An Outer Approximation Algorithm for Generating AllEfficient Extreme Points in the Outcome Set of a Multiple ObjectiveLinear Programming Problem

  • Authors:

  • Harold P. Benson

  • Affiliations:

  • College of Business Administration, Department of Decision and Imformation Sciences, University of Florida, P.O. Box 117169, Gainesville, FL 32611–7169, USA E-mail: cyeonwc@nervm.nerdc.ufl.e ...

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 1998

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Abstract

Various difficulties have been encountered in usingdecision set-based vector maximization methods to solve a multipleobjective linear programming problem (MOLP). Motivated by thesedifficulties, some researchers in recent years have suggested thatoutcome set-based approaches should instead be developed and used tosolve problem (MOLP). In this article, we present a finite algorithm,called the Outer Approximation Algorithm, for generating the set of allefficient extreme points in the outcome set of problem (MOLP). To ourknowledge, the Outer Approximation Algorithm is the first algorithmcapable of generating this set. As a by-product, the algorithm alsogenerates the weakly efficient outcome set of problem (MOLP). Because itworks in the outcome setrather than in the decision set of problem (MOLP), the OuterApproximation Algorithm has several advantages over decision set-basedalgorithms. It is also relatively easy to implement. Preliminarycomputational results for a set of randomly-generated problems arereported. These results tangibly demonstrate the usefulness of usingthe outcome set approach of the Outer Approximation Algorithm insteadof a decision set-based approach.