Approximating combinatorial optimization problems with the ordered weighted averaging criterion

André Chassein, Marc Goerigk, Adam Kasperski and Paweł Zieliński

European Journal of Operational Research, 2020, vol. 286, issue 3, 828-838

Abstract: This paper deals with combinatorial optimization problems with K cost scenarios, inducing K linear objectives. The popular Ordered Weighted Averaging (OWA) criterion is used to aggregate the objectives and compute a solution. It is well-known that minimizing OWA for most basic combinatorial problems is weakly NP-hard even if the number of scenarios K equals two, and strongly NP-hard when K is a part of the input. In this paper, the problem with nonincreasing weights in the OWA criterion and a large K is first considered. A method of reducing the number of scenarios, by appropriately aggregating the costs before solving the problem, is proposed. It is shown that an optimal solution to the reduced problem has a guaranteed worst-case approximation ratio. Some new approximation results for the Hurwicz criterion, which is a special case of OWA, are also presented.

Keywords: Robustness and sensitivity analysis; Ordered weighted averaging; Combinatorial optimization; Approximation algorithms (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:286:y:2020:i:3:p:828-838

DOI: 10.1016/j.ejor.2020.04.018

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