the max-cut problem. The instance arises when minimizing so-called breaks in sports tournaments. - sporttournament12

- sporttournament14

- sporttournament16

- sporttournament18

- sporttournament20

- sporttournament22

- sporttournament24

- sporttournament26

- sporttournament28

- sporttournament30

- sporttournament32

- sporttournament34

- sporttournament36

- sporttournament38

- sporttournament40

- sporttournament42

- sporttournament44

- sporttournament46

- sporttournament48

- sporttournament50

**Statistics:**

**Stratified Sample Design:**

**Structural Optimization:**

- shiporig

This model designs a vertically corrugated transverse bulkhead of an oil tanker. The objective is to design for minimum weight and meet stress, moment of inertia and plate thickness constraints. This version of ship corresponds to the current version of ship from the GAMS model library. It corresponds to the original version from the paper, plus an extra lower bound on variable x10.

**Supply Chain Design with Stochastic Inventory Management:**

- supplychain
- supplychainp1_020306
- supplychainp1_022020
- supplychainp1_030510
- supplychainp1_053050
- supplychainr1_020306
- supplychainr1_022020
- supplychainr1_030510
- supplychainr1_053050

**Synthesis of General Distillation Sequences:**

**Synthesis of processing system:**

- syn05h

Selection of optimal configuration and parameters for a processing system selected from a superstructure containing alternative processing units and interconnections. - syn05m

Selection of optimal configuration and parameters for a processing system selected from a superstructure containing alternative processing units and interconnections. - syn05m02h

Selection of optimal configuration and parameters for a processing system selected from a superstructure containing alternative processing units and interconnections. - syn05m02m

- syn05m03h

- syn05m03m

- syn05m04h

- syn05m04m

- syn10h

- syn10m

- syn10m02h

- syn10m02m

- syn10m03h

- syn10m03m

- syn10m04h

- syn10m04m

- syn15h

- syn15m

- syn15m02h

- syn15m02m

- syn15m03h

- syn15m03m

- syn15m04h

- syn15m04m

- syn20h

- syn20m

- syn20m02h

- syn20m02m

- syn20m03h

- syn20m03m

- syn20m04h

- syn20m04m

- syn30h

- syn30m

- syn30m02h

- syn30m02m

- syn30m03h

- syn30m03m

- syn30m04h

- syn30m04m

- syn40h

- syn40m

- syn40m02h

- syn40m02m

- syn40m03h

- syn40m03m

- syn40m04h

- syn40m04m

- synthes1
- synthes2
- synthes3

**Synthesis of Space Truss:**

**Tank Size Design:**

- tanksize

We discuss a tank design problem for a multi product plant, in which the optimal cycle time and the optimal campaign size are unknown. A mixed integer nonlinear programming formulation is presented, where non-convexities are due to the tank investment cost, storage cost, campaign setup cost and variable production rates. The objective of the optimization model is to minimize the sum of the production cost per ton per product produced. A continuous-time mathematical programming formulation for the problem is implemented with a fixed number of event points.

**Telecommunication:**

- routingdelay_bigm

Delay Constrained Routing Problem - routingdelay_proj

Delay Constrained Routing Problem

**Test Problem:**

- cvxnonsep_normcon20

convex MINLP test problem with non-separable 2-norm constraint see also problem description (PDF). - cvxnonsep_normcon20r

separable reformulation of convex MINLP test problem with non-separable 2-norm constraint (cvxnonsep_normcon20) see also problem description (PDF). - cvxnonsep_normcon30

convex MINLP test problem with non-separable 2-norm constraint see also problem description (PDF). - cvxnonsep_normcon30r

separable reformulation of convex MINLP test problem with non-separable 2-norm constraint (cvxnonsep_normcon30) see also problem description (PDF). - cvxnonsep_normcon40

convex MINLP test problem with non-separable 2-norm constraint see also problem description (PDF). - cvxnonsep_normcon40r

separable reformulation of convex MINLP test problem with non-separable 2-norm constraint (cvxnonsep_normcon40) see also problem description (PDF). - cvxnonsep_nsig20

convex MINLP test problem with non-separable signomial constraint function see also problem description (PDF). - cvxnonsep_nsig20r

separable reformulation of convex MINLP test problem with non-separable signomial constraint function (cvxnonsep_nsig20) see also problem description (PDF). - cvxnonsep_nsig30

convex MINLP test problem with non-separable signomial constraint function see also problem description (PDF). - cvxnonsep_nsig30r

separable reformulation of convex MINLP test problem with non-separable signomial constraint function (cvxnonsep_nsig30) see also problem description (PDF). - cvxnonsep_nsig40

convex MINLP test problem with non-separable signomial constraint function see also problem description (PDF). - cvxnonsep_nsig40r

separable reformulation of convex MINLP test problem with non-separable signomial constraint function (cvxnonsep_nsig40) see also problem description (PDF). - cvxnonsep_pcon20

convex MINLP test problem with non-separable power constraint see also problem description (PDF). - cvxnonsep_pcon20r

separable reformulation of convex MINLP test problem with non-separable power constraint (cvxnonsep_pcon20) see also problem description (PDF). - cvxnonsep_pcon30

convex MINLP test problem with non-separable power constraint see also problem description (PDF). - cvxnonsep_pcon30r

separable reformulation of convex MINLP test problem with non-separable power constraint (cvxnonsep_pcon30) see also problem description (PDF). - cvxnonsep_pcon40

