Although some traditional MOEAs and MOSIOAs can effectively solve two- and three-objective problems, they show poor performance in solutions diversity and convergence when solving many-objective optimization problems (MaOPs). A number of multi-objective evolutionary algorithms (MOEAs) and swarm intelligence optimization algorithms (MOSIOAs) have been proposed to solve MOOPs for they can obtain a well-distributed and well-converged set of near Pareto-optimal solutions. There are many practical multi-objective optimization problems (MOOPs) in engineering and scientific research. The results show that by taking the advantages of the CMPMO/des framework, CMPMO-HHO achieves promising performance in solving multi/many-objective optimization problems. We comprehensively evaluated the performance of CMPMO-HHO on 34 multi-objective and 19 many-objective benchmark problems and extensively compared it with 13 state-of-the-art multi/many-objective optimization algorithms, three variants of CMPMO-HHO, and a CMPMO/des based many-objective genetic algorithm named CMPMO-GA. Notably, however, the proposed CMPMO/des framework can work with any other single objective optimizer without modification. Thereafter, in each subpopulation, HHO is used as the single objective optimizer for its impressive high performance.
With four excellent strategies, namely the one-to-one correspondence framework between the optimization objectives and the subpopulations, the global archive for information exchange and cooperation among subpopulations, the logistic chaotic single-dimensional perturbation strategy, and the dual elite selection mechanism based on the fast non-dominated sorting and the reference point-based approach, CMPMO/des achieves considerably high performance on solutions convergence and diversity. Specifically, this paper firstly proposes a novel cooperative multi-populations framework with dual elite selection named CMPMO/des. This paper presents an efficient cooperative multi-populations swarm intelligence algorithm based on the Harris Hawks optimization (HHO) algorithm, named CMPMO-HHO, to solve multi-/many-objective optimization problems.
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