MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance autocorr_bern50-06
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ⓘ | -3316.00000000 (ANTIGONE) -2780.13315800 (BARON) -6336.00000000 (COUENNE) -2160.00000000 (DynamicProgramming) -2560.00000000 (GUROBI) -6528.00000000 (LINDO) -2199.87000000 (PQCR) -3675.26995600 (SCIP) -10009.88864000 (SHOT) -5702.87249700 (XPRESS) |
| 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.50.6 |
| Applicationⓘ | Autocorrelated Sequences |
| Added to libraryⓘ | 26 Feb 2014 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 51 |
| #Binary Variablesⓘ | 50 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 50 |
| #Nonlinear Binary Variablesⓘ | 50 |
| #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ⓘ | 51 |
| #Nonlinear Nonzeros in Jacobianⓘ | 50 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 470 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 50 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 50 |
| Average blocksize in Hessian of Lagrangianⓘ | 50.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 2.7200e+02 |
| 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
* 51 1 50 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 51 1 50 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,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36
,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,objvar;
Binary Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17
,b18,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34
,b35,b36,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50;
Equations e1;
e1.. 64*b1*b2*b3*b4 + 64*b1*b2*b4*b5 + 64*b1*b2*b5*b6 + 64*b1*b3*b4*b6 + 128*b2
*b3*b4*b5 + 128*b2*b3*b5*b6 + 64*b2*b3*b6*b7 + 64*b2*b4*b5*b7 + 192*b3*b4*
b5*b6 + 128*b3*b4*b6*b7 + 64*b3*b4*b7*b8 + 64*b3*b5*b6*b8 + 192*b4*b5*b6*
b7 + 128*b4*b5*b7*b8 + 64*b4*b5*b8*b9 + 64*b4*b6*b7*b9 + 192*b5*b6*b7*b8
+ 128*b5*b6*b8*b9 + 64*b5*b6*b9*b10 + 64*b5*b7*b8*b10 + 192*b6*b7*b8*b9
+ 128*b6*b7*b9*b10 + 64*b6*b7*b10*b11 + 64*b6*b8*b9*b11 + 192*b7*b8*b9*
b10 + 128*b7*b8*b10*b11 + 64*b7*b8*b11*b12 + 64*b7*b9*b10*b12 + 192*b8*b9*
b10*b11 + 128*b8*b9*b11*b12 + 64*b8*b9*b12*b13 + 64*b8*b10*b11*b13 + 192*
b9*b10*b11*b12 + 128*b9*b10*b12*b13 + 64*b9*b10*b13*b14 + 64*b9*b11*b12*
b14 + 192*b10*b11*b12*b13 + 128*b10*b11*b13*b14 + 64*b10*b11*b14*b15 + 64*
