Epsilon Dominance and Constraint Partitioningin Multiple Objective Problems

Authors:
D. J. White
Affiliations:
Department of Decision Theory, University of Manchester, Manchester, UK
Venue:
Journal of Global Optimization
Year:
1998

Citing 3
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Abstract

In this paper we consider efficient sets of multiple objective problems,in which the feasible action set is the intersection of two other sets, andwhere one of these sets has a special structure, such as an assignment ortransportation structure. The objective is to find the efficient set of thespecial structure set, and its intersection with the other set, and toexamine how good an approximation this set is to the desired efficient set.The approximation set is called an ϵ-efficient solutionset. Some theoretical partition results are given for a special constraintstructure with upper bounds on the objective function levels. For the caseof 0-efficient solution sets, and finite explicit sets, a computational costanalysis of two computational sequences is given. We also consider two other0-efficient solution set cases. Then ϵ-efficiency isconsidered for linear problems. Finally, the approach is illustrated by aspecial multiple objective transportation problem.