Enhancing the scalability of multi-objective optimization via restricted Boltzmann machine-based estimation of distribution algorithm

The exploitation of probability distribution of the solution set and linkage information among decision variables in guiding the search towards optimality is the main characteristic of estimation of distribution algorithms (EDAs). In this paper, the restricted Boltzmann machine (RBM) is modeled as a novel EDA in the context of multi-objective optimization. RBM is an energy-based stochastic neural network. The probabilities of the joint configuration over the visible and hidden units in the network are trained using contrastive divergence until the distribution over the global state reaches a certain level of thermal equilibrium. Subsequently, the probabilistic model is constructed using the energy function of the network. In addition, clustering in the phenotypic space is incorporated into the proposed algorithm. The effects on clustering and the stability of the trained network on optimization performance are rigorously examined. Experimental studies are conducted to analyze the performance of the proposed algorithm in scalable problems with large number of objective functions and decision variables.