Reference line-based Estimation of Distribution Algorithm for many-objective optimization

Multi-Objective Evolutionary Algorithms (MOEAs) are preferred in solving multi-objective optimization problems due to their considerable performance giving decision-maker a set of not only convergent but diversified promising solutions. However, the scalability of MOEAs deteriorates in addressing many-objective optimization problems which involve more than three conflicting objectives. The principal reason is largely due to the deficiency of the existing genetic operators which cannot generate promising offspring from parents chosen by the Pareto-dominance rule in these MOEAs. Estimation of Distribution Algorithms (EDAs) generate offspring with a probabilistic model built from the statistics extracting upon existing solutions to expectedly alleviate the weakness arisen in genetic operators. In this paper, a reference line-based EDA is proposed for effectively solving many-objective optimization problems. Specifically, the estimation model is built based on the reference lines in the decision space to sample solutions with favorable proximity. Then solutions with considerable diversity in Pareto-optimal front are selected. These two phases collectively promote the needed convergence and diversity for the proposed algorithm. To evaluate the performance, extensive experiments are performed against four state-of-the-art many-objective evolutionary algorithms and two EDAs over DTLZ and WFG test suites with 5-, 8-, 10-, and 15-objective. Experimental results quantified by the selected performance metrics indicate that the proposed algorithm shows significant competitiveness in tackling many-objective optimization problems.