Probabilistic Analysis of Pareto Front Approximation for a Hybrid Multi-objective Bayesian Estimation of Distribution Algorithm

Metaheuristics that explore the decision variables space to construct probabilistic modeling from promising solutions, like estimation of distribution algorithms (EDAs), are becoming very popular in the context of Multi-objective Evolutionary Algorithms (MOEAs). The probabilistic model used in EDAs captures certain statistics of problem variables and their interdependencies. Moreover, the incorporation of local search methods tends to achieve synergy of MOEAs' operators and local heuristics aiming to improve the performance. In this work, we aim to scrutinize the probabilistic graphic model (PGM) presented in Hybrid Multi-objective Bayesian Estimation of Distribution Algorithm (HMOBEDA), which is based on a Bayesian network. Different from traditional EDA-based approaches, the PGM of HMOBEDA provides the joint probability of decision variables, objectives, and configuration parameters of an embedded local search. HMOBEDA has shown to be very competitive on instances of Multi-Objective Knapsack Problem (MOKP), outperforming state-of-the-art approaches. Two variants of HMOBEDA are proposed in this paper using different sample methods. We aim to compare the learnt structure in terms of the probabilistic Pareto Front approximation produced at the end of evolution. Results on instances of MOKP with 2 to 8 objectives show that both proposed variants outperformthe original approach, providing not only the best values for hypervolume and inverted generational distance indicators, butalso a higher diversity in the solution set.