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Launch Pad Method in Multiextremal Multiobjective Optimization Problems

Abstract

A new method is proposed for approximating the Edgeworth–Pareto hull of a feasible objective set in a multiobjective optimization (MOO) problem with criteria functions having numerous local extrema. The method is based on constructing a launch pad, i.e., a subset of the feasible decision set such that gradient procedures for local optimization of criteria and scalarizing functions of criteria starting at these points yield efficient decisions of the MOO problem. A launch pad is constructed using the optima injection method, which combines the usual multistart approach with a genetic algorithm for Pareto frontier approximation. It is shown that the proposed launch pad method (LPM) can also be used to approximate