An Improved Hypervolume-Based Evolutionary Algorithm for Many-Objective Optimization

The hypervolume indicator is commonly utilized in indicator-based evolutionary algorithms due to its strict adherence to the Pareto domination relationship. However, its high computational complexity in high-dimensional objective spaces limits its widespread adoption and application. In this paper, we propose a fast and efficient method for approximating the overall hypervolume to overcome this challenge. We then integrate this method into the basic evolutionary computation framework, forming an algorithm for solving many-objective optimization problems. To evaluate its performance, we compared our proposed algorithm with six state-of-the-art algorithms on WFG and DTLZ test problems with 3, 5, 10, and 15 objectives. The results demonstrate that our proposed method is highly competitive in most cases.