b10*b12*b13*b15 + 192*b11*b12*b13*b14 + 128*b11*b12*b14*b15 + 64*b11*b12*
b15*b16 + 64*b11*b13*b14*b16 + 192*b12*b13*b14*b15 + 128*b12*b13*b15*b16
+ 64*b12*b13*b16*b17 + 64*b12*b14*b15*b17 + 192*b13*b14*b15*b16 + 128*b13
*b14*b16*b17 + 64*b13*b14*b17*b18 + 64*b13*b15*b16*b18 + 192*b14*b15*b16*
b17 + 128*b14*b15*b17*b18 + 64*b14*b15*b18*b19 + 64*b14*b16*b17*b19 + 192*
b15*b16*b17*b18 + 128*b15*b16*b18*b19 + 64*b15*b16*b19*b20 + 64*b15*b17*
b18*b20 + 192*b16*b17*b18*b19 + 128*b16*b17*b19*b20 + 64*b16*b17*b20*b21
+ 64*b16*b18*b19*b21 + 192*b17*b18*b19*b20 + 128*b17*b18*b20*b21 + 64*b17
*b18*b21*b22 + 64*b17*b19*b20*b22 + 192*b18*b19*b20*b21 + 128*b18*b19*b21*
b22 + 64*b18*b19*b22*b23 + 64*b18*b20*b21*b23 + 192*b19*b20*b21*b22 + 128*
b19*b20*b22*b23 + 64*b19*b20*b23*b24 + 64*b19*b21*b22*b24 + 192*b20*b21*
b22*b23 + 128*b20*b21*b23*b24 + 64*b20*b21*b24*b25 + 64*b20*b22*b23*b25 +
192*b21*b22*b23*b24 + 128*b21*b22*b24*b25 + 64*b21*b22*b25*b26 + 64*b21*
b23*b24*b26 + 192*b22*b23*b24*b25 + 128*b22*b23*b25*b26 + 64*b22*b23*b26*
b27 + 64*b22*b24*b25*b27 + 192*b23*b24*b25*b26 + 128*b23*b24*b26*b27 + 64*
b23*b24*b27*b28 + 64*b23*b25*b26*b28 + 192*b24*b25*b26*b27 + 128*b24*b25*
b27*b28 + 64*b24*b25*b28*b29 + 64*b24*b26*b27*b29 + 192*b25*b26*b27*b28 +
128*b25*b26*b28*b29 + 64*b25*b26*b29*b30 + 64*b25*b27*b28*b30 + 192*b26*
b27*b28*b29 + 128*b26*b27*b29*b30 + 64*b26*b27*b30*b31 + 64*b26*b28*b29*
b31 + 192*b27*b28*b29*b30 + 128*b27*b28*b30*b31 + 64*b27*b28*b31*b32 + 64*
b27*b29*b30*b32 + 192*b28*b29*b30*b31 + 128*b28*b29*b31*b32 + 64*b28*b29*
b32*b33 + 64*b28*b30*b31*b33 + 192*b29*b30*b31*b32 + 128*b29*b30*b32*b33
+ 64*b29*b30*b33*b34 + 64*b29*b31*b32*b34 + 192*b30*b31*b32*b33 + 128*b30
*b31*b33*b34 + 64*b30*b31*b34*b35 + 64*b30*b32*b33*b35 + 192*b31*b32*b33*
b34 + 128*b31*b32*b34*b35 + 64*b31*b32*b35*b36 + 64*b31*b33*b34*b36 + 192*
b32*b33*b34*b35 + 128*b32*b33*b35*b36 + 64*b32*b33*b36*b37 + 64*b32*b34*
b35*b37 + 192*b33*b34*b35*b36 + 128*b33*b34*b36*b37 + 64*b33*b34*b37*b38
+ 64*b33*b35*b36*b38 + 192*b34*b35*b36*b37 + 128*b34*b35*b37*b38 + 64*b34
*b35*b38*b39 + 64*b34*b36*b37*b39 + 192*b35*b36*b37*b38 + 128*b35*b36*b38*
b39 + 64*b35*b36*b39*b40 + 64*b35*b37*b38*b40 + 192*b36*b37*b38*b39 + 128*
b36*b37*b39*b40 + 64*b36*b37*b40*b41 + 64*b36*b38*b39*b41 + 192*b37*b38*
