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Finding efficient solutions in robust multiple objective optimization with SOS-convex polynomial data

  • S.I.: MOPGP 2017
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Abstract

In this article, a mathematical programming problem under affinely parameterized uncertain data with multiple objective functions given by SOS-convex polynomials, denoting by (UMP), is considered; moreover, its robust counterpart, denoting by (RMP), is proposed by following the robust optimization approach (worst-case approach). Then, by employing the well-known \(\epsilon \)-constraint method (a scalarization technique), we substitute (RMP) by a class of scalar problems. Under some suitable conditions, a zero duality gap result, between each scalar problem and its relaxation problems, is established; moreover, the relationship of their solutions is also discussed. As a consequence, we observe that finding robust efficient solutions to (UMP) is tractable by such a scalarization method. Finally, a nontrivial numerical example is designed to show how to find robust efficient solutions to (UMP) by applying our results.

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Acknowledgements

The authors would like to express their sincere thanks to anonymous referees for their very helpful and valuable suggestions and comments for the paper.

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Authors and Affiliations

  1. Finance Fishery Manufacture Industrial Mathematics Center on Big Data, Pusan National University, Busan, 46241, Republic of Korea

    Liguo Jiao

  2. Department of Applied Mathematics, Pukyong National University, Busan, 48513, Republic of Korea

    Jae Hyoung Lee

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  1. Liguo Jiao
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  2. Jae Hyoung Lee
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Correspondence to Jae Hyoung Lee.

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The first author was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (NRF-2017R1A5A1015722). The second author was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (NRF-2018R1C1B6001842).

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Jiao, L., Lee, J.H. Finding efficient solutions in robust multiple objective optimization with SOS-convex polynomial data. Ann Oper Res 296, 803–820 (2021). https://doi.org/10.1007/s10479-019-03216-z

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