MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance autocorr_bern45-05
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.
| Formatsⓘ | ams gms mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -1170.40000000 (ANTIGONE) -1098.77359500 (BARON) -2610.00000000 (COUENNE) -1068.00000000 (DynamicProgramming) -1068.00000000 (GUROBI) -2220.00000000 (LINDO) -1068.00000000 (PQCR) -1192.48228200 (SCIP) -2708.22222200 (SHOT) -2145.67195800 (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.45.5 |
| Applicationⓘ | Autocorrelated Sequences |
| Added to libraryⓘ | 26 Feb 2014 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 46 |
| #Binary Variablesⓘ | 45 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 45 |
| #Nonlinear Binary Variablesⓘ | 45 |
| #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ⓘ | 46 |
| #Nonlinear Nonzeros in Jacobianⓘ | 45 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 340 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 45 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 45 |
| Average blocksize in Hessian of Lagrangianⓘ | 45.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 1.2800e+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
* 46 1 45 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 46 1 45 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,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;
Equations e1;
e1.. 64*b1*b2*b3*b4 + 64*b1*b2*b4*b5 + 128*b2*b3*b4*b5 + 64*b2*b3*b5*b6 + 128*
b3*b4*b5*b6 + 64*b3*b4*b6*b7 + 128*b4*b5*b6*b7 + 64*b4*b5*b7*b8 + 128*b5*
b6*b7*b8 + 64*b5*b6*b8*b9 + 128*b6*b7*b8*b9 + 64*b6*b7*b9*b10 + 128*b7*b8*
b9*b10 + 64*b7*b8*b10*b11 + 128*b8*b9*b10*b11 + 64*b8*b9*b11*b12 + 128*b9*
b10*b11*b12 + 64*b9*b10*b12*b13 + 128*b10*b11*b12*b13 + 64*b10*b11*b13*b14
+ 128*b11*b12*b13*b14 + 64*b11*b12*b14*b15 + 128*b12*b13*b14*b15 + 64*b12
*b13*b15*b16 + 128*b13*b14*b15*b16 + 64*b13*b14*b16*b17 + 128*b14*b15*b16*
b17 + 64*b14*b15*b17*b18 + 128*b15*b16*b17*b18 + 64*b15*b16*b18*b19 + 128*
b16*b17*b18*b19 + 64*b16*b17*b19*b20 + 128*b17*b18*b19*b20 + 64*b17*b18*
b20*b21 + 128*b18*b19*b20*b21 + 64*b18*b19*b21*b22 + 128*b19*b20*b21*b22
+ 64*b19*b20*b22*b23 + 128*b20*b21*b22*b23 + 64*b20*b21*b23*b24 + 128*b21
*b22*b23*b24 + 64*b21*b22*b24*b25 + 128*b22*b23*b24*b25 + 64*b22*b23*b25*
b26 + 128*b23*b24*b25*b26 + 64*b23*b24*b26*b27 + 128*b24*b25*b26*b27 + 64*
