MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics

Instance autocorr_bern20-05

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 py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-416.00000000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-416.00000040 (ANTIGONE) -416.00000040 (BARON) -416.00000010 (COUENNE) -416.00000000 (LINDO) -416.00000000 (PQCR) -416.00000000 (SCIP) -416.00000000 (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.20.5
Applicationⓘ	Autocorrelated Sequences
Added to libraryⓘ	26 Feb 2014
Problem typeⓘ	MBNLP
#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ⓘ	0
#Polynomial Constraintsⓘ	1
#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ⓘ	140
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	20
Maximal blocksize in Hessian of Lagrangianⓘ	20
Average blocksize in Hessian of Lagrangianⓘ	20.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	1.2800e+02
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
*         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.. 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 + 64*b17*b18*b19*b20 - 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 - 
     96*b17*b18*b19 - 32*b17*b18*b20 - 64*b17*b19*b20 - 32*b18*b19*b20 + 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 + 96*b17*b18 + 80*b17*
     b19 + 32*b17*b20 + 64*b18*b19 + 24*b18*b20 + 32*b19*b20 - 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 - 104*b17 - 76*
     b18 - 52*b19 - 24*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;