Many-objective evolutionary optimization based on reference points

Graphical abstractThis figure illustrates the flowchart of the proposed reference points-based evolutionary algorithm (RPEA). Its basic procedure is similar to most generational multi-objective evolutionary algorithms. First, an initial population is formed by randomly generating individuals. Then, genetic operators are performed to obtain an offspring population. Next, a set of reference points is generated based on the combined population. Finally, superior solutions are selected according to the reference points to update the parent population. It can be seen that there are two key operators in RPEA: generation of reference points and selection of individuals. In this study, reference points with good performances in convergence and distribution are generated by making full use of information provided by the current population. In addition, superior individuals are selected based on the evaluation of each individual by calculating the distances between the reference points and the individual in the objective space. Display Omitted HighlightsA reference points-based EA for many-objective optimization is proposed.An approach for adaptively generating reference points is proposed.A method of selecting superior individuals based on reference points is proposed.The proposed algorithm performs well on problems with irregular Pareto fronts. Many-objective optimization problems are common in real-world applications, few evolutionary optimization methods, however, are suitable for solving them up to date due to their difficulties. A reference points-based evolutionary algorithm (RPEA) was proposed in this paper to solve many-objective optimization problems. The aim of this study is to exploit the potential of the reference points-based approach to strengthen the selection pressure towards the Pareto front while maintaining an extensive and uniform distribution among solutions. In RPEA, a series of reference points with good performances in convergence and distribution are continuously generated according to the current population to guide the evolution. Furthermore, superior individuals are selected based on the evaluation of each individual by calculating the distances between the reference points and the individual in the objective space. The proposed algorithm was applied to seven benchmark optimization problems and compared with ź-MOEA, HypE, MOEA/D and NSGA-III. The results empirically show that the proposed algorithm has a good adaptability to problems with irregular or degenerate Pareto fronts, whereas the other reference points-based algorithms do not. Moreover, it outperforms the other four in 8 out of 21 test instances, demonstrating that it has an advantage in obtaining a Pareto optimal set with good performances.

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