One-exact approximate Pareto sets

Arne Herzel (), Cristina Bazgan (), Stefan Ruzika (), Clemens Thielen () and Daniel Vanderpooten ()
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Arne Herzel: University of Kaiserslautern
Cristina Bazgan: Université Paris-Dauphine
Stefan Ruzika: University of Kaiserslautern
Clemens Thielen: Technical University of Munich
Daniel Vanderpooten: Université Paris-Dauphine

Journal of Global Optimization, 2021, vol. 80, issue 1, No 5, 87-115

Abstract: Abstract Papadimitriou and Yannakakis (Proceedings of the 41st annual IEEE symposium on the Foundations of Computer Science (FOCS), pp 86–92, 2000) show that the polynomial-time solvability of a certain auxiliary problem determines the class of multiobjective optimization problems that admit a polynomial-time computable $$(1+\varepsilon , \dots , 1+\varepsilon )$$ ( 1 + ε , ⋯ , 1 + ε ) -approximate Pareto set (also called an $$\varepsilon $$ ε -Pareto set). Similarly, in this article, we characterize the class of multiobjective optimization problems having a polynomial-time computable approximate $$\varepsilon $$ ε -Pareto set that is exact in one objective by the efficient solvability of an appropriate auxiliary problem. This class includes important problems such as multiobjective shortest path and spanning tree, and the approximation guarantee we provide is, in general, best possible. Furthermore, for biobjective optimization problems from this class, we provide an algorithm that computes a one-exact $$\varepsilon $$ ε -Pareto set of cardinality at most twice the cardinality of a smallest such set and show that this factor of 2 is best possible. For three or more objective functions, however, we prove that no constant-factor approximation on the cardinality of the set can be obtained efficiently.

Keywords: Multiobjective optimization; Approximation algorithm; Approximate Pareto set; scalarization; 90C29; 90C59 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-020-00951-7

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