Adapting Decomposed Directions for Evolutionary Multiobjective Optimization.

Decomposition methods have been widely employed in evolutionary algorithms for tackling multiobjective optimization problems (MOPs) due to their good mathematical explanation and promising performance. However, most decomposition methods only use a single ideal or nadir point to guide the evolution, which are not so effective for solving MOPs with extremely convex/concave Pareto fronts (PFs). To solve this problem, this article proposes an effective method to adapt decomposed directions (ADDs) for solving MOPs. Instead of using one single ideal or nadir point, each weight vector has one exclusive ideal point in our method for decomposition, in which the decomposed directions are adapted during the search process. In this way, the adapted decomposed directions can evenly and entirely cover the PF of the target MOP. The effectiveness of our method is analyzed theoretically and verified experimentally when embedding it into three representative multiobjective evolutionary algorithms (MOEAs), which can significantly improve their performance. When compared to seven competitive MOEAs, the experiments also validate the advantages of our method for solving 39 artificial MOPs with various PFs and one real-world MOP.