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This page contains Sven's small collection or multiobjective testproblems. All models are written in AMPL.

Multiobjective Testproblems

The following table gives the name of the testproblem, the AMPL model and data file (if applicable), and the problem characteristics (where n-m-q are the number of variables, constraints and objectives respectively).

Testproblem AMPL Model File AMPL Data File Characteristitcs (n-m-q)
ABC-comp ABC-comp.mod 2-3-2
ex001 ex001.mod 5-3-2
ex002 ex002.mod 5-2-2
ex003 ex003.mod 5-2-2
ex004 ex004.mod 2-3-2
ex005 ex005.mod 2-0-2
hs05x hs05x.mod 5-3-3
liswetm liswetm.mod 7-5-2
MOLPg-1 MOLPg.mod MOLPg-001.dat 8-8-3
MOLPg-2 MOLPg.mod MOLPg-002.dat 12-16-3
MOLPg-3 MOLPg.mod MOLPg-003.dat 10-14-3
MOQP-1 MOQP.mod moqp-001.dat 20-10-3
MOQP-2 MOQP.mod moqp-002.dat 20-10-3
MOQP-3 MOQP.mod moqp-003.dat 20-10-3

Formulations with Complementarity Constraints

The following table gives the AMPL models for the formulation of the MOOPs as mathematical programs with complementarity constraints (MPCCs). The MPCC models are derived in this technical report.

Testproblem Convex Combination Convex Combination (2) GOAL Programming AMPL Data File
ABC-comp ABC-comp-SUMe.mod ABC-comp-SUM1e.mod ABC-comp-GOALe.mod
ex001 ex001-SUMe.mod ex001-SUM1e.mod ex001-GOAL.mod
ex002 ex002-SUMe.mod ex002-SUM1e.mod ex002-GOAL.mod
ex003 ex003-SUMe.mod ex003-SUM1e.mod ex003-GOAL.mod
ex004 ex004-SUMe.mod ex004-SUM1e.mod ex004-GOAL.mod
ex005 ex005-SUMe.mod ex005-SUM1e.mod ex005-GOAL.mod
hs05x hs05x-SUMe.mod hs05x-SUM1e.mod hs05x-GAL.mod
liswetm liswetm-SUMe.mod liswetm-SUM1e.mod liswetm-GOALe.mod
MOLPg-1 MOLPg-SUMe.mod MOLPg-SUM1e.mod MOLPg-GOALe.mod MOLPg-001.dat
MOLPg-2 MOLPg-SUMe.mod MOLPg-SUM1e.mod MOLPg-GOALe.mod MOLPg-002.dat
MOLPg-3 MOLPg-SUMe.mod MOLPg-SUM1e.mod MOLPg-GOALe.mod MOLPg-003.dat
MOQP-1 MOQP-SUMe.mod MOQP-SUM1e.mod MOQP-GOALe.mod moqp-001.dat
MOQP-2 MOQP-SUMe.mod MOQP-SUM1e.mod MOQP-GOALe.mod moqp-002.dat
MOQP-3 MOQP-SUMe.mod MOQP-SUM1e.mod MOQP-GOALe.mod moqp-003.dat

Random MOOP Generator in MATLAB

We also provide a random MOOP generator written in matlab.