Solving Many-Objective Optimization Problems by a Pareto-Based Evolutionary Algorithm With Preprocessing and a Penalty Mechanism

It is known that the Pareto-based approach is not well suited for optimization problems with a large number of objectives, even though it is a class of mainstream methods in multiobjective optimization. Typically, a Pareto-based algorithm comprises two parts: 1) a Pareto dominance-based criterion and 2) a diversity estimator. The former guides the selection toward the optimal front, while the latter promotes the diversity of the population. However, the Pareto dominance-based criterion becomes ineffective in solving optimization problems with many objectives (e.g., more than 3) and, thus, the diversity estimator will determine the performance of the algorithm. Unfortunately, the diversity estimator usually has a strong bias toward dominance resistance solutions (DRSs), thereby failing to push the population forward. DRSs are solutions that are far away from the Pareto-optimal front but cannot be easily dominated. In this article, we propose a new Pareto-based algorithm to resolve the above issue. First, to eliminate the DRSs, we design an interquartile range method to preprocess the solution set. Second, to balance convergence and diversity, we present a penalty mechanism of alternating operations between selection and penalty. The proposed algorithm is compared with five state-of-the-art algorithms on a number of well-known benchmarks with 3-15 objectives. The experimental results show that the proposed algorithm can perform well on most of the test functions and generally outperforms its competitors.

Automated summary

The Pareto-based approach is not well suited for optimization problems with a large number of objectives, prompting the proposal of a new algorithm in this article to address this issue. The algorithm tackles the problem by eliminating DRSs using an interquartile range method and balancing convergence and diversity through a penalty mechanism of alternating operations. Experimental results show that the proposed algorithm generally outperforms its competitors on a variety of test functions with 3-15 objectives.