Abstract
Balancing convergence and diversity has become a key point especially in many-objective optimization where the large numbers of objectives pose many challenges to the evolutionary algorithms. In this paper, an opposition-based evolutionary algorithm with the adaptive clustering mechanism is proposed for solving the complex optimization problem. In particular, opposition-based learning is integrated in the proposed algorithm to initialize the solution, and the nondominated sorting scheme with a new adaptive clustering mechanism is adopted in the environmental selection phase to ensure both convergence and diversity. The proposed method is compared with other nine evolutionary algorithms on a number of test problems with up to fifteen objectives, which verify the best performance of the proposed algorithm. Also, the algorithm is applied to a variety of multiobjective engineering optimization problems. The experimental results have shown the competitiveness and effectiveness of our proposed algorithm in solving challenging real-world problems.
Highlights
Over the last two decades, evolutionary algorithm (EA) has been proven to be prevalent and efficient to solve real-world optimization problem [1]
Most algorithms belong to these categories use the angle or distance solely to measure the quality of the population members with the reference set, which may lose some good solutions due to their simplex selection mechanism. It has been logically proved by the No Free-Lunch (NFL) theorem [56] that none of these algorithms is able to solve all optimization problems, which allows the researchers to propose new methods or improve the current algorithms for better solving the problems [33, 57]. erefore, this paper proposes an opposition-based multiobjective evolutionary algorithm with an adaptive clustering mechanism, in short named OBEA to strengthen the selection mechanism through comprehensive consideration of the angle and the distances. e main properties of OBEA can be summarized as follows: (i) A new initialization approach is designed with the assistance of the opposition-based learning (OBL) to generate the population
Statistical results of the Inverted Generational Distance (IGD) values obtained by OBEA and four algorithms named multiobjective evolutionary algorithm (MOEA)/D, dMOPSO, MOMBI2, and Îľ-MOEA are summarized in Tables 4 and 5, where the best results are italicized. e significance of difference between OBEA and the peer algorithms is determined by using the Wilcoxon rank sum test, where â+,â ââ,â and â â indicate the competitor is better than, worse than, or similar to the proposed OBEA, respectively, and the results are summarized as âw/l,â which denotes that corresponding competitor wins on w functions, loses on l functions, and ties on t functions, compared with the proposed OBEA
Summary
Over the last two decades, evolutionary algorithm (EA) has been proven to be prevalent and efficient to solve real-world optimization problem [1]. Most algorithms belong to these categories use the angle or distance solely to measure the quality of the population members with the reference set, which may lose some good solutions due to their simplex selection mechanism. It has been logically proved by the No Free-Lunch (NFL) theorem [56] that none of these algorithms is able to solve all optimization problems, which allows the researchers to propose new methods or improve the current algorithms for better solving the problems [33, 57].
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