b24*b25*b27*b28 + 128*b25*b26*b27*b28 + 64*b25*b26*b28*b29 + 128*b26*b27*
b28*b29 + 64*b26*b27*b29*b30 + 128*b27*b28*b29*b30 + 64*b27*b28*b30*b31 +
128*b28*b29*b30*b31 + 64*b28*b29*b31*b32 + 128*b29*b30*b31*b32 + 64*b29*
b30*b32*b33 + 128*b30*b31*b32*b33 + 64*b30*b31*b33*b34 + 128*b31*b32*b33*
b34 + 64*b31*b32*b34*b35 + 128*b32*b33*b34*b35 + 64*b32*b33*b35*b36 + 128*
b33*b34*b35*b36 + 64*b33*b34*b36*b37 + 128*b34*b35*b36*b37 + 64*b34*b35*
b37*b38 + 128*b35*b36*b37*b38 + 64*b35*b36*b38*b39 + 128*b36*b37*b38*b39
+ 64*b36*b37*b39*b40 + 128*b37*b38*b39*b40 + 64*b37*b38*b40*b41 + 128*b38
*b39*b40*b41 + 64*b38*b39*b41*b42 + 128*b39*b40*b41*b42 + 64*b39*b40*b42*
b43 + 128*b40*b41*b42*b43 + 64*b40*b41*b43*b44 + 128*b41*b42*b43*b44 + 64*
b41*b42*b44*b45 + 64*b42*b43*b44*b45 - 32*b1*b2*b3 - 64*b1*b2*b4 - 32*b1*
b2*b5 - 32*b1*b3*b4 - 32*b1*b4*b5 - 96*b2*b3*b4 - 96*b2*b3*b5 - 32*b2*b3*
b6 - 96*b2*b4*b5 - 32*b2*b5*b6 - 128*b3*b4*b5 - 96*b3*b4*b6 - 32*b3*b4*b7
- 96*b3*b5*b6 - 32*b3*b6*b7 - 128*b4*b5*b6 - 96*b4*b5*b7 - 32*b4*b5*b8 -
96*b4*b6*b7 - 32*b4*b7*b8 - 128*b5*b6*b7 - 96*b5*b6*b8 - 32*b5*b6*b9 - 96*
b5*b7*b8 - 32*b5*b8*b9 - 128*b6*b7*b8 - 96*b6*b7*b9 - 32*b6*b7*b10 - 96*b6
*b8*b9 - 32*b6*b9*b10 - 128*b7*b8*b9 - 96*b7*b8*b10 - 32*b7*b8*b11 - 96*b7
*b9*b10 - 32*b7*b10*b11 - 128*b8*b9*b10 - 96*b8*b9*b11 - 32*b8*b9*b12 - 96
*b8*b10*b11 - 32*b8*b11*b12 - 128*b9*b10*b11 - 96*b9*b10*b12 - 32*b9*b10*
b13 - 96*b9*b11*b12 - 32*b9*b12*b13 - 128*b10*b11*b12 - 96*b10*b11*b13 -
32*b10*b11*b14 - 96*b10*b12*b13 - 32*b10*b13*b14 - 128*b11*b12*b13 - 96*
b11*b12*b14 - 32*b11*b12*b15 - 96*b11*b13*b14 - 32*b11*b14*b15 - 128*b12*
b13*b14 - 96*b12*b13*b15 - 32*b12*b13*b16 - 96*b12*b14*b15 - 32*b12*b15*
b16 - 128*b13*b14*b15 - 96*b13*b14*b16 - 32*b13*b14*b17 - 96*b13*b15*b16
- 32*b13*b16*b17 - 128*b14*b15*b16 - 96*b14*b15*b17 - 32*b14*b15*b18 - 96
*b14*b16*b17 - 32*b14*b17*b18 - 128*b15*b16*b17 - 96*b15*b16*b18 - 32*b15*
b16*b19 - 96*b15*b17*b18 - 32*b15*b18*b19 - 128*b16*b17*b18 - 96*b16*b17*
b19 - 32*b16*b17*b20 - 96*b16*b18*b19 - 32*b16*b19*b20 - 128*b17*b18*b19
- 96*b17*b18*b20 - 32*b17*b18*b21 - 96*b17*b19*b20 - 32*b17*b20*b21 - 128
*b18*b19*b20 - 96*b18*b19*b21 - 32*b18*b19*b22 - 96*b18*b20*b21 - 32*b18*
b21*b22 - 128*b19*b20*b21 - 96*b19*b20*b22 - 32*b19*b20*b23 - 96*b19*b21*
