A comparison of neighborhood search techniques for multi-objective combinatorial problems

In this paper the authors compare the performance of simulated annealing and tabu search when both are applied to a large, complex multi-objective flow-shop problem. Repeated descent, an older neighborhood search technique, is used as a basis for comparison. The best parameters needed for the methods and their subsequent performance are compared on two further levels: as the total number of perturbations allowed increases and as the number of objectives increases. It is shown that, as the number of objectives (and thus the complexity of the problem) increases, simulated annealing (which epitomizes randomized search methods) becomes more attractive than tabu search (which epitomizes deterministic search methods). In addition, the relative value of simulated annealing is greater when only a small number of perturbations are allowed. Reasons are offered for these phenomena. These experiments identify the need for appropriate measures of complexity of a combinatorial problem. Two such measures are described, and it is shown that these can lead us to revise our a priori notions about the complexity of multi-objective combinatorial problems. In particular, the complexity of a combinatorial problem may be strongly influenced by the type of objectives as well as their number.