We propose an evolutionary metaheuristic for multiobjective combinatorial optimization problems that interacts with the decision maker (DM) to guide the search effort toward his or her preferred solutions. Solutions are presented to the DM, whose pairwise comparisons are then used to estimate the desirability or fitness of newly generated solutions. The evolutionary algorithm comprising the skeleton of the metaheuristic makes use of selection strategies specifically designed to address the multiobjective nature of the problem. Interactions with the DM are triggered by a probabilistic evaluation of estimated fitnesses, while memory structures with indifference thresholds restrict the presentation of solutions resembling those that have already been rejected. The algorithm has been tested on a number of random instances of the Multiobjective Knapsack Problem (MOKP) and the Multiobjective Spanning Tree Problem (MOST). Simulation results indicate that the algorithm requires only a small number of comparisons to be made for satisfactory solutions to be found.Evolutionary Algorithm, Multiobjective Combinatorial Optimization, Metaheuristic

W e 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.