Generating equidistant representations in biobjective programming

Authors:
Stacey L. Faulkenberg;Margaret M. Wiecek
Affiliations:
Department of Mathematical Sciences, Clemson University, Clemson, USA;Department of Mathematical Sciences, Clemson University, Clemson, USA
Venue:
Computational Optimization and Applications
Year:
2012

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Abstract

In recent years, emphasis has been placed on generating quality representations of the nondominated set of multiobjective optimization problems. This paper presents two methods for generating discrete representations with equidistant points for biobjective problems with solution sets determined by convex, polyhedral cones. The Constraint Controlled-Spacing method is based on the epsilon-constraint method with an additional constraint to control the spacing of generated points. The Bilevel Controlled-Spacing method has a bilevel structure with the lower-level generating the nondominated points and the upper-level controlling the spacing, and is extended to multiobjective problems. Both methods are proven to produce (weakly) nondominated points and are demonstrated on a variety of test problems.