On the hierarchical structure of Pareto critical sets

Bennet Gebken (), Sebastian Peitz and Michael Dellnitz
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Bennet Gebken: Paderborn University
Sebastian Peitz: Paderborn University
Michael Dellnitz: Paderborn University

Journal of Global Optimization, 2019, vol. 73, issue 4, No 10, 913 pages

Abstract: Abstract In this article we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems where only a subset of the set of objective functions is taken into account. If the Pareto critical set is completely described by its boundary (e.g., if we have more objective functions than dimensions in decision space), then this can be used to efficiently solve the MOP by solving a number of MOPs with fewer objective functions. If this is not the case, the results can still give insight into the structure of the Pareto critical set.

Keywords: Multiobjective optimization; Many-objective optimization; Pareto set; Pareto critical set (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10898-019-00737-6

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