A hybrid multi-objective bayesian estimation of distribution algorithm

Abstract

Nowadays, a number of metaheuristics have been developed for dealing with multiobjective optimization problems. Estimation of distribution algorithms (EDAs) are a special class of metaheuristics that explore the decision variable space to construct probabilistic models from promising solutions. The probabilistic model used in EDA captures statistics of decision variables and their interdependencies with the optimization problem. Moreover, the aggregation of local search methods can notably improve the results of multi-objective evolutionary algorithms. Therefore, these hybrid approaches have been jointly applied to multi-objective problems. In this work, a Hybrid Multi-objective Bayesian Estimation of Distribution Algorithm (HMOBEDA), which is based on a Bayesian network, is proposed to multi and many objective scenarios by modeling the joint probability of decision variables, objectives, and configuration parameters of an embedded local search (LS). We tested different versions of HMOBEDA using instances of the multi-objective knapsack problem for two to five and eight objectives. HMOBEDA is also compared with five cutting edge evolutionary algorithms (including a modified version of NSGA-III, for combinatorial optimization) applied to the same knapsack instances, as well to a set of MNK-landscape instances for two, three, five and eight objectives. An analysis of the resulting Bayesian network structures and parameters has also been carried to evaluate the approximated Pareto front from a probabilistic point of view, and also to evaluate how the interactions among variables, objectives and local search parameters are captured by the Bayesian networks. Results show that HMOBEDA outperforms the other approaches. It not only provides the best values for hypervolume, capacity and inverted generational distance indicators in most of the experiments, but it also presents a high diversity solution set close to the estimated Pareto front.