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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
Primal Bounds
-960.00000000 p1 ( gdx sol )
(infeas: 0)
Dual Bounds
-960.00000100 (ANTIGONE)
-960.00000190 (BARON)
-960.00000000 (COUENNE)
-1088.00000000 (LINDO)
-960.00000000 (SCIP)
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
Infeasibility of initial point 0
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of 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: 2018-08-07 Git hash: fccdb193
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