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Instance autocorr_bern25-03

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.

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-92.00000000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-92.00000009 (ANTIGONE) -92.00000009 (BARON) -92.00000002 (COUENNE) -92.00000008 (CPLEX) -92.00000000 (GUROBI) -92.00000000 (LINDO) -92.00000000 (PQCR) -92.00000000 (SCIP) -92.00000000 (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.25.3
Applicationⓘ	Autocorrelated Sequences
Added to libraryⓘ	26 Feb 2014
Problem typeⓘ	MBQCP
#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ⓘ	1
#Polynomial Constraintsⓘ	0
#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ⓘ	46
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	2
Minimal blocksize in Hessian of Lagrangianⓘ	12
Maximal blocksize in Hessian of Lagrangianⓘ	13
Average blocksize in Hessian of Lagrangianⓘ	12.5
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	8.0000e+00
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.. 8*b1*b3 - 4*b1 - 8*b3 + 8*b2*b4 - 4*b2 - 8*b4 + 8*b3*b5 - 8*b5 + 8*b4*b6
      - 8*b6 + 8*b5*b7 - 8*b7 + 8*b6*b8 - 8*b8 + 8*b7*b9 - 8*b9 + 8*b8*b10 - 8*
     b10 + 8*b9*b11 - 8*b11 + 8*b10*b12 - 8*b12 + 8*b11*b13 - 8*b13 + 8*b12*b14
      - 8*b14 + 8*b13*b15 - 8*b15 + 8*b14*b16 - 8*b16 + 8*b15*b17 - 8*b17 + 8*
     b16*b18 - 8*b18 + 8*b17*b19 - 8*b19 + 8*b18*b20 - 8*b20 + 8*b19*b21 - 8*
     b21 + 8*b20*b22 - 8*b22 + 8*b21*b23 - 8*b23 + 8*b22*b24 - 4*b24 + 8*b23*
     b25 - 4*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;