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Instance autocorr_bern35-04

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)ⓘ	-384.00000000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-384.00000040 (ANTIGONE) -384.00000040 (BARON) -472.00000000 (COUENNE) -448.00000000 (LINDO) -384.00000000 (PQCR) -384.00000000 (SCIP) -384.00000000 (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.35.4
Applicationⓘ	Autocorrelated Sequences
Added to libraryⓘ	26 Feb 2014
Problem typeⓘ	MBNLP
#Variablesⓘ	36
#Binary Variablesⓘ	35
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	35
#Nonlinear Binary Variablesⓘ	35
#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ⓘ	36
#Nonlinear Nonzeros in Jacobianⓘ	35
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	198
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	35
Maximal blocksize in Hessian of Lagrangianⓘ	35
Average blocksize in Hessian of Lagrangianⓘ	35.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	6.4000e+01
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
*         36        1       35        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         36        1       35        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
          ,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;

Equations  e1;


e1.. 64*b1*b2*b3*b4 + 64*b2*b3*b4*b5 + 64*b3*b4*b5*b6 + 64*b4*b5*b6*b7 + 64*b5*
     b6*b7*b8 + 64*b6*b7*b8*b9 + 64*b7*b8*b9*b10 + 64*b8*b9*b10*b11 + 64*b9*b10
     *b11*b12 + 64*b10*b11*b12*b13 + 64*b11*b12*b13*b14 + 64*b12*b13*b14*b15 + 
     64*b13*b14*b15*b16 + 64*b14*b15*b16*b17 + 64*b15*b16*b17*b18 + 64*b16*b17*
     b18*b19 + 64*b17*b18*b19*b20 + 64*b18*b19*b20*b21 + 64*b19*b20*b21*b22 + 
     64*b20*b21*b22*b23 + 64*b21*b22*b23*b24 + 64*b22*b23*b24*b25 + 64*b23*b24*
     b25*b26 + 64*b24*b25*b26*b27 + 64*b25*b26*b27*b28 + 64*b26*b27*b28*b29 + 
     64*b27*b28*b29*b30 + 64*b28*b29*b30*b31 + 64*b29*b30*b31*b32 + 64*b30*b31*
     b32*b33 + 64*b31*b32*b33*b34 + 64*b32*b33*b34*b35 - 32*b1*b2*b3 - 32*b1*b2
     *b4 - 32*b1*b3*b4 - 64*b2*b3*b4 - 32*b2*b3*b5 - 32*b2*b4*b5 - 64*b3*b4*b5
      - 32*b3*b4*b6 - 32*b3*b5*b6 - 64*b4*b5*b6 - 32*b4*b5*b7 - 32*b4*b6*b7 - 
     64*b5*b6*b7 - 32*b5*b6*b8 - 32*b5*b7*b8 - 64*b6*b7*b8 - 32*b6*b7*b9 - 32*
     b6*b8*b9 - 64*b7*b8*b9 - 32*b7*b8*b10 - 32*b7*b9*b10 - 64*b8*b9*b10 - 32*
     b8*b9*b11 - 32*b8*b10*b11 - 64*b9*b10*b11 - 32*b9*b10*b12 - 32*b9*b11*b12
      - 64*b10*b11*b12 - 32*b10*b11*b13 - 32*b10*b12*b13 - 64*b11*b12*b13 - 32*
     b11*b12*b14 - 32*b11*b13*b14 - 64*b12*b13*b14 - 32*b12*b13*b15 - 32*b12*
     b14*b15 - 64*b13*b14*b15 - 32*b13*b14*b16 - 32*b13*b15*b16 - 64*b14*b15*
     b16 - 32*b14*b15*b17 - 32*b14*b16*b17 - 64*b15*b16*b17 - 32*b15*b16*b18 - 