b39*b40 + 128*b37*b38*b40*b41 + 64*b37*b38*b41*b42 + 64*b37*b39*b40*b42 +
192*b38*b39*b40*b41 + 128*b38*b39*b41*b42 + 64*b38*b39*b42*b43 + 64*b38*
b40*b41*b43 + 192*b39*b40*b41*b42 + 128*b39*b40*b42*b43 + 64*b39*b40*b43*
b44 + 64*b39*b41*b42*b44 + 192*b40*b41*b42*b43 + 128*b40*b41*b43*b44 + 64*
b40*b41*b44*b45 + 64*b40*b42*b43*b45 + 192*b41*b42*b43*b44 + 128*b41*b42*
b44*b45 + 64*b41*b42*b45*b46 + 64*b41*b43*b44*b46 + 192*b42*b43*b44*b45 +
128*b42*b43*b45*b46 + 64*b42*b43*b46*b47 + 64*b42*b44*b45*b47 + 192*b43*
b44*b45*b46 + 128*b43*b44*b46*b47 + 64*b43*b44*b47*b48 + 64*b43*b45*b46*
b48 + 192*b44*b45*b46*b47 + 128*b44*b45*b47*b48 + 64*b44*b45*b48*b49 + 64*
b44*b46*b47*b49 + 192*b45*b46*b47*b48 + 128*b45*b46*b48*b49 + 64*b45*b46*
b49*b50 + 64*b45*b47*b48*b50 + 128*b46*b47*b48*b49 + 64*b46*b47*b49*b50 +
64*b47*b48*b49*b50 - 32*b1*b2*b3 - 64*b1*b2*b4 - 64*b1*b2*b5 - 32*b1*b2*b6
- 64*b1*b3*b4 - 32*b1*b3*b6 - 32*b1*b4*b5 - 32*b1*b4*b6 - 32*b1*b5*b6 -
96*b2*b3*b4 - 128*b2*b3*b5 - 96*b2*b3*b6 - 32*b2*b3*b7 - 128*b2*b4*b5 - 32
*b2*b4*b7 - 96*b2*b5*b6 - 32*b2*b5*b7 - 32*b2*b6*b7 - 160*b3*b4*b5 - 192*
b3*b4*b6 - 96*b3*b4*b7 - 32*b3*b4*b8 - 192*b3*b5*b6 - 32*b3*b5*b8 - 96*b3*
b6*b7 - 32*b3*b6*b8 - 32*b3*b7*b8 - 192*b4*b5*b6 - 192*b4*b5*b7 - 96*b4*b5
*b8 - 32*b4*b5*b9 - 192*b4*b6*b7 - 32*b4*b6*b9 - 96*b4*b7*b8 - 32*b4*b7*b9
- 32*b4*b8*b9 - 192*b5*b6*b7 - 192*b5*b6*b8 - 96*b5*b6*b9 - 32*b5*b6*b10
- 192*b5*b7*b8 - 32*b5*b7*b10 - 96*b5*b8*b9 - 32*b5*b8*b10 - 32*b5*b9*b10
- 192*b6*b7*b8 - 192*b6*b7*b9 - 96*b6*b7*b10 - 32*b6*b7*b11 - 192*b6*b8*
b9 - 32*b6*b8*b11 - 96*b6*b9*b10 - 32*b6*b9*b11 - 32*b6*b10*b11 - 192*b7*
b8*b9 - 192*b7*b8*b10 - 96*b7*b8*b11 - 32*b7*b8*b12 - 192*b7*b9*b10 - 32*
b7*b9*b12 - 96*b7*b10*b11 - 32*b7*b10*b12 - 32*b7*b11*b12 - 192*b8*b9*b10
- 192*b8*b9*b11 - 96*b8*b9*b12 - 32*b8*b9*b13 - 192*b8*b10*b11 - 32*b8*
b10*b13 - 96*b8*b11*b12 - 32*b8*b11*b13 - 32*b8*b12*b13 - 192*b9*b10*b11
- 192*b9*b10*b12 - 96*b9*b10*b13 - 32*b9*b10*b14 - 192*b9*b11*b12 - 32*b9
*b11*b14 - 96*b9*b12*b13 - 32*b9*b12*b14 - 32*b9*b13*b14 - 192*b10*b11*b12
- 192*b10*b11*b13 - 96*b10*b11*b14 - 32*b10*b11*b15 - 192*b10*b12*b13 -
32*b10*b12*b15 - 96*b10*b13*b14 - 32*b10*b13*b15 - 32*b10*b14*b15 - 192*
b11*b12*b13 - 192*b11*b12*b14 - 96*b11*b12*b15 - 32*b11*b12*b16 - 192*b11*
