MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance 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.
| Formatsⓘ | ams gms mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -2936.00000300 (ANTIGONE) -2936.00000300 (BARON) -2936.00000000 (COUENNE) -2936.00000000 (LINDO) -2936.00000000 (PQCR) -2936.00000000 (SCIP) -2936.00000000 (SHOT) |
| Referencesⓘ | Liers, Frauke, Marinari, Enzo, Pagacz, Ulrike, Ricci-Tersenghi, Federico, and Schmitz, Vera, A Non-Disordered Glassy Model with a Tunable Interaction Range, Journal of Statistical Mechanics: Theory and Experiment, 2010, L05003. |
| Sourceⓘ | POLIP instance autocorrelated_sequences/bernasconi.20.10 |
| Applicationⓘ | Autocorrelated Sequences |
| Added to libraryⓘ | 26 Feb 2014 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 21 |
| #Binary Variablesⓘ | 20 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 20 |
| #Nonlinear Binary Variablesⓘ | 20 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 1 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 1 |
| #Linear Constraintsⓘ | 0 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 1 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 21 |
| #Nonlinear Nonzeros in Jacobianⓘ | 20 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 270 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 20 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 20 |
| Average blocksize in Hessian of Lagrangianⓘ | 20.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 1.7600e+03 |
| Infeasibility of initial pointⓘ | 0 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 1 0 0 1 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 21 1 20 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 21 1 20 0
*
* Solve m using MINLP minimizing objvar;
Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19
,b20,objvar;
Binary Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17
,b18,b19,b20;
Equations e1;
e1.. 64*b1*b2*b3*b4 + 64*b1*b2*b4*b5 + 64*b1*b2*b5*b6 + 64*b1*b2*b6*b7 + 64*b1*
b2*b7*b8 + 64*b1*b2*b8*b9 + 64*b1*b2*b9*b10 + 64*b1*b3*b4*b6 + 64*b1*b3*b5
*b7 + 64*b1*b3*b6*b8 + 64*b1*b3*b7*b9 + 64*b1*b3*b8*b10 + 64*b1*b4*b5*b8
+ 64*b1*b4*b6*b9 + 64*b1*b4*b7*b10 + 64*b1*b5*b6*b10 + 128*b2*b3*b4*b5 +
