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Instance: autocorr_bern20-03

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
Primal Bounds
-72.00000000 p1 ( gdx sol )
(infeas: 0)
Dual Bounds
-72.00000007 (ANTIGONE)
-72.00000007 (BARON)
-72.00000001 (COUENNE)
-72.00000000 (LINDO)
-72.00000000 (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.20.3
Application Autocorrelated Sequences
Added to library 26 Feb 2014
Problem type MBQCP
#Variables 21
#Binary Variables 20
#Integer Variables 0
#Nonlinear Variables 20
#Nonlinear Binary Variables 20
#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 21
#Nonlinear Nonzeros in Jacobian 20
#Nonzeros in (Upper-Left) Hessian of Lagrangian 36
#Nonzeros in Diagonal of Hessian of Lagrangian 0
#Blocks in Hessian of Lagrangian 2
Minimal blocksize in Hessian of Lagrangian 10
Maximal blocksize in Hessian of Lagrangian 10
Average blocksize in Hessian of Lagrangian 10.0
#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
*         21        1       20        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         21        1       20        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,objvar;

Binary Variables  b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17
          ,b18,b19,b20;

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 - 4*b19 + 8*b18*b20 - 4*b20 - 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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