HMOBEDA: Hybrid Multi-objective Bayesian Estimation of Distribution Algorithm

Marcella S. R. Martins, Myriam Regattieri de Biase da Silva Delgado, Roberto Santana, Ricardo Lüders, Richard Aderbal Gonçalves, Carolina Paula de Almeida

Abstract: Probabilistic modeling of selected solutions and incorporation of local search methods are approaches that can notably improve the results of multi-objective evolutionary algorithms (MOEAs). In the past, these approaches have been jointly applied to multi-objective problems (MOPs) with excellent results. In this paper, we introduce for the first time a joint probabilistic modeling of (1) local search methods with (2) decision variables and (3) the objectives in a framework named HMOBEDA. The proposed approach is compared with six evolutionary methods (including a modified version of NSGA-III, adapted to solve combinatorial optimization) on instances of the multi-objective knapsack problem with 3, 4, and 5 objectives. Results show that HMOBEDA is a competitive approach. It outperforms the other methods according to the hypervolume indicator.