128*b2*b3*b5*b6 + 128*b2*b3*b6*b7 + 128*b2*b3*b7*b8 + 128*b2*b3*b8*b9 +
128*b2*b3*b9*b10 + 64*b2*b3*b10*b11 + 128*b2*b4*b5*b7 + 128*b2*b4*b6*b8 +
128*b2*b4*b7*b9 + 128*b2*b4*b8*b10 + 64*b2*b4*b9*b11 + 128*b2*b5*b6*b9 +
128*b2*b5*b7*b10 + 64*b2*b5*b8*b11 + 64*b2*b6*b7*b11 + 192*b3*b4*b5*b6 +
192*b3*b4*b6*b7 + 192*b3*b4*b7*b8 + 192*b3*b4*b8*b9 + 192*b3*b4*b9*b10 +
128*b3*b4*b10*b11 + 64*b3*b4*b11*b12 + 192*b3*b5*b6*b8 + 192*b3*b5*b7*b9
+ 192*b3*b5*b8*b10 + 128*b3*b5*b9*b11 + 64*b3*b5*b10*b12 + 192*b3*b6*b7*
b10 + 128*b3*b6*b8*b11 + 64*b3*b6*b9*b12 + 64*b3*b7*b8*b12 + 256*b4*b5*b6*
b7 + 256*b4*b5*b7*b8 + 256*b4*b5*b8*b9 + 256*b4*b5*b9*b10 + 192*b4*b5*b10*
b11 + 128*b4*b5*b11*b12 + 64*b4*b5*b12*b13 + 256*b4*b6*b7*b9 + 256*b4*b6*
b8*b10 + 192*b4*b6*b9*b11 + 128*b4*b6*b10*b12 + 64*b4*b6*b11*b13 + 192*b4*
b7*b8*b11 + 128*b4*b7*b9*b12 + 64*b4*b7*b10*b13 + 64*b4*b8*b9*b13 + 320*b5
*b6*b7*b8 + 320*b5*b6*b8*b9 + 320*b5*b6*b9*b10 + 256*b5*b6*b10*b11 + 192*
b5*b6*b11*b12 + 128*b5*b6*b12*b13 + 64*b5*b6*b13*b14 + 320*b5*b7*b8*b10 +
256*b5*b7*b9*b11 + 192*b5*b7*b10*b12 + 128*b5*b7*b11*b13 + 64*b5*b7*b12*
b14 + 192*b5*b8*b9*b12 + 128*b5*b8*b10*b13 + 64*b5*b8*b11*b14 + 64*b5*b9*
b10*b14 + 384*b6*b7*b8*b9 + 384*b6*b7*b9*b10 + 320*b6*b7*b10*b11 + 256*b6*
b7*b11*b12 + 192*b6*b7*b12*b13 + 128*b6*b7*b13*b14 + 64*b6*b7*b14*b15 +
320*b6*b8*b9*b11 + 256*b6*b8*b10*b12 + 192*b6*b8*b11*b13 + 128*b6*b8*b12*
b14 + 64*b6*b8*b13*b15 + 192*b6*b9*b10*b13 + 128*b6*b9*b11*b14 + 64*b6*b9*
b12*b15 + 64*b6*b10*b11*b15 + 448*b7*b8*b9*b10 + 384*b7*b8*b10*b11 + 320*
b7*b8*b11*b12 + 256*b7*b8*b12*b13 + 192*b7*b8*b13*b14 + 128*b7*b8*b14*b15
+ 64*b7*b8*b15*b16 + 320*b7*b9*b10*b12 + 256*b7*b9*b11*b13 + 192*b7*b9*
b12*b14 + 128*b7*b9*b13*b15 + 64*b7*b9*b14*b16 + 192*b7*b10*b11*b14 + 128*
b7*b10*b12*b15 + 64*b7*b10*b13*b16 + 64*b7*b11*b12*b16 + 448*b8*b9*b10*b11
+ 384*b8*b9*b11*b12 + 320*b8*b9*b12*b13 + 256*b8*b9*b13*b14 + 192*b8*b9*
b14*b15 + 128*b8*b9*b15*b16 + 64*b8*b9*b16*b17 + 320*b8*b10*b11*b13 + 256*
b8*b10*b12*b14 + 192*b8*b10*b13*b15 + 128*b8*b10*b14*b16 + 64*b8*b10*b15*
b17 + 192*b8*b11*b12*b15 + 128*b8*b11*b13*b16 + 64*b8*b11*b14*b17 + 64*b8*
b12*b13*b17 + 448*b9*b10*b11*b12 + 384*b9*b10*b12*b13 + 320*b9*b10*b13*b14
+ 256*b9*b10*b14*b15 + 192*b9*b10*b15*b16 + 128*b9*b10*b16*b17 + 64*b9*
