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It has generally been acknowledged that both proximity to the Pareto front and a certain diversity along the front, should be targeted when using evolutionary multiobjective optimization. Recently, a new partitioning mechanism, the Part and Select Algorithm (PSA), has been introduced. It was shown that this partitioning allows for the selection of a well-diversified set out of an arbitrary given set, while maintaining low computational cost. When embedded into an evolutionary search (NSGA-II), the PSA has significantly enhanced the exploitation of diversity. In this paper, the ability of the PSA to enhance evolutionary multiobjective algorithms (EMOAs) is further investigated. Two research directions are explored here. The first one deals with the integration of the PSA within an EMOA with a novel strategy. Contrary to most EMOAs, that give a higher priority to proximity over diversity, this new strategy promotes the balance between the two. The suggested algorithm allows some dominated solutions to survive, if they contribute to diversity. It is shown that such an approach substantially reduces the risk of the algorithm to fail in finding the Pareto front. The second research direction explores the use of the PSA as an archiving selection mechanism, to improve the averaged Hausdorff distance obtained by existing EMOAs. It is shown that the integration of the PSA into NSGA-II-I and ∆ p -EMOA as an archiving mechanism leads to algorithms that are superior to base EMOAS on problems with disconnected Pareto fronts.

In this article, a novel solution to multi-objective problems involving the optimization of transient responses is suggested. It is claimed that the common approach of treating such problems by introducing auxiliary objectives overlooks tradeoffs that should be presented to the decision makers. This means that, if at some time during the responses, one of the responses is optimal, it should not be overlooked. An evolutionary multi-objective algorithm is suggested in order to search for these optimal solutions. For this purpose, state-wise domination is utilized with a new crowding measure for ordered sets being suggested. The approach is tested on both artificial as well as on real life problems in order to explain the methodology and demonstrate its applicability and importance. The results indicate that, from an engineering point of view, the approach possesses several advantages over existing approaches. Moreover, the applications highlight the importance of set-based evolution.

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