Probabilistic Graphical Approaches for Learning, Modeling, and Sampling in Evolutionary Multi-objective Optimization

Multi-objective optimization is widely found in many fields, such as logistics, economics, engineering, or whenever optimal decisions need to be made in the presence of tradeoff between two or more conflicting objectives. The synergy of probabilistic graphical approaches in evolutionary mechanism may enhance the iterative search process when interrelationships of the archived data has been learned, modeled, and used in the reproduction. This paper presents the implementation of probabilistic graphical approaches in solving multi-objective optimization problems under the evolutionary paradigm. First, the existing work on the synergy between probabilistic graphical models and evolutionary algorithms in the multi-objective framework will be presented. We will then show that the optimization problems can be solved using a restricted Boltzmann machine (RBM). The learning, modeling as well as sampling mechanisms of the RBM will be highlighted. Lastly, five studies that implement the RBM for solving multi-objective optimization problems will be discussed.