b10*b17*b18 + 320*b9*b11*b12*b14 + 256*b9*b11*b13*b15 + 192*b9*b11*b14*b16
+ 128*b9*b11*b15*b17 + 64*b9*b11*b16*b18 + 192*b9*b12*b13*b16 + 128*b9*
b12*b14*b17 + 64*b9*b12*b15*b18 + 64*b9*b13*b14*b18 + 448*b10*b11*b12*b13
+ 384*b10*b11*b13*b14 + 320*b10*b11*b14*b15 + 256*b10*b11*b15*b16 + 192*
b10*b11*b16*b17 + 128*b10*b11*b17*b18 + 64*b10*b11*b18*b19 + 320*b10*b12*
b13*b15 + 256*b10*b12*b14*b16 + 192*b10*b12*b15*b17 + 128*b10*b12*b16*b18
+ 64*b10*b12*b17*b19 + 192*b10*b13*b14*b17 + 128*b10*b13*b15*b18 + 64*b10
*b13*b16*b19 + 64*b10*b14*b15*b19 + 448*b11*b12*b13*b14 + 384*b11*b12*b14*
b15 + 320*b11*b12*b15*b16 + 256*b11*b12*b16*b17 + 192*b11*b12*b17*b18 +
128*b11*b12*b18*b19 + 64*b11*b12*b19*b20 + 320*b11*b13*b14*b16 + 256*b11*
b13*b15*b17 + 192*b11*b13*b16*b18 + 128*b11*b13*b17*b19 + 64*b11*b13*b18*
b20 + 192*b11*b14*b15*b18 + 128*b11*b14*b16*b19 + 64*b11*b14*b17*b20 + 64*
b11*b15*b16*b20 + 384*b12*b13*b14*b15 + 320*b12*b13*b15*b16 + 256*b12*b13*
b16*b17 + 192*b12*b13*b17*b18 + 128*b12*b13*b18*b19 + 64*b12*b13*b19*b20
+ 256*b12*b14*b15*b17 + 192*b12*b14*b16*b18 + 128*b12*b14*b17*b19 + 64*
b12*b14*b18*b20 + 128*b12*b15*b16*b19 + 64*b12*b15*b17*b20 + 320*b13*b14*
b15*b16 + 256*b13*b14*b16*b17 + 192*b13*b14*b17*b18 + 128*b13*b14*b18*b19
+ 64*b13*b14*b19*b20 + 192*b13*b15*b16*b18 + 128*b13*b15*b17*b19 + 64*b13
*b15*b18*b20 + 64*b13*b16*b17*b20 + 256*b14*b15*b16*b17 + 192*b14*b15*b17*
b18 + 128*b14*b15*b18*b19 + 64*b14*b15*b19*b20 + 128*b14*b16*b17*b19 + 64*
b14*b16*b18*b20 + 192*b15*b16*b17*b18 + 128*b15*b16*b18*b19 + 64*b15*b16*
b19*b20 + 64*b15*b17*b18*b20 + 128*b16*b17*b18*b19 + 64*b16*b17*b19*b20 +
64*b17*b18*b19*b20 - 32*b1*b2*b3 - 64*b1*b2*b4 - 64*b1*b2*b5 - 64*b1*b2*b6
- 64*b1*b2*b7 - 64*b1*b2*b8 - 64*b1*b2*b9 - 32*b1*b2*b10 - 64*b1*b3*b4 -
32*b1*b3*b5 - 64*b1*b3*b6 - 64*b1*b3*b7 - 64*b1*b3*b8 - 32*b1*b3*b9 - 32*
b1*b3*b10 - 64*b1*b4*b5 - 64*b1*b4*b6 - 32*b1*b4*b7 - 32*b1*b4*b8 - 32*b1*
b4*b9 - 32*b1*b4*b10 - 64*b1*b5*b6 - 32*b1*b5*b7 - 32*b1*b5*b8 - 32*b1*b5*
b10 - 32*b1*b6*b7 - 32*b1*b6*b8 - 32*b1*b6*b9 - 32*b1*b6*b10 - 32*b1*b7*b8
- 32*b1*b7*b9 - 32*b1*b7*b10 - 32*b1*b8*b9 - 32*b1*b8*b10 - 32*b1*b9*b10
- 96*b2*b3*b4 - 128*b2*b3*b5 - 128*b2*b3*b6 - 128*b2*b3*b7 - 128*b2*b3*b8
- 128*b2*b3*b9 - 96*b2*b3*b10 - 32*b2*b3*b11 - 160*b2*b4*b5 - 64*b2*b4*b6
