Hyperplane-driven and projection-assisted search for solving many-objective optimization problems

Counterpoising convergence and distribution becomes more intractable in many-objective optimization where the number of objectives exceeds three, evolutionary algorithms (EAs) via decomposition are prominent in convergence promotion yet suffer from diversity loss. The setting of direction vectors (DVs), scalarizing function (SF) and selection strategy can significantly affect the performance of this sort of algorithms. To remedy the issue, we develop a hyperplane driven and projection assisted EA, referred here as HPEA, using three-stage search. At the very beginning, search is performed only along the extreme objective-wise points to capture the corners of Pareto front (PF). After that, the convergence and diversity are coordinated, a set of DVs, adapted by the evolving population itself, is utilized to extend the search wideness, and two novel SFs are exploited to collect elites in each subregion for approaching a more complete PF. At last, diversity is emphasized, a projection distance aided elimination mechanism is employed to prune poorly diversified solutions one by one. Note that hyperplane utilized at second stage aims at identifying well-converged solutions, the rationale behind using two novel SFs is to take complementary effects of different criteria. The resultant HPEA is compared with several state-of-theart multiobjective EAs on handling various types of many-objective problems. Extensive empirical studies demonstrate the effectiveness and competitiveness of the proposal in obtaining high quality solution set. (c) 2021 Elsevier Inc. All rights reserved.