lmp3.gms : Linear Multiplicative Model - Type 3
Generate and solves random linear multiplicative models of
"Type 3." Problem instances are generated as proposed by
Benson and Boger. Model developed by N. Sahinidis.
References:
- Tawarmalani, M, and Sahinidis, N, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications. Kluwer, 2002.
- Benson, H P, and Boger, G M, Multiplicative programming problems: Analysis and efficient point search heuristic. Journal of Optimization Theory and Applications 94 (1997), 487-510.
Large Model of Type: NLP
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$Title Linear Multiplicative Programs - Type 3 (LMP3, SEQ=253)
$Ontext
Generate and solves random linear multiplicative models of
"Type 3." Problem instances are generated as proposed by
Benson and Boger. Model developed by N. Sahinidis.
H. P. Benson and G. M. Boger, "Multiplicative programming problems:
Analysis and efficient point search heuristic",
Journal of Optimization Theory and Applications, 94(487-510), 1997.
M. Tawarmalani and N. Sahinidis, Convexification and Global
Optimization in Continuous and Mixed-Integer Nonlinear
Programming: Theory, Algorithms, Software, and Applications,
Kluwer Academic Publishers, 2002.
$Offtext
Options
optcr = 0,
optca = 1.e-6,
limrow = 0,
limcol = 0,
solprint = off;
* reslim = 10000;
Sets mm /m1*m220/
nn /n1*n200/
pp /p1*p4/;
Sets m(mm) constraints
n(nn) variables
p(pp) products;
Sets c cases /c1*c9/
i instances /i1*i5/ ;
* For each case to be solved, we use a different (m,n,p) triplet
Table cases(c,*)
m n p
c1 20 30 2
c2 120 100 2
c3 220 200 2
c4 20 30 3
c5 120 120 3
c6 200 180 3
c7 20 30 4
c8 100 100 4
c9 200 200 4 ;
Parameters cc(pp,nn) cost coefficients
A(mm,nn) constraint coefficients
b(mm) left-hand-side
rep(c,*) summary report ;
Parameters mactual, nactual, pactual,
ResMin, Resmax, NodMin, Nodmax;
Variables y(pp), x(nn), obj ;
x.lo(nn) = 1;
Equations Objective,
Constraints(mm),
Products(pp);
Objective.. obj =E= prod(p, y(p));
Products(p).. y(p) =E= sum(n, cc(p,n)*x(n));
Constraints(m).. b(m) =L= sum(n, A(m,n)*x(n)) ;
Model lmp3 /all/;
lmp3.workspace = 32;
rep(c,'AvgResUsd') = 0;
rep(c,'AvgNodUsd') = 0;
loop (c,
m(mm) = ord(mm)<= cases(c,'m');
n(nn) = ord(nn)<= cases(c,'n');
p(pp) = ord(pp)<= cases(c,'p');
mactual = cases(c,'m');
nactual = cases(c,'n');
pactual = cases(c,'p');
ResMin = inf;
Resmax = 0;
NodMin = inf;
Nodmax = 0;
loop(i,
cc(p,n) = round(uniform(1,10));
A(m,n) = round(uniform(1,10));
b(m) = sum(n, A(m,n)**2);
x.up(n) = smax(m, b(m));
* Set initial starting point for all models to 0
x.l(n)=0; y.l(p)=0;
Solve lmp3 minimizing obj using nlp;
rep(c,'AvgResUsd') = rep(c,'AvgResUsd') + lmp3.resusd;
rep(c,'AvgNodUsd') = rep(c,'AvgNodUsd') + lmp3.nodusd;
ResMin = min(ResMin, lmp3.resusd);
NodMin = min(NodMin, lmp3.nodusd);
ResMax = max(ResMax, lmp3.resusd);
NodMax = max(NodMax, lmp3.nodusd);
);
rep(c,'MinResUsd') = ResMin;
rep(c,'MaxResUsd') = ResMax;
rep(c,'MinNodUsd') = NodMin;
rep(c,'MaxNodUsd') = NodMax;
);
rep(c,'AvgResUsd') = rep(c,'AvgResUsd')/card(i);
rep(c,'AvgNodUsd') = rep(c,'AvgnodUsd')/card(i);
Display rep;
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