- 128*b2*b4*b7 - 128*b2*b4*b8 - 96*b2*b4*b9 - 64*b2*b4*b10 - 32*b2*b4*b11
- 160*b2*b5*b6 - 128*b2*b5*b7 - 32*b2*b5*b8 - 64*b2*b5*b9 - 64*b2*b5*b10
- 32*b2*b5*b11 - 128*b2*b6*b7 - 64*b2*b6*b8 - 64*b2*b6*b9 - 32*b2*b6*b11
- 96*b2*b7*b8 - 64*b2*b7*b9 - 64*b2*b7*b10 - 32*b2*b7*b11 - 96*b2*b8*b9
- 64*b2*b8*b10 - 32*b2*b8*b11 - 96*b2*b9*b10 - 32*b2*b9*b11 - 32*b2*b10*
b11 - 160*b3*b4*b5 - 224*b3*b4*b6 - 192*b3*b4*b7 - 192*b3*b4*b8 - 192*b3*
b4*b9 - 160*b3*b4*b10 - 96*b3*b4*b11 - 32*b3*b4*b12 - 256*b3*b5*b6 - 128*
b3*b5*b7 - 192*b3*b5*b8 - 160*b3*b5*b9 - 128*b3*b5*b10 - 64*b3*b5*b11 - 32
*b3*b5*b12 - 256*b3*b6*b7 - 192*b3*b6*b8 - 32*b3*b6*b9 - 96*b3*b6*b10 - 64
*b3*b6*b11 - 32*b3*b6*b12 - 192*b3*b7*b8 - 128*b3*b7*b9 - 96*b3*b7*b10 -
32*b3*b7*b12 - 160*b3*b8*b9 - 128*b3*b8*b10 - 64*b3*b8*b11 - 32*b3*b8*b12
- 160*b3*b9*b10 - 64*b3*b9*b11 - 32*b3*b9*b12 - 96*b3*b10*b11 - 32*b3*b10
*b12 - 32*b3*b11*b12 - 224*b4*b5*b6 - 320*b4*b5*b7 - 288*b4*b5*b8 - 256*b4
*b5*b9 - 224*b4*b5*b10 - 160*b4*b5*b11 - 96*b4*b5*b12 - 32*b4*b5*b13 - 352
*b4*b6*b7 - 192*b4*b6*b8 - 256*b4*b6*b9 - 192*b4*b6*b10 - 128*b4*b6*b11 -
64*b4*b6*b12 - 32*b4*b6*b13 - 320*b4*b7*b8 - 256*b4*b7*b9 - 64*b4*b7*b10
- 96*b4*b7*b11 - 64*b4*b7*b12 - 32*b4*b7*b13 - 256*b4*b8*b9 - 192*b4*b8*
b10 - 96*b4*b8*b11 - 32*b4*b8*b13 - 224*b4*b9*b10 - 128*b4*b9*b11 - 64*b4*
b9*b12 - 32*b4*b9*b13 - 160*b4*b10*b11 - 64*b4*b10*b12 - 32*b4*b10*b13 -
96*b4*b11*b12 - 32*b4*b11*b13 - 32*b4*b12*b13 - 288*b5*b6*b7 - 416*b5*b6*
b8 - 384*b5*b6*b9 - 320*b5*b6*b10 - 224*b5*b6*b11 - 160*b5*b6*b12 - 96*b5*
b6*b13 - 32*b5*b6*b14 - 448*b5*b7*b8 - 224*b5*b7*b9 - 320*b5*b7*b10 - 192*
b5*b7*b11 - 128*b5*b7*b12 - 64*b5*b7*b13 - 32*b5*b7*b14 - 384*b5*b8*b9 -
320*b5*b8*b10 - 64*b5*b8*b11 - 96*b5*b8*b12 - 64*b5*b8*b13 - 32*b5*b8*b14
- 320*b5*b9*b10 - 192*b5*b9*b11 - 96*b5*b9*b12 - 32*b5*b9*b14 - 224*b5*
b10*b11 - 128*b5*b10*b12 - 64*b5*b10*b13 - 32*b5*b10*b14 - 160*b5*b11*b12
- 64*b5*b11*b13 - 32*b5*b11*b14 - 96*b5*b12*b13 - 32*b5*b12*b14 - 32*b5*
b13*b14 - 352*b6*b7*b8 - 512*b6*b7*b9 - 448*b6*b7*b10 - 320*b6*b7*b11 -
224*b6*b7*b12 - 160*b6*b7*b13 - 96*b6*b7*b14 - 32*b6*b7*b15 - 512*b6*b8*b9
- 256*b6*b8*b10 - 320*b6*b8*b11 - 192*b6*b8*b12 - 128*b6*b8*b13 - 64*b6*
b8*b14 - 32*b6*b8*b15 - 448*b6*b9*b10 - 320*b6*b9*b11 - 64*b6*b9*b12 - 96*
