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Evolutionary algorithms based on modeling the statistical dependencies(interactions) between the variables have been proposed to solve a wide rangeof complex problems. These algorithms learn and sample probabilistic graphicalmodels able to encode and exploit the regularities of the problem. This paperinvestigates the effect of using probabilistic modeling techniques as a way toenhance the behavior of MOEA/D framework. MOEA/D is a decomposition basedevolutionary algorithm that decomposes a multi-objective optimization problem(MOP) in a number of scalar single-objective subproblems and optimizes them ina collaborative manner. MOEA/D framework has been widely used to solve severalMOPs. The proposed algorithm, MOEA/D using probabilistic Graphical Models(MOEA/D-GM) is able to instantiate both univariate and multi-variateprobabilistic models for each subproblem. To validate the introduced frameworkalgorithm, an experimental study is conducted on a multi-objective version ofthe deceptive function Trap5. The results show that the variant of theframework (MOEA/D-Tree), where tree models are learned from the matrices of themutual information between the variables, is able to capture the structure ofthe problem. MOEA/D-Tree is able to achieve significantly better results thanboth MOEA/D using genetic operators and MOEA/D using univariate probabilitymodels, in terms of the approximation to the true Pareto front.

MOEA/D-GM: Using probabilistic graphical models in MOEA/D for solving combinatorial optimization problems