Generating equidistant representations in biobjective programming

Generating equidistant representations in biobjective programming

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Article ID: iaor20122510
Volume: 51
Issue: 3
Start Page Number: 1173
End Page Number: 1210
Publication Date: Apr 2012
Journal: Computational Optimization and Applications
Authors: ,
Keywords: programming: multiple criteria, programming: convex
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.

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