b6*b9*b13 - 64*b6*b9*b14 - 32*b6*b9*b15 - 320*b6*b10*b11 - 192*b6*b10*b12
- 96*b6*b10*b13 - 32*b6*b10*b15 - 224*b6*b11*b12 - 128*b6*b11*b13 - 64*b6
*b11*b14 - 32*b6*b11*b15 - 160*b6*b12*b13 - 64*b6*b12*b14 - 32*b6*b12*b15
- 96*b6*b13*b14 - 32*b6*b13*b15 - 32*b6*b14*b15 - 416*b7*b8*b9 - 576*b7*
b8*b10 - 448*b7*b8*b11 - 320*b7*b8*b12 - 224*b7*b8*b13 - 160*b7*b8*b14 -
96*b7*b8*b15 - 32*b7*b8*b16 - 576*b7*b9*b10 - 256*b7*b9*b11 - 320*b7*b9*
b12 - 192*b7*b9*b13 - 128*b7*b9*b14 - 64*b7*b9*b15 - 32*b7*b9*b16 - 448*b7
*b10*b11 - 320*b7*b10*b12 - 64*b7*b10*b13 - 96*b7*b10*b14 - 64*b7*b10*b15
- 32*b7*b10*b16 - 320*b7*b11*b12 - 192*b7*b11*b13 - 96*b7*b11*b14 - 32*b7
*b11*b16 - 224*b7*b12*b13 - 128*b7*b12*b14 - 64*b7*b12*b15 - 32*b7*b12*b16
- 160*b7*b13*b14 - 64*b7*b13*b15 - 32*b7*b13*b16 - 96*b7*b14*b15 - 32*b7*
b14*b16 - 32*b7*b15*b16 - 448*b8*b9*b10 - 576*b8*b9*b11 - 448*b8*b9*b12 -
320*b8*b9*b13 - 224*b8*b9*b14 - 160*b8*b9*b15 - 96*b8*b9*b16 - 32*b8*b9*
b17 - 576*b8*b10*b11 - 256*b8*b10*b12 - 320*b8*b10*b13 - 192*b8*b10*b14 -
128*b8*b10*b15 - 64*b8*b10*b16 - 32*b8*b10*b17 - 448*b8*b11*b12 - 320*b8*
b11*b13 - 64*b8*b11*b14 - 96*b8*b11*b15 - 64*b8*b11*b16 - 32*b8*b11*b17 -
320*b8*b12*b13 - 192*b8*b12*b14 - 96*b8*b12*b15 - 32*b8*b12*b17 - 224*b8*
b13*b14 - 128*b8*b13*b15 - 64*b8*b13*b16 - 32*b8*b13*b17 - 160*b8*b14*b15
- 64*b8*b14*b16 - 32*b8*b14*b17 - 96*b8*b15*b16 - 32*b8*b15*b17 - 32*b8*
b16*b17 - 448*b9*b10*b11 - 576*b9*b10*b12 - 448*b9*b10*b13 - 320*b9*b10*
b14 - 224*b9*b10*b15 - 160*b9*b10*b16 - 96*b9*b10*b17 - 32*b9*b10*b18 -
576*b9*b11*b12 - 256*b9*b11*b13 - 320*b9*b11*b14 - 192*b9*b11*b15 - 128*b9
*b11*b16 - 64*b9*b11*b17 - 32*b9*b11*b18 - 448*b9*b12*b13 - 320*b9*b12*b14
- 64*b9*b12*b15 - 96*b9*b12*b16 - 64*b9*b12*b17 - 32*b9*b12*b18 - 320*b9*
b13*b14 - 192*b9*b13*b15 - 96*b9*b13*b16 - 32*b9*b13*b18 - 224*b9*b14*b15
- 128*b9*b14*b16 - 64*b9*b14*b17 - 32*b9*b14*b18 - 160*b9*b15*b16 - 64*b9
*b15*b17 - 32*b9*b15*b18 - 96*b9*b16*b17 - 32*b9*b16*b18 - 32*b9*b17*b18
- 448*b10*b11*b12 - 576*b10*b11*b13 - 448*b10*b11*b14 - 320*b10*b11*b15
- 224*b10*b11*b16 - 160*b10*b11*b17 - 96*b10*b11*b18 - 32*b10*b11*b19 -
576*b10*b12*b13 - 256*b10*b12*b14 - 320*b10*b12*b15 - 192*b10*b12*b16 -
