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An Evolutionary Metaheuristic for Approximating Preference-Nondominated Solutions

Department of Industrial Engineering, Middle East Technical University, 06531 Ankara, Turkey
Department of Accounting, Business, Economics, and Management Information Systems, Westminster College, Fulton, Missouri 65251, USA
koksalan{at}ie.metu.edu.tr
phelpss{at}westminster-mo.edu

We propose an evolutionary metaheuristic for approximating the preference-nondominated solutions of a decision maker in multiobjective combinatorial problems. The method starts out with some partial preference information provided by the decision maker, and utilizes an individualized fitness function to converge toward a representative set of solutions favored by the information at hand. The breadth of the set depends on the precision of the partial information available on the decision maker’s preferences. The algorithm simultaneously evolves the population of solutions out toward the efficient frontier, focuses the population on those segments of the efficient frontier that will appeal to the decision maker, and disperses it over these segments to have an adequate representation. Simulation runs carried out on randomly generated instances of the multiobjective knapsack problem and the multiobjective spanning-tree problem have found the algorithm to yield highly satisfactory results.

Key words: multiple criteria; combinatorial optimization; evolutionary heuristic
History: received September 2001; revised September 2005; accepted November 2005.

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