Decomposition-Based Multiobjective Evolutionary Algorithm With Genetically Hybrid Differential Evolution Strategy

Abstract

In the decomposition-based multiobjective evolutionary algorithms (MOEA/Ds), a set of subproblems are optimized by using the evolutionary search to exploit the feasible regions. In recent studies of MOEA/Ds, it was found that the design of recombination operators would significantly affect their performances. Therefore, this paper proposes a novel genetically hybrid differential evolution strategy (GHDE) for recombination in MOEA/Ds, which works effectively to strengthen the search capability. Inspired by the existing studies of recombination operators in MOEA/Ds, two composite operator pools are introduced, each of which includes two distinct differential evolution (DE) mutation strategies, one emphasizing convergence and the other focusing on diversity. Regarding each selected operator pool, two DEs are applied on parents' genes to hybridize offspring by adaptive parameters tuning. Moreover, a fitness-rate-rank-based multiarmed bandit (FRRMAB) is embedded into our algorithm to select the best operator pool by collecting their recently achieved fitness improvement rates. After embedding GHDE into an MOEA/D variant with dynamical resource allocation, a variant named MOEA/D-GHDE is presented. Various test multiobjective optimization problems (MOPs), i.e., UF, F test suites, and MOPs with difficult-to-approximate (DtA) PF boundaries, are used to assess performances. Compared to several competitive MOEA/D variants, the comprehensive experiments validate the superiority of our algorithm.

Decomposition Multi-Objective Evolutionary Optimization: From State-of-the-Art to Future Opportunities

“…MOEA/D-FRRMAB [117], MOEA/D-UCB-Tuned and MOEA/D-UCB-V [55] Adaptive operator selection NSGA-III AP and NSGA-III PM [58], SaMOEA/D [184], MOEA/D-DYTS [198] MPADE [25], MOEA/D-CDE [126], AMOEA/D [127] Parameter control MOEA/D-GHDE [140], EF-PD [218], MOEA/D-IMA [231] Ensemble of operators MAB-HH [45], MOEA/D-HH {SW} [56], MOEA/D-HH [57], MOEA/D-DRA-UCB [181] Hyper-heuristics BoostMOEA/D-DRA [182], MOEA/D-LinUCB [54], MAB-based HH [27] Mathematical programming MOEA/D-LS [147], MOEA/D-RBF [149], MONSS [150], NSS-MO [152] Direct search method MOEA/D-QS [180], MOEA/D-NMS [245] NSGA-III-KKTPM [2,3,191] KKTPM Memetic search MOMAD [96], PPLS/D [193] Pareto local search CoMOLS/D [15], MONSD [73], MOMNS/D and MOMNS/V [211], LS/D [258] Neighborhood search MOEA/D-TS [5], MOEA-MA [38], DMTS [259], MOEA/D-GLS [4] EMOSA [109,110], MOMA-SA [14], EOMO [90] Simulated annealing MOEA/D-GRASP [6], HEMH [94]…”

“…In addition to AOS, [142][143][144] also consider adaptively control the parameters associated with the reproduction operator in order to achieve the best algorithm setup. Rather than adaptively selecting the "appropriate" reproduction operator on the fly, another line of research (e.g., [145][146][147]) is to build an ensemble of reproduction operators and use them simultaneously.…”