b22 - 32*b19*b22*b23 - 128*b20*b21*b22 - 96*b20*b21*b23 - 32*b20*b21*b24
- 96*b20*b22*b23 - 32*b20*b23*b24 - 128*b21*b22*b23 - 96*b21*b22*b24 - 32
*b21*b22*b25 - 96*b21*b23*b24 - 32*b21*b24*b25 - 128*b22*b23*b24 - 96*b22*
b23*b25 - 32*b22*b23*b26 - 96*b22*b24*b25 - 32*b22*b25*b26 - 128*b23*b24*
b25 - 96*b23*b24*b26 - 32*b23*b24*b27 - 96*b23*b25*b26 - 32*b23*b26*b27 -
128*b24*b25*b26 - 96*b24*b25*b27 - 32*b24*b25*b28 - 96*b24*b26*b27 - 32*
b24*b27*b28 - 128*b25*b26*b27 - 96*b25*b26*b28 - 32*b25*b26*b29 - 96*b25*
b27*b28 - 32*b25*b28*b29 - 128*b26*b27*b28 - 96*b26*b27*b29 - 32*b26*b27*
b30 - 96*b26*b28*b29 - 32*b26*b29*b30 - 128*b27*b28*b29 - 96*b27*b28*b30
- 32*b27*b28*b31 - 96*b27*b29*b30 - 32*b27*b30*b31 - 128*b28*b29*b30 - 96
*b28*b29*b31 - 32*b28*b29*b32 - 96*b28*b30*b31 - 32*b28*b31*b32 - 128*b29*
b30*b31 - 96*b29*b30*b32 - 32*b29*b30*b33 - 96*b29*b31*b32 - 32*b29*b32*
b33 - 128*b30*b31*b32 - 96*b30*b31*b33 - 32*b30*b31*b34 - 96*b30*b32*b33
- 32*b30*b33*b34 - 128*b31*b32*b33 - 96*b31*b32*b34 - 32*b31*b32*b35 - 96
*b31*b33*b34 - 32*b31*b34*b35 - 128*b32*b33*b34 - 96*b32*b33*b35 - 32*b32*
b33*b36 - 96*b32*b34*b35 - 32*b32*b35*b36 - 128*b33*b34*b35 - 96*b33*b34*
b36 - 32*b33*b34*b37 - 96*b33*b35*b36 - 32*b33*b36*b37 - 128*b34*b35*b36
- 96*b34*b35*b37 - 32*b34*b35*b38 - 96*b34*b36*b37 - 32*b34*b37*b38 - 128
*b35*b36*b37 - 96*b35*b36*b38 - 32*b35*b36*b39 - 96*b35*b37*b38 - 32*b35*
b38*b39 - 128*b36*b37*b38 - 96*b36*b37*b39 - 32*b36*b37*b40 - 96*b36*b38*
b39 - 32*b36*b39*b40 - 128*b37*b38*b39 - 96*b37*b38*b40 - 32*b37*b38*b41
- 96*b37*b39*b40 - 32*b37*b40*b41 - 128*b38*b39*b40 - 96*b38*b39*b41 - 32
*b38*b39*b42 - 96*b38*b40*b41 - 32*b38*b41*b42 - 128*b39*b40*b41 - 96*b39*
b40*b42 - 32*b39*b40*b43 - 96*b39*b41*b42 - 32*b39*b42*b43 - 128*b40*b41*
b42 - 96*b40*b41*b43 - 32*b40*b41*b44 - 96*b40*b42*b43 - 32*b40*b43*b44 -
128*b41*b42*b43 - 96*b41*b42*b44 - 32*b41*b42*b45 - 96*b41*b43*b44 - 32*
b41*b44*b45 - 96*b42*b43*b44 - 32*b42*b43*b45 - 64*b42*b44*b45 - 32*b43*
b44*b45 + 32*b1*b2 + 24*b1*b3 + 32*b1*b4 + 24*b1*b5 + 64*b2*b3 + 80*b2*b4
+ 64*b2*b5 + 24*b2*b6 + 96*b3*b4 + 104*b3*b5 + 64*b3*b6 + 24*b3*b7 + 128*
b4*b5 + 104*b4*b6 + 64*b4*b7 + 24*b4*b8 + 128*b5*b6 + 104*b5*b7 + 64*b5*b8
+ 24*b5*b9 + 128*b6*b7 + 104*b6*b8 + 64*b6*b9 + 24*b6*b10 + 128*b7*b8 +
104*b7*b9 + 64*b7*b10 + 24*b7*b11 + 128*b8*b9 + 104*b8*b10 + 64*b8*b11 +
