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Construction of global optimization constrainedNLP test cases from unconstrained problems

Martin S.C. Chan
Ehecatl Antonio del Rio-Chanona
Fabio Fiorelli
Harvey Arellano-Garcia
V.S. Vassiliadis
Organization: University of Cambridge
Department: Department of Chemical Engineering and Biotechnology
Journal / Anthology

Chemical Engineering Research and Design
Year: 2016
Volume: 109
Page range: 753-769

This paper presents a novel construction technique for constrained nonconvex Nonlin-ear Programming Problem (NLP) test cases, derived from the evaluation tree structure ofstandardized bound constrained problems for which the global solution is known. It isdemonstrated in a step-by-step procedure how first an equality constrained problem canbe derived from an unconstrained one, with bounds imposed on all variables, using theDirected Acyclic Graph (DAG) of the unconstrained objective function and the use of intervalarithmetic to derive bounds for the new variables introduced. An advantage of the proposedmethodology is that several standard unconstrained global optimization test cases can beconstructed for varying number of optimization variables, thus leading to adjustable sizederived NLP’s. Further to this in a second step it is demonstrated how any subset of theequalities derived can be relaxed into inequalities giving an equivalent optimization prob-lem. Finally, in a third step it is demonstrated how, by reducing the number of equalityconstraints derived, it is possible to obtain more complex expressions in the constraints andobjective function. The methodology is highlighted throughout by motivating examples anda sample code in MathematicaTMis provided in the Appendix.

*Engineering > Chemical Engineering