128*b10*b12*b17 - 64*b10*b12*b18 - 32*b10*b12*b19 - 448*b10*b13*b14 - 320*
b10*b13*b15 - 64*b10*b13*b16 - 96*b10*b13*b17 - 64*b10*b13*b18 - 32*b10*
b13*b19 - 320*b10*b14*b15 - 192*b10*b14*b16 - 96*b10*b14*b17 - 32*b10*b14*
b19 - 224*b10*b15*b16 - 128*b10*b15*b17 - 64*b10*b15*b18 - 32*b10*b15*b19
- 160*b10*b16*b17 - 64*b10*b16*b18 - 32*b10*b16*b19 - 96*b10*b17*b18 - 32
*b10*b17*b19 - 32*b10*b18*b19 - 448*b11*b12*b13 - 576*b11*b12*b14 - 448*
b11*b12*b15 - 320*b11*b12*b16 - 224*b11*b12*b17 - 160*b11*b12*b18 - 96*b11
*b12*b19 - 32*b11*b12*b20 - 576*b11*b13*b14 - 256*b11*b13*b15 - 320*b11*
b13*b16 - 192*b11*b13*b17 - 128*b11*b13*b18 - 64*b11*b13*b19 - 32*b11*b13*
b20 - 448*b11*b14*b15 - 320*b11*b14*b16 - 64*b11*b14*b17 - 96*b11*b14*b18
- 64*b11*b14*b19 - 32*b11*b14*b20 - 320*b11*b15*b16 - 192*b11*b15*b17 -
96*b11*b15*b18 - 32*b11*b15*b20 - 224*b11*b16*b17 - 128*b11*b16*b18 - 64*
b11*b16*b19 - 32*b11*b16*b20 - 160*b11*b17*b18 - 64*b11*b17*b19 - 32*b11*
b17*b20 - 96*b11*b18*b19 - 32*b11*b18*b20 - 32*b11*b19*b20 - 416*b12*b13*
b14 - 512*b12*b13*b15 - 384*b12*b13*b16 - 256*b12*b13*b17 - 160*b12*b13*
b18 - 96*b12*b13*b19 - 32*b12*b13*b20 - 512*b12*b14*b15 - 224*b12*b14*b16
- 256*b12*b14*b17 - 128*b12*b14*b18 - 64*b12*b14*b19 - 32*b12*b14*b20 -
384*b12*b15*b16 - 256*b12*b15*b17 - 32*b12*b15*b18 - 64*b12*b15*b19 - 32*
b12*b15*b20 - 256*b12*b16*b17 - 160*b12*b16*b18 - 64*b12*b16*b19 - 192*b12
*b17*b18 - 96*b12*b17*b19 - 32*b12*b17*b20 - 128*b12*b18*b19 - 32*b12*b18*
b20 - 64*b12*b19*b20 - 352*b13*b14*b15 - 448*b13*b14*b16 - 320*b13*b14*b17
- 192*b13*b14*b18 - 96*b13*b14*b19 - 32*b13*b14*b20 - 416*b13*b15*b16 -
192*b13*b15*b17 - 192*b13*b15*b18 - 64*b13*b15*b19 - 32*b13*b15*b20 - 288*
b13*b16*b17 - 192*b13*b16*b18 - 32*b13*b16*b19 - 32*b13*b16*b20 - 192*b13*
b17*b18 - 128*b13*b17*b19 - 32*b13*b17*b20 - 128*b13*b18*b19 - 64*b13*b18*
b20 - 64*b13*b19*b20 - 288*b14*b15*b16 - 352*b14*b15*b17 - 256*b14*b15*b18
- 128*b14*b15*b19 - 32*b14*b15*b20 - 320*b14*b16*b17 - 128*b14*b16*b18 -
128*b14*b16*b19 - 32*b14*b16*b20 - 192*b14*b17*b18 - 128*b14*b17*b19 - 32*
b14*b17*b20 - 128*b14*b18*b19 - 64*b14*b18*b20 - 64*b14*b19*b20 - 224*b15*
b16*b17 - 256*b15*b16*b18 - 160*b15*b16*b19 - 64*b15*b16*b20 - 224*b15*b17
*b18 - 64*b15*b17*b19 - 64*b15*b17*b20 - 128*b15*b18*b19 - 64*b15*b18*b20