24*b8*b12 + 128*b9*b10 + 104*b9*b11 + 64*b9*b12 + 24*b9*b13 + 128*b10*b11
+ 104*b10*b12 + 64*b10*b13 + 24*b10*b14 + 128*b11*b12 + 104*b11*b13 + 64*
b11*b14 + 24*b11*b15 + 128*b12*b13 + 104*b12*b14 + 64*b12*b15 + 24*b12*b16
+ 128*b13*b14 + 104*b13*b15 + 64*b13*b16 + 24*b13*b17 + 128*b14*b15 + 104
*b14*b16 + 64*b14*b17 + 24*b14*b18 + 128*b15*b16 + 104*b15*b17 + 64*b15*
b18 + 24*b15*b19 + 128*b16*b17 + 104*b16*b18 + 64*b16*b19 + 24*b16*b20 +
128*b17*b18 + 104*b17*b19 + 64*b17*b20 + 24*b17*b21 + 128*b18*b19 + 104*
b18*b20 + 64*b18*b21 + 24*b18*b22 + 128*b19*b20 + 104*b19*b21 + 64*b19*b22
+ 24*b19*b23 + 128*b20*b21 + 104*b20*b22 + 64*b20*b23 + 24*b20*b24 + 128*
b21*b22 + 104*b21*b23 + 64*b21*b24 + 24*b21*b25 + 128*b22*b23 + 104*b22*
b24 + 64*b22*b25 + 24*b22*b26 + 128*b23*b24 + 104*b23*b25 + 64*b23*b26 +
24*b23*b27 + 128*b24*b25 + 104*b24*b26 + 64*b24*b27 + 24*b24*b28 + 128*b25
*b26 + 104*b25*b27 + 64*b25*b28 + 24*b25*b29 + 128*b26*b27 + 104*b26*b28
+ 64*b26*b29 + 24*b26*b30 + 128*b27*b28 + 104*b27*b29 + 64*b27*b30 + 24*
b27*b31 + 128*b28*b29 + 104*b28*b30 + 64*b28*b31 + 24*b28*b32 + 128*b29*
b30 + 104*b29*b31 + 64*b29*b32 + 24*b29*b33 + 128*b30*b31 + 104*b30*b32 +
64*b30*b33 + 24*b30*b34 + 128*b31*b32 + 104*b31*b33 + 64*b31*b34 + 24*b31*
b35 + 128*b32*b33 + 104*b32*b34 + 64*b32*b35 + 24*b32*b36 + 128*b33*b34 +
104*b33*b35 + 64*b33*b36 + 24*b33*b37 + 128*b34*b35 + 104*b34*b36 + 64*b34
*b37 + 24*b34*b38 + 128*b35*b36 + 104*b35*b37 + 64*b35*b38 + 24*b35*b39 +
128*b36*b37 + 104*b36*b38 + 64*b36*b39 + 24*b36*b40 + 128*b37*b38 + 104*
b37*b39 + 64*b37*b40 + 24*b37*b41 + 128*b38*b39 + 104*b38*b40 + 64*b38*b41
+ 24*b38*b42 + 128*b39*b40 + 104*b39*b41 + 64*b39*b42 + 24*b39*b43 + 128*
b40*b41 + 104*b40*b42 + 64*b40*b43 + 24*b40*b44 + 128*b41*b42 + 104*b41*
b43 + 64*b41*b44 + 24*b41*b45 + 96*b42*b43 + 80*b42*b44 + 32*b42*b45 + 64*
b43*b44 + 24*b43*b45 + 32*b44*b45 - 24*b1 - 52*b2 - 76*b3 - 104*b4 - 128*
b5 - 128*b6 - 128*b7 - 128*b8 - 128*b9 - 128*b10 - 128*b11 - 128*b12 - 128
*b13 - 128*b14 - 128*b15 - 128*b16 - 128*b17 - 128*b18 - 128*b19 - 128*b20
- 128*b21 - 128*b22 - 128*b23 - 128*b24 - 128*b25 - 128*b26 - 128*b27 -
128*b28 - 128*b29 - 128*b30 - 128*b31 - 128*b32 - 128*b33 - 128*b34 - 128*
b35 - 128*b36 - 128*b37 - 128*b38 - 128*b39 - 128*b40 - 128*b41 - 104*b42
- 76*b43 - 52*b44 - 24*b45 - 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