An Energy-Based Sampling Technique for Multi-Objective Restricted Boltzmann Machine

Estimation of distribution algorithms are gaining increased research interest due to their advantage in exploiting linkage information. This paper examines the sampling techniques of a restricted Boltzmann machine-based multi-objective (MO) estimation of distribution algorithm (REDA). The behaviors of the sampling techniques in terms of energy levels are rigorously investigated, and a sampling mechanism that exploits the energy information of the solutions in a trained network is proposed to improve the search capability of the algorithm. The REDA is then hybridized, with a genetic algorithm and a local search based on an evolutionary gradient approach, to enhance the exploration and exploitation capabilities of the algorithm. Thirty-one benchmark test problems, which consist of different difficulties and characteristics, are used to examine the efficiency of the proposed algorithm. Empirical studies show that the proposed algorithm gives promising results in terms of inverted generational distance and nondominance ratio in most of the test problems.