- 64*b15*b19*b20 - 160*b16*b17*b18 - 160*b16*b17*b19 - 64*b16*b17*b20 -
128*b16*b18*b19 - 32*b16*b18*b20 - 64*b16*b19*b20 - 96*b17*b18*b19 - 64*
b17*b18*b20 - 64*b17*b19*b20 - 32*b18*b19*b20 + 112*b1*b2 + 104*b1*b3 + 96
*b1*b4 + 88*b1*b5 + 96*b1*b6 + 88*b1*b7 + 80*b1*b8 + 72*b1*b9 + 64*b1*b10
+ 224*b2*b3 + 224*b2*b4 + 208*b2*b5 + 192*b2*b6 + 208*b2*b7 + 192*b2*b8
+ 176*b2*b9 + 144*b2*b10 + 64*b2*b11 + 352*b3*b4 + 344*b3*b5 + 336*b3*b6
+ 328*b3*b7 + 336*b3*b8 + 296*b3*b9 + 256*b3*b10 + 144*b3*b11 + 64*b3*b12
+ 496*b4*b5 + 480*b4*b6 + 464*b4*b7 + 464*b4*b8 + 448*b4*b9 + 384*b4*b10
+ 256*b4*b11 + 144*b4*b12 + 64*b4*b13 + 656*b5*b6 + 616*b5*b7 + 592*b5*b8
+ 568*b5*b9 + 544*b5*b10 + 384*b5*b11 + 256*b5*b12 + 144*b5*b13 + 64*b5*
b14 + 800*b6*b7 + 736*b6*b8 + 704*b6*b9 + 656*b6*b10 + 544*b6*b11 + 384*b6
*b12 + 256*b6*b13 + 144*b6*b14 + 64*b6*b15 + 928*b7*b8 + 856*b7*b9 + 800*
b7*b10 + 656*b7*b11 + 544*b7*b12 + 384*b7*b13 + 256*b7*b14 + 144*b7*b15 +
64*b7*b16 + 1040*b8*b9 + 960*b8*b10 + 800*b8*b11 + 656*b8*b12 + 544*b8*b13
+ 384*b8*b14 + 256*b8*b15 + 144*b8*b16 + 64*b8*b17 + 1152*b9*b10 + 960*b9
*b11 + 800*b9*b12 + 656*b9*b13 + 544*b9*b14 + 384*b9*b15 + 256*b9*b16 +
144*b9*b17 + 64*b9*b18 + 1152*b10*b11 + 960*b10*b12 + 800*b10*b13 + 656*
b10*b14 + 544*b10*b15 + 384*b10*b16 + 256*b10*b17 + 144*b10*b18 + 64*b10*
b19 + 1152*b11*b12 + 960*b11*b13 + 800*b11*b14 + 656*b11*b15 + 544*b11*b16
+ 384*b11*b17 + 256*b11*b18 + 144*b11*b19 + 64*b11*b20 + 1040*b12*b13 +
856*b12*b14 + 704*b12*b15 + 568*b12*b16 + 448*b12*b17 + 296*b12*b18 + 176*
b12*b19 + 72*b12*b20 + 928*b13*b14 + 736*b13*b15 + 592*b13*b16 + 464*b13*
b17 + 336*b13*b18 + 192*b13*b19 + 80*b13*b20 + 800*b14*b15 + 616*b14*b16
+ 464*b14*b17 + 328*b14*b18 + 208*b14*b19 + 88*b14*b20 + 656*b15*b16 +
480*b15*b17 + 336*b15*b18 + 192*b15*b19 + 96*b15*b20 + 496*b16*b17 + 344*
b16*b18 + 208*b16*b19 + 88*b16*b20 + 352*b17*b18 + 224*b17*b19 + 96*b17*
b20 + 224*b18*b19 + 104*b18*b20 + 112*b19*b20 - 144*b1 - 312*b2 - 496*b3
- 688*b4 - 880*b5 - 1072*b6 - 1264*b7 - 1448*b8 - 1616*b9 - 1760*b10 -
1760*b11 - 1616*b12 - 1448*b13 - 1264*b14 - 1072*b15 - 880*b16 - 688*b17
- 496*b18 - 312*b19 - 144*b20 - objvar =L= 0;
Model m / all /;
m.limrow=0; m.limcol=0;
m.tolproj=0.0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc