Description
Test problem 9.2.9 in Handbook of Test Problems in Local and Global Optimization Test problem 9.1.8 on http://titan.princeton.edu/TestProblems/chapter9.html References: Floudas, C A, Pardalos, P M, Adjiman, C S, Esposito, W R, Gumus, Z H, Harding, S T, Klepeis, J L, Meyer, C A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization. Kluwer Academic Publishers, 1999. Jonathan F. Bard, James E. Falk: An explicit solution to the multi-level programming problem. Computers & OR 9(1): 77-100 (1982) Contributor: Alex Meeraus and Jan-H. Jagla, December 2009
Small Model of Type : BP
Category : GAMS EMP library
Main file : flds918.gms
$title Princeton Bilevel Optimization Example 9.1.8 (FLDS918,SEQ=34)
$onText
Test problem 9.2.9 in Handbook of Test Problems in Local and Global Optimization
Test problem 9.1.8 on http://titan.princeton.edu/TestProblems/chapter9.html
References:
Floudas, C A, Pardalos, P M, Adjiman, C S, Esposito, W R, Gumus, Z H, Harding,
S T, Klepeis, J L, Meyer, C A, and Schweiger, C A, Handbook of Test Problems in
Local and Global Optimization. Kluwer Academic Publishers, 1999.
Jonathan F. Bard, James E. Falk: An explicit solution to the multi-level
programming problem. Computers & OR 9(1): 77-100 (1982)
Contributor: Alex Meeraus and Jan-H. Jagla, December 2009
$offText
*Solution of problem 9.1.8 on the web
scalar x1_l / 2 /
x2_l / 0 /
y1_l / 1.5 /
y2_l / 0 /
tol / 1e-6 /;
Variables z, z_in; Positive Variables x1, x2, y1, y2;
equations ob, c0, ob_in, c1, c2, c3, c4;
ob.. - 2*x1 + x2 + 0.5*y1 =e= z;
c0.. x1 + x2 =l= 2;
ob_in.. - 4*y1 + y2 =e= z_in;
c1.. - 2*x1 + y1 - y2 =l= -2.5;
c2.. x1 - 3*x2 + y2 =l= 2;
c3.. - y1 =l= 0;
c4.. - y2 =l= 0;
Model bilevel / all /;
$echo bilevel x1 x2 min z_in y1 y2 ob_in c1 c2 c3 c4 > "%emp.info%"
*Start from reported solution
x1.l = x1_l;
x2.l = x2_l;
y1.l = y1_l;
y2.l = y2_l;
solve bilevel using emp minimizing z;
abort$( (abs(x1.l - x1_l) > tol)
or (abs(x2.l - x2_l) > tol)
or (abs(y1.l - y1_l) > tol)
or (abs(y2.l - y2_l) > tol) ) 'Deviated from reported solution';