     32*b15*b17*b18 - 64*b16*b17*b18 - 32*b16*b17*b19 - 32*b16*b18*b19 - 64*b17
     *b18*b19 - 32*b17*b18*b20 - 32*b17*b19*b20 - 64*b18*b19*b20 - 32*b18*b19*
     b21 - 32*b18*b20*b21 - 64*b19*b20*b21 - 32*b19*b20*b22 - 32*b19*b21*b22 - 
     64*b20*b21*b22 - 32*b20*b21*b23 - 32*b20*b22*b23 - 64*b21*b22*b23 - 32*b21
     *b22*b24 - 32*b21*b23*b24 - 64*b22*b23*b24 - 32*b22*b23*b25 - 32*b22*b24*
     b25 - 64*b23*b24*b25 - 32*b23*b24*b26 - 32*b23*b25*b26 - 64*b24*b25*b26 - 
     32*b24*b25*b27 - 32*b24*b26*b27 - 64*b25*b26*b27 - 32*b25*b26*b28 - 32*b25
     *b27*b28 - 64*b26*b27*b28 - 32*b26*b27*b29 - 32*b26*b28*b29 - 64*b27*b28*
     b29 - 32*b27*b28*b30 - 32*b27*b29*b30 - 64*b28*b29*b30 - 32*b28*b29*b31 - 
     32*b28*b30*b31 - 64*b29*b30*b31 - 32*b29*b30*b32 - 32*b29*b31*b32 - 64*b30
     *b31*b32 - 32*b30*b31*b33 - 32*b30*b32*b33 - 64*b31*b32*b33 - 32*b31*b32*
     b34 - 32*b31*b33*b34 - 64*b32*b33*b34 - 32*b32*b33*b35 - 32*b32*b34*b35 - 
     32*b33*b34*b35 + 16*b1*b2 + 24*b1*b3 + 16*b1*b4 + 32*b2*b3 + 48*b2*b4 + 16
     *b2*b5 + 48*b3*b4 + 48*b3*b5 + 16*b3*b6 + 48*b4*b5 + 48*b4*b6 + 16*b4*b7
      + 48*b5*b6 + 48*b5*b7 + 16*b5*b8 + 48*b6*b7 + 48*b6*b8 + 16*b6*b9 + 48*b7
     *b8 + 48*b7*b9 + 16*b7*b10 + 48*b8*b9 + 48*b8*b10 + 16*b8*b11 + 48*b9*b10
      + 48*b9*b11 + 16*b9*b12 + 48*b10*b11 + 48*b10*b12 + 16*b10*b13 + 48*b11*
     b12 + 48*b11*b13 + 16*b11*b14 + 48*b12*b13 + 48*b12*b14 + 16*b12*b15 + 48*
     b13*b14 + 48*b13*b15 + 16*b13*b16 + 48*b14*b15 + 48*b14*b16 + 16*b14*b17
      + 48*b15*b16 + 48*b15*b17 + 16*b15*b18 + 48*b16*b17 + 48*b16*b18 + 16*b16
     *b19 + 48*b17*b18 + 48*b17*b19 + 16*b17*b20 + 48*b18*b19 + 48*b18*b20 + 16
     *b18*b21 + 48*b19*b20 + 48*b19*b21 + 16*b19*b22 + 48*b20*b21 + 48*b20*b22
      + 16*b20*b23 + 48*b21*b22 + 48*b21*b23 + 16*b21*b24 + 48*b22*b23 + 48*b22
     *b24 + 16*b22*b25 + 48*b23*b24 + 48*b23*b25 + 16*b23*b26 + 48*b24*b25 + 48
     *b24*b26 + 16*b24*b27 + 48*b25*b26 + 48*b25*b27 + 16*b25*b28 + 48*b26*b27
      + 48*b26*b28 + 16*b26*b29 + 48*b27*b28 + 48*b27*b29 + 16*b27*b30 + 48*b28
     *b29 + 48*b28*b30 + 16*b28*b31 + 48*b29*b30 + 48*b29*b31 + 16*b29*b32 + 48
     *b30*b31 + 48*b30*b32 + 16*b30*b33 + 48*b31*b32 + 48*b31*b33 + 16*b31*b34
      + 48*b32*b33 + 48*b32*b34 + 16*b32*b35 + 32*b33*b34 + 24*b33*b35 + 16*b34
     *b35 - 12*b1 - 24*b2 - 36*b3 - 48*b4 - 48*b5 - 48*b6 - 48*b7 - 48*b8 - 48*
     b9 - 48*b10 - 48*b11 - 48*b12 - 48*b13 - 48*b14 - 48*b15 - 48*b16 - 48*b17
      - 48*b18 - 48*b19 - 48*b20 - 48*b21 - 48*b22 - 48*b23 - 48*b24 - 48*b25
      - 48*b26 - 48*b27 - 48*b28 - 48*b29 - 48*b30 - 48*b31 - 48*b32 - 36*b33
      - 24*b34 - 12*b35 - 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;