b13*b14 - 32*b11*b13*b16 - 96*b11*b14*b15 - 32*b11*b14*b16 - 32*b11*b15*
b16 - 192*b12*b13*b14 - 192*b12*b13*b15 - 96*b12*b13*b16 - 32*b12*b13*b17
- 192*b12*b14*b15 - 32*b12*b14*b17 - 96*b12*b15*b16 - 32*b12*b15*b17 - 32
*b12*b16*b17 - 192*b13*b14*b15 - 192*b13*b14*b16 - 96*b13*b14*b17 - 32*b13
*b14*b18 - 192*b13*b15*b16 - 32*b13*b15*b18 - 96*b13*b16*b17 - 32*b13*b16*
b18 - 32*b13*b17*b18 - 192*b14*b15*b16 - 192*b14*b15*b17 - 96*b14*b15*b18
- 32*b14*b15*b19 - 192*b14*b16*b17 - 32*b14*b16*b19 - 96*b14*b17*b18 - 32
*b14*b17*b19 - 32*b14*b18*b19 - 192*b15*b16*b17 - 192*b15*b16*b18 - 96*b15
*b16*b19 - 32*b15*b16*b20 - 192*b15*b17*b18 - 32*b15*b17*b20 - 96*b15*b18*
b19 - 32*b15*b18*b20 - 32*b15*b19*b20 - 192*b16*b17*b18 - 192*b16*b17*b19
- 96*b16*b17*b20 - 32*b16*b17*b21 - 192*b16*b18*b19 - 32*b16*b18*b21 - 96
*b16*b19*b20 - 32*b16*b19*b21 - 32*b16*b20*b21 - 192*b17*b18*b19 - 192*b17
*b18*b20 - 96*b17*b18*b21 - 32*b17*b18*b22 - 192*b17*b19*b20 - 32*b17*b19*
b22 - 96*b17*b20*b21 - 32*b17*b20*b22 - 32*b17*b21*b22 - 192*b18*b19*b20
- 192*b18*b19*b21 - 96*b18*b19*b22 - 32*b18*b19*b23 - 192*b18*b20*b21 -
32*b18*b20*b23 - 96*b18*b21*b22 - 32*b18*b21*b23 - 32*b18*b22*b23 - 192*
b19*b20*b21 - 192*b19*b20*b22 - 96*b19*b20*b23 - 32*b19*b20*b24 - 192*b19*
b21*b22 - 32*b19*b21*b24 - 96*b19*b22*b23 - 32*b19*b22*b24 - 32*b19*b23*
b24 - 192*b20*b21*b22 - 192*b20*b21*b23 - 96*b20*b21*b24 - 32*b20*b21*b25
- 192*b20*b22*b23 - 32*b20*b22*b25 - 96*b20*b23*b24 - 32*b20*b23*b25 - 32
*b20*b24*b25 - 192*b21*b22*b23 - 192*b21*b22*b24 - 96*b21*b22*b25 - 32*b21
*b22*b26 - 192*b21*b23*b24 - 32*b21*b23*b26 - 96*b21*b24*b25 - 32*b21*b24*
b26 - 32*b21*b25*b26 - 192*b22*b23*b24 - 192*b22*b23*b25 - 96*b22*b23*b26
- 32*b22*b23*b27 - 192*b22*b24*b25 - 32*b22*b24*b27 - 96*b22*b25*b26 - 32
*b22*b25*b27 - 32*b22*b26*b27 - 192*b23*b24*b25 - 192*b23*b24*b26 - 96*b23
*b24*b27 - 32*b23*b24*b28 - 192*b23*b25*b26 - 32*b23*b25*b28 - 96*b23*b26*
b27 - 32*b23*b26*b28 - 32*b23*b27*b28 - 192*b24*b25*b26 - 192*b24*b25*b27
- 96*b24*b25*b28 - 32*b24*b25*b29 - 192*b24*b26*b27 - 32*b24*b26*b29 - 96
*b24*b27*b28 - 32*b24*b27*b29 - 32*b24*b28*b29 - 192*b25*b26*b27 - 192*b25
*b26*b28 - 96*b25*b26*b29 - 32*b25*b26*b30 - 192*b25*b27*b28 - 32*b25*b27*
b30 - 96*b25*b28*b29 - 32*b25*b28*b30 - 32*b25*b29*b30 - 192*b26*b27*b28
- 192*b26*b27*b29 - 96*b26*b27*b30 - 32*b26*b27*b31 - 192*b26*b28*b29 -
32*b26*b28*b31 - 96*b26*b29*b30 - 32*b26*b29*b31 - 32*b26*b30*b31 - 192*
b27*b28*b29 - 192*b27*b28*b30 - 96*b27*b28*b31 - 32*b27*b28*b32 - 192*b27*
b29*b30 - 32*b27*b29*b32 - 96*b27*b30*b31 - 32*b27*b30*b32 - 32*b27*b31*
b32 - 192*b28*b29*b30 - 192*b28*b29*b31 - 96*b28*b29*b32 - 32*b28*b29*b33
- 192*b28*b30*b31 - 32*b28*b30*b33 - 96*b28*b31*b32 - 32*b28*b31*b33 - 32
*b28*b32*b33 - 192*b29*b30*b31 - 192*b29*b30*b32 - 96*b29*b30*b33 - 32*b29
*b30*b34 - 192*b29*b31*b32 - 32*b29*b31*b34 - 96*b29*b32*b33 - 32*b29*b32*
b34 - 32*b29*b33*b34 - 192*b30*b31*b32 - 192*b30*b31*b33 - 96*b30*b31*b34
- 32*b30*b31*b35 - 192*b30*b32*b33 - 32*b30*b32*b35 - 96*b30*b33*b34 - 32
*b30*b33*b35 - 32*b30*b34*b35 - 192*b31*b32*b33 - 192*b31*b32*b34 - 96*b31
*b32*b35 - 32*b31*b32*b36 - 192*b31*b33*b34 - 32*b31*b33*b36 - 96*b31*b34*
b35 - 32*b31*b34*b36 - 32*b31*b35*b36 - 192*b32*b33*b34 - 192*b32*b33*b35
- 96*b32*b33*b36 - 32*b32*b33*b37 - 192*b32*b34*b35 - 32*b32*b34*b37 - 96
*b32*b35*b36 - 32*b32*b35*b37 - 32*b32*b36*b37 - 192*b33*b34*b35 - 192*b33
*b34*b36 - 96*b33*b34*b37 - 32*b33*b34*b38 - 192*b33*b35*b36 - 32*b33*b35*
b38 - 96*b33*b36*b37 - 32*b33*b36*b38 - 32*b33*b37*b38 - 192*b34*b35*b36
- 192*b34*b35*b37 - 96*b34*b35*b38 - 32*b34*b35*b39 - 192*b34*b36*b37 -
32*b34*b36*b39 - 96*b34*b37*b38 - 32*b34*b37*b39 - 32*b34*b38*b39 - 192*
b35*b36*b37 - 192*b35*b36*b38 - 96*b35*b36*b39 - 32*b35*b36*b40 - 192*b35*
b37*b38 - 32*b35*b37*b40 - 96*b35*b38*b39 - 32*b35*b38*b40 - 32*b35*b39*
b40 - 192*b36*b37*b38 - 192*b36*b37*b39 - 96*b36*b37*b40 - 32*b36*b37*b41
- 192*b36*b38*b39 - 32*b36*b38*b41 - 96*b36*b39*b40 - 32*b36*b39*b41 - 32
*b36*b40*b41 - 192*b37*b38*b39 - 192*b37*b38*b40 - 96*b37*b38*b41 - 32*b37
*b38*b42 - 192*b37*b39*b40 - 32*b37*b39*b42 - 96*b37*b40*b41 - 32*b37*b40*
b42 - 32*b37*b41*b42 - 192*b38*b39*b40 - 192*b38*b39*b41 - 96*b38*b39*b42
- 32*b38*b39*b43 - 192*b38*b40*b41 - 32*b38*b40*b43 - 96*b38*b41*b42 - 32
*b38*b41*b43 - 32*b38*b42*b43 - 192*b39*b40*b41 - 192*b39*b40*b42 - 96*b39
*b40*b43 - 32*b39*b40*b44 - 192*b39*b41*b42 - 32*b39*b41*b44 - 96*b39*b42*
b43 - 32*b39*b42*b44 - 32*b39*b43*b44 - 192*b40*b41*b42 - 192*b40*b41*b43
- 96*b40*b41*b44 - 32*b40*b41*b45 - 192*b40*b42*b43 - 32*b40*b42*b45 - 96
*b40*b43*b44 - 32*b40*b43*b45 - 32*b40*b44*b45 - 192*b41*b42*b43 - 192*b41
*b42*b44 - 96*b41*b42*b45 - 32*b41*b42*b46 - 192*b41*b43*b44 - 32*b41*b43*
b46 - 96*b41*b44*b45 - 32*b41*b44*b46 - 32*b41*b45*b46 - 192*b42*b43*b44
- 192*b42*b43*b45 - 96*b42*b43*b46 - 32*b42*b43*b47 - 192*b42*b44*b45 -
32*b42*b44*b47 - 96*b42*b45*b46 - 32*b42*b45*b47 - 32*b42*b46*b47 - 192*
b43*b44*b45 - 192*b43*b44*b46 - 96*b43*b44*b47 - 32*b43*b44*b48 - 192*b43*
b45*b46 - 32*b43*b45*b48 - 96*b43*b46*b47 - 32*b43*b46*b48 - 32*b43*b47*
b48 - 192*b44*b45*b46 - 192*b44*b45*b47 - 96*b44*b45*b48 - 32*b44*b45*b49
- 192*b44*b46*b47 - 32*b44*b46*b49 - 96*b44*b47*b48 - 32*b44*b47*b49 - 32
*b44*b48*b49 - 192*b45*b46*b47 - 192*b45*b46*b48 - 96*b45*b46*b49 - 32*b45
*b46*b50 - 192*b45*b47*b48 - 32*b45*b47*b50 - 96*b45*b48*b49 - 32*b45*b48*
b50 - 32*b45*b49*b50 - 160*b46*b47*b48 - 128*b46*b47*b49 - 32*b46*b47*b50
- 128*b46*b48*b49 - 64*b46*b49*b50 - 96*b47*b48*b49 - 64*b47*b48*b50 - 64
*b47*b49*b50 - 32*b48*b49*b50 + 48*b1*b2 + 40*b1*b3 + 48*b1*b4 + 40*b1*b5
+ 32*b1*b6 + 96*b2*b3 + 96*b2*b4 + 112*b2*b5 + 80*b2*b6 + 32*b2*b7 + 160*
b3*b4 + 152*b3*b5 + 160*b3*b6 + 80*b3*b7 + 32*b3*b8 + 208*b4*b5 + 192*b4*
b6 + 160*b4*b7 + 80*b4*b8 + 32*b4*b9 + 256*b5*b6 + 192*b5*b7 + 160*b5*b8
+ 80*b5*b9 + 32*b5*b10 + 256*b6*b7 + 192*b6*b8 + 160*b6*b9 + 80*b6*b10 +
32*b6*b11 + 256*b7*b8 + 192*b7*b9 + 160*b7*b10 + 80*b7*b11 + 32*b7*b12 +
256*b8*b9 + 192*b8*b10 + 160*b8*b11 + 80*b8*b12 + 32*b8*b13 + 256*b9*b10
+ 192*b9*b11 + 160*b9*b12 + 80*b9*b13 + 32*b9*b14 + 256*b10*b11 + 192*b10
*b12 + 160*b10*b13 + 80*b10*b14 + 32*b10*b15 + 256*b11*b12 + 192*b11*b13
+ 160*b11*b14 + 80*b11*b15 + 32*b11*b16 + 256*b12*b13 + 192*b12*b14 + 160
*b12*b15 + 80*b12*b16 + 32*b12*b17 + 256*b13*b14 + 192*b13*b15 + 160*b13*
b16 + 80*b13*b17 + 32*b13*b18 + 256*b14*b15 + 192*b14*b16 + 160*b14*b17 +
80*b14*b18 + 32*b14*b19 + 256*b15*b16 + 192*b15*b17 + 160*b15*b18 + 80*b15
*b19 + 32*b15*b20 + 256*b16*b17 + 192*b16*b18 + 160*b16*b19 + 80*b16*b20
+ 32*b16*b21 + 256*b17*b18 + 192*b17*b19 + 160*b17*b20 + 80*b17*b21 + 32*
b17*b22 + 256*b18*b19 + 192*b18*b20 + 160*b18*b21 + 80*b18*b22 + 32*b18*
b23 + 256*b19*b20 + 192*b19*b21 + 160*b19*b22 + 80*b19*b23 + 32*b19*b24 +
256*b20*b21 + 192*b20*b22 + 160*b20*b23 + 80*b20*b24 + 32*b20*b25 + 256*
b21*b22 + 192*b21*b23 + 160*b21*b24 + 80*b21*b25 + 32*b21*b26 + 256*b22*
b23 + 192*b22*b24 + 160*b22*b25 + 80*b22*b26 + 32*b22*b27 + 256*b23*b24 +
192*b23*b25 + 160*b23*b26 + 80*b23*b27 + 32*b23*b28 + 256*b24*b25 + 192*
b24*b26 + 160*b24*b27 + 80*b24*b28 + 32*b24*b29 + 256*b25*b26 + 192*b25*
b27 + 160*b25*b28 + 80*b25*b29 + 32*b25*b30 + 256*b26*b27 + 192*b26*b28 +
160*b26*b29 + 80*b26*b30 + 32*b26*b31 + 256*b27*b28 + 192*b27*b29 + 160*
b27*b30 + 80*b27*b31 + 32*b27*b32 + 256*b28*b29 + 192*b28*b30 + 160*b28*
b31 + 80*b28*b32 + 32*b28*b33 + 256*b29*b30 + 192*b29*b31 + 160*b29*b32 +
80*b29*b33 + 32*b29*b34 + 256*b30*b31 + 192*b30*b32 + 160*b30*b33 + 80*b30
*b34 + 32*b30*b35 + 256*b31*b32 + 192*b31*b33 + 160*b31*b34 + 80*b31*b35
+ 32*b31*b36 + 256*b32*b33 + 192*b32*b34 + 160*b32*b35 + 80*b32*b36 + 32*
b32*b37 + 256*b33*b34 + 192*b33*b35 + 160*b33*b36 + 80*b33*b37 + 32*b33*
b38 + 256*b34*b35 + 192*b34*b36 + 160*b34*b37 + 80*b34*b38 + 32*b34*b39 +
256*b35*b36 + 192*b35*b37 + 160*b35*b38 + 80*b35*b39 + 32*b35*b40 + 256*
b36*b37 + 192*b36*b38 + 160*b36*b39 + 80*b36*b40 + 32*b36*b41 + 256*b37*
b38 + 192*b37*b39 + 160*b37*b40 + 80*b37*b41 + 32*b37*b42 + 256*b38*b39 +
192*b38*b40 + 160*b38*b41 + 80*b38*b42 + 32*b38*b43 + 256*b39*b40 + 192*
b39*b41 + 160*b39*b42 + 80*b39*b43 + 32*b39*b44 + 256*b40*b41 + 192*b40*
b42 + 160*b40*b43 + 80*b40*b44 + 32*b40*b45 + 256*b41*b42 + 192*b41*b43 +
160*b41*b44 + 80*b41*b45 + 32*b41*b46 + 256*b42*b43 + 192*b42*b44 + 160*
b42*b45 + 80*b42*b46 + 32*b42*b47 + 256*b43*b44 + 192*b43*b45 + 160*b43*
b46 + 80*b43*b47 + 32*b43*b48 + 256*b44*b45 + 192*b44*b46 + 160*b44*b47 +
80*b44*b48 + 32*b44*b49 + 256*b45*b46 + 192*b45*b47 + 160*b45*b48 + 80*b45
*b49 + 32*b45*b50 + 208*b46*b47 + 152*b46*b48 + 112*b46*b49 + 40*b46*b50
+ 160*b47*b48 + 96*b47*b49 + 48*b47*b50 + 96*b48*b49 + 40*b48*b50 + 48*
b49*b50 - 40*b1 - 88*b2 - 136*b3 - 184*b4 - 232*b5 - 272*b6 - 272*b7 - 272
*b8 - 272*b9 - 272*b10 - 272*b11 - 272*b12 - 272*b13 - 272*b14 - 272*b15
- 272*b16 - 272*b17 - 272*b18 - 272*b19 - 272*b20 - 272*b21 - 272*b22 -
272*b23 - 272*b24 - 272*b25 - 272*b26 - 272*b27 - 272*b28 - 272*b29 - 272*
b30 - 272*b31 - 272*b32 - 272*b33 - 272*b34 - 272*b35 - 272*b36 - 272*b37
- 272*b38 - 272*b39 - 272*b40 - 272*b41 - 272*b42 - 272*b43 - 272*b44 -
272*b45 - 232*b46 - 184*b47 - 136*b48 - 88*b49 - 40*b50 - 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