Objective Extraction for Simplifying Many-Objective Solution Sets

Multi-objective evolutionary algorithms (MOEAs) can find a set of Pareto solutions to the multi-objective optimization problem. However, it is still a challenge for the decision-maker to understand the relationship between various Pareto solutions and pick up the really preferred solution. This article proposes an objective extraction method to simplify the many-objective solution set by reducing the objective dimensionality but keeping the dominance and distribution relationships between solutions. First, a sparse regularized self-representation (SRSR) model is developed to learn the linear relationship among objectives, in which all objectives are determined by a set of base ones. Second, an alternating direction method of multipliers (ADMM) is constructed to solve such a model. Finally, an objective extraction method (SRSR-OE) that can preserve the dominance and distribution relationships between solutions is invented by exploiting the learned relationship. Experimental results show that our SRSR model and ADMM algorithm are efficient for extracting the linear objective relationship, and the developed objective extraction method also has advantages over some state-of-the-art ones in preserving dominance and distribution relationships between solutions after solution set simplification.