An Interactive Evolutionary Metaheuristic for Multiobjective Combinatorial Optimization

Abstract

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.