lmp1.gms : Linear Multiplicative Model - Type 1
Generates and solves random linear multiplicative models of
"Type 1." Problem instances are generated as proposed by
Konno and Kuno. Model developed by N. Sahinidis.
References:
- Konno, H, and Kuno, T, Linear multiplicative programming. Mathematical Programming 56 (1992), 51-64.
- Tawarmalani, M, and Sahinidis, N, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications. Kluwer, 2002.
Large Model of Type: NLP
<![CDATA[
$Title Linear Multiplicative Programs - Type 1 (LMP1, SEQ=251)
$Ontext
Generates and solves random linear multiplicative models of
"Type 1." Problem instances are generated as proposed by
Konno and Kuno. Model developed by N. Sahinidis.
H. Konno and T. Kuno, "Linear multiplicative programming,"
Mathematical Programming, 56(51-64), 1992.
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*p5/;
Sets m(mm) constraints
n(nn) variables
p(pp) products;
Sets c cases /c1*c10/
i instances /i1*i5/;
* For each case to be solved, we use different (m,n,p) triplets
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
c10 200 200 5;
Parameters cc(pp,nn) cost coefficients
A(mm,nn) constraint coefficients
b(mm) left-hand-side
rep(c,*) summary report ;
Parameters ResMin, Resmax, NodMin, Nodmax;
Variables y(pp), x(nn), obj ;
x.lo(nn) = 0;
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 lmp1 /all/;
lmp1.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');
ResMin = inf;
Resmax = 0;
NodMin = inf;
Nodmax = 0;
loop(i,
cc(p,n) = uniform(0,100);
A(m,n) = uniform(0,100);
b(m) = uniform(0,100);
* Set initial starting point for all models to 0
x.l(n)=0; y.l(p)=0;
Solve lmp1 minimizing obj using nlp;
rep(c,'AvgResUsd') = rep(c,'AvgResUsd') + lmp1.resusd;
rep(c,'AvgNodUsd') = rep(c,'AvgNodUsd') + lmp1.nodusd;
ResMin = min(ResMin, lmp1.resusd);
NodMin = min(NodMin, lmp1.nodusd);
ResMax = max(ResMax, lmp1.resusd);
NodMax = max(NodMax, lmp1.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;
]]></plaintext></body></div>