Description

Tests the XPRESS multiobjective optimization features.

Contributor: Renke Kuhlmann, December 2025

Small Model of Type : LP

Category : GAMS Test library

Main file : xpress08.gms

$title 'XPRESS test suite - multiobjective test' (XPRESS08,SEQ=831)
$onText
Tests the XPRESS multiobjective optimization features.

Contributor: Renke Kuhlmann, December 2025
$offText

option solver = xpress;

Variables x, y, z, z1, z2;
Equations obj_1, obj1, obj2, obj3, obj4, con1, con2;
obj_1.. z =e= 1.1 * z1 + z2;
obj1.. z1 =e= x;
obj2.. z2 =e= y;
obj3.. z2 =e= y;
obj4.. z1 =e= x;
con1.. 2 * x + y =l= 3;
con2.. 0.5 * x + y =l= 1.5;
x.lo = 0;
y.lo = 0;

Model m1 / obj_1, obj1, obj2, con1, con2 /;
Solve m1 using lp maximizing z;

abort$(x.l <> 1 or z1.l <> x.l) 'false value x';
abort$(obj1.l <> 0) 'false value obj1';
abort$(y.l <> 1 or z2.l <> y.l) 'false value y';
abort$(obj2.l <> 0) 'false value obj2';


file fxpx 'Xpress Option file' / xpress.opt /;

m1.optfile=1;
putclose fxpx 'multobj 1';
Solve m1 using lp maximizing z;

abort$(x.l <> 1.5 or z1.l <> x.l) 'false value x';
abort$(obj1.l <> 0) 'false value obj1';
abort$(y.l <> 0 or z2.l <> y.l) 'false value y';
abort$(obj2.l <> 0) 'false value obj2';


putclose fxpx 'multobj 1' / 'objnabstol z1 0.5' / 'multiObjOps_rcFixing 0';
Solve m1 using lp maximizing z;

abort$(x.l <> 1) 'false value x';
abort$(z1.l <> 1) 'false value z1';
abort$(obj1.l <> 0) 'false value obj1';
abort$(y.l <> 1) 'false value y';
abort$(z2.l <> 1) 'false value z2';
abort$(obj2.l <> 0) 'false value obj2';


putclose fxpx 'multobj 1' / 'objnabstol z1 1.5';
Solve m1 using lp maximizing z;

abort$(x.l <> 0) 'false value x';
abort$(z1.l <> 0) 'false value z1';
abort$(obj1.l <> 0) 'false value obj1';
abort$(y.l <> 1.5) 'false value y';
abort$(z2.l <> 1.5) 'false value z2';
abort$(obj2.l <> 0) 'false value obj2';


* test with different objective ordering

Model m2 / obj_1, obj3, obj4, con1, con2 /;
Solve m2 using lp maximizing z;

abort$(x.l <> 1 or z1.l <> x.l) 'false value x';
abort$(obj4.l <> 0) 'false value obj4';
abort$(y.l <> 1 or z2.l <> y.l) 'false value y';
abort$(obj3.l <> 0) 'false value obj3';

m2.optfile=1;
putclose fxpx 'multobj 1';
Solve m2 using lp maximizing z;

abort$(x.l <> 1.5 or z1.l <> x.l) 'false value x';
abort$(obj4.l <> 0) 'false value obj4';
abort$(y.l <> 0 or z2.l <> y.l) 'false value y';
abort$(obj3.l <> 0) 'false value obj3';


putclose fxpx 'multobj 1' / 'objnabstol z1 0.5' / 'multiObjOps_rcFixing 0';
Solve m2 using lp maximizing z;

abort$(x.l <> 1) 'false value x';
abort$(z1.l <> 1) 'false value z1';
abort$(obj4.l <> 0) 'false value obj4';
abort$(y.l <> 1) 'false value y';
abort$(z2.l <> 1) 'false value z2';
abort$(obj3.l <> 0) 'false value obj3';


putclose fxpx 'multobj 1' / 'objnabstol z1 1.5';
Solve m2 using lp maximizing z;

abort$(x.l <> 0) 'false value x';
abort$(z1.l <> 0) 'false value z1';
abort$(obj4.l <> 0) 'false value obj4';
abort$(y.l <> 1.5) 'false value y';
abort$(z2.l <> 1.5) 'false value z2';
abort$(obj3.l <> 0) 'false value obj3';