convex MINLP test problem with non-separable power constraint see also problem description (PDF). - cvxnonsep_pcon40r

separable reformulation of convex MINLP test problem with non-separable power constraint (cvxnonsep_pcon40) see also problem description (PDF). - cvxnonsep_psig20

convex MINLP test problem with non-separable signomial objective function see also problem description (PDF). - cvxnonsep_psig20r

separable reformulation of convex MINLP test problem with non-separable signomial objective function (cvxnonsep_psig20) see also problem description (PDF). - cvxnonsep_psig30

convex MINLP test problem with non-separable signomial objective function see also problem description (PDF). - cvxnonsep_psig30r

separable reformulation of convex MINLP test problem with non-separable signomial objective function (cvxnonsep_psig30) see also problem description (PDF). - cvxnonsep_psig40

convex MINLP test problem with non-separable signomial objective function see also problem description (PDF). - cvxnonsep_psig40r

separable reformulation of convex MINLP test problem with non-separable signomial objective function (cvxnonsep_psig40) see also problem description (PDF). - fct
- himmel11
- hs62
- mathopt1
- mathopt2
- mathopt3
- mathopt4
- mathopt5_1
- mathopt5_2
- mathopt5_3
- mathopt5_4
- mathopt5_5
- mathopt5_6
- mathopt5_7
- mathopt5_8
- mathopt6

The Hundred-dollar, Hundred-digit Challenge Problems as stated by N. Trefethen, Oxford University. - mhw4d
- rbrock
- trig
- trigx

**Topology Optimization:**

- topopt-cantilever_60x40_50

Topology Optimization of 2D structures - topopt-mbb_60x40_50

Topology Optimization of 2D structures - topopt-zhou-rozvany_75

Topology Optimization of 2D structures

**Traveling Salesman Problem with Neighborhoods:**

**Trim loss minimization problem:**

- ex1263
- ex1263a
- ex1264
- ex1264a
- ex1265
- ex1265a
- ex1266
- ex1266a
- tln12
- tln2
- tln4
- tln5
- tln6
- tln7
- tloss
- tls12
- tls2
- tls4
- tls5
- tls6
- tls7
- tltr

**Unit Commitment:**

- dispatch
- eniplac
- fuel
- unitcommit_200_0_5_mod_7
- unitcommit_200_100_1_mod_8
- unitcommit_200_100_2_mod_7
- unitcommit_200_100_2_mod_8
- unitcommit_50_20_2_mod_8

**Waste paper treatment:**

- wastepaper3

Layout-Optimization of Screening Systems in Recovered Paper Production - 3 Screens - wastepaper4

Layout-Optimization of Screening Systems in Recovered Paper Production - 4 Screens - wastepaper5

Layout-Optimization of Screening Systems in Recovered Paper Production- 5 Screens - wastepaper6

Layout-Optimization of Screening Systems in Recovered Paper Production - 6 Screens

**Waste Water Treatment:**

- waste
- wastewater02m1
- wastewater02m2
- wastewater04m1
- wastewater04m2
- wastewater05m1
- wastewater05m2
- wastewater11m1
- wastewater11m2
- wastewater12m1
- wastewater12m2
- wastewater13m1
- wastewater13m2
- wastewater14m1
- wastewater14m2
- wastewater15m1
- wastewater15m2

**Water Network Contamination:**

- watercontamination0202

Inverse problem for the determination of contamination sources in municipal water networks. The constraints come from discretized dynamic models of the water network quality model. The objective is the least squares error between calculated and measured network concentrations with a regularization term to force a unique solution. Integer variables are added to restrict the allowable contamination scenarios. - watercontamination0202r

Inverse problem for the determination of contamination sources in municipal water networks. The constraints come from discretized dynamic models of the water network quality model. The objective is the least squares error between calculated and measured network concentrations with a regularization term to force a unique solution. Integer variables are added to restrict the allowable contamination scenarios. - watercontamination0303

Inverse problem for the determination of contamination sources in municipal water networks. The constraints come from discretized dynamic models of the water network quality model. The objective is the least squares error between calculated and measured network concentrations with a regularization term to force a unique solution. Integer variables are added to restrict the allowable contamination scenarios. - watercontamination0303r

**Water Network Design:**

- water
- water3
- water4
- waterful2
- waternd1
- waternd2
- waternd_blacksburg
- waternd_fossiron
- waternd_fosspoly0
- waternd_fosspoly1
- waternd_hanoi
- waternd_modena
- waternd_pescara
- waternd_shamir
- waters
- watersbp
- watersym1
- watersym2
- watertreatnd_conc

Concentration Based Approach - watertreatnd_flow

Flow Based Approach - waterund01
- waterund08
- waterund11
- waterund14
- waterund17
- waterund18
- waterund22
- waterund25
- waterund27
- waterund28
- waterund32
- waterund36
- waterx
- waterz

**Water Network Operation:**

- waterno1_01
- waterno1_02
- waterno1_03
- waterno1_04
- waterno1_06
- waterno1_09
- waterno1_12
- waterno1_18
- waterno1_24
- waterno2_01
- waterno2_02
- waterno2_03
- waterno2_04
- waterno2_06
- waterno2_09
- waterno2_12
- waterno2_18
- waterno2_24

**Water Resource Management:**

**Weapons Assignment:**

**Winding Factor of Electrical Machines:**

Last updated: 2018-09-14 Git hash: ac5a5314