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Instance: autocorr_bern40-05

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
Primal Bounds
-932.00000000 p1 ( gdx sol )
(infeas: 0)
-936.00000000 p2 ( gdx sol )
(infeas: 0)
Dual Bounds
-1021.00000000 (ANTIGONE)
-936.09360940 (BARON)
-1936.00000000 (COUENNE)
-1812.00000000 (LINDO)
-2648.26891300 (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.40.5
Application Autocorrelated Sequences
Added to library 26 Feb 2014
Problem type MBNLP
#Variables 41
#Binary Variables 40
#Integer Variables 0
#Nonlinear Variables 40
#Nonlinear Binary Variables 40
#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 41
#Nonlinear Nonzeros in Jacobian 40
#Nonzeros in (Upper-Left) Hessian of Lagrangian 300
#Nonzeros in Diagonal of Hessian of Lagrangian 0
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 40
Maximal blocksize in Hessian of Lagrangian 40
Average blocksize in Hessian of Lagrangian 40.0
#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
*         41        1       40        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         41        1       40        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,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;

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 + 64*b37*b38*b39*b40 - 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 - 96*b37*b38*b39 - 32*b37*b38*b40 - 64*b37*b39*
     b40 - 32*b38*b39*b40 + 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 + 96*b37*
     b38 + 80*b37*b39 + 32*b37*b40 + 64*b38*b39 + 24*b38*b40 + 32*b39*b40 - 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 - 104*b37 - 76*b38 - 52
     *b39 - 24*b40 - 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: 2018-09-14 Git hash: ac5a5314
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