Journal
IEEE TRANSACTIONS ON CYBERNETICS
Volume 51, Issue 11, Pages 5585-5594Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2020.2988896
Keywords
Sociology; Statistics; Optimization; Convergence; Evolutionary computation; Maintenance engineering; Resistance; Dominance resistance solutions (DRSs); evolutionary algorithm; many-objective optimization
Categories
Funding
- National Natural Science Foundation of China [61572177]
- National Outstanding Youth Science Program of National Natural Science Foundation of China [61625202]
- International (Regional) Cooperation and Exchange Program of National Natural Science Foundation of China [61661146006]
- Postgraduate Scientific Research Innovation Project of Hunan [CX20190309]
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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.
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.
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