On upper approximations of Pareto fronts

I. Kaliszewski () and J. Miroforidis
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I. Kaliszewski: Polish Academy of Sciences
J. Miroforidis: Polish Academy of Sciences

Journal of Global Optimization, 2018, vol. 72, issue 3, No 5, 475-490

Abstract: Abstract In one of our earlier works, we proposed to approximate Pareto fronts to multiobjective optimization problems by two-sided approximations, one from inside and another from outside of the feasible objective set, called, respectively, lower shell and upper shell. We worked there under the assumption that for a given problem an upper shell exists. As it is not always the case, in this paper we give some sufficient conditions for the existence of upper shells. We also investigate how to constructively search infeasible sets to derive upper shells. We approach this issue by means of problem relaxations. We formally show that under certain conditions some subsets of lower shells to relaxed multiobjective optimization problems are upper shells in the respective unrelaxed problems. Results are illustrated by a numerical example representing a small but real mechanical problem. Practical implications of the results are discussed.

Keywords: Multiobjective optimization; Global Pareto optimum; Two-sided Pareto front approximations; Pareto front upper approximation existence; Evolutionary multiobjective optimization (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10898-018-0642-1

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