MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance autocorr_bern25-06
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ⓘ | -960.00000100 (ANTIGONE) -960.00000190 (BARON) -960.00000000 (COUENNE) -1088.00000000 (LINDO) -960.00000000 (PQCR) -960.00000000 (SCIP) -960.00000000 (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.25.6 |
| Applicationⓘ | Autocorrelated Sequences |
| Added to libraryⓘ | 26 Feb 2014 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 26 |
| #Binary Variablesⓘ | 25 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 25 |
| #Nonlinear Binary Variablesⓘ | 25 |
| #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ⓘ | 26 |
| #Nonlinear Nonzeros in Jacobianⓘ | 25 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 220 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 25 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 25 |
| Average blocksize in Hessian of Lagrangianⓘ | 25.0 |
| #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
* 26 1 25 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 26 1 25 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,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;
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 +
128*b21*b22*b23*b24 + 64*b21*b22*b24*b25 + 64*b22*b23*b24*b25 - 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 - 160*b21*b22*b23
- 128*b21*b22*b24 - 32*b21*b22*b25 - 128*b21*b23*b24 - 64*b21*b24*b25 -
96*b22*b23*b24 - 64*b22*b23*b25 - 64*b22*b24*b25 - 32*b23*b24*b25 + 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 + 208*b21*b22 + 152*b21*b23 + 112*b21*b24 +
40*b21*b25 + 160*b22*b23 + 96*b22*b24 + 48*b22*b25 + 96*b23*b24 + 40*b23*
b25 + 48*b24*b25 - 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 - 232*b21 - 184*
b22 - 136*b23 - 88*b24 - 40*b25 - 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