A method for generating a well-distributed Pareto set in nonlinear multiobjective optimization

Authors:
S. V. Utyuzhnikov;P. Fantini;M. D. Guenov
Affiliations:
Department Aerospace Engineering, School of Engineering Cranfield University, Cranfield, Bedfordshire, MK43 0AL, UK and School of Mechanical, Aerospace & Civil Engineering, University of Mancheste ...;Department Aerospace Engineering, School of Engineering Cranfield University, Cranfield, Bedfordshire, MK43 0AL, UK;Department Aerospace Engineering, School of Engineering Cranfield University, Cranfield, Bedfordshire, MK43 0AL, UK
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

A method is presented for generating a well-distributed Pareto set in nonlinear multiobjective optimization. The approach shares conceptual similarity with the Physical Programming-based method, the Normal-Boundary Intersection and the Normal Constraint methods, in its systematic approach investigating the objective space in order to obtain a well-distributed Pareto set. The proposed approach is based on the generalization of the class functions which allows the orientation of the search domain to be conducted in the objective space. It is shown that the proposed modification allows the method to generate an even representation of the entire Pareto surface. The generation is performed for both convex and nonconvex Pareto frontiers. A simple algorithm has been proposed to remove local Pareto solutions. The suggested approach has been verified by several test cases, including the generation of both convex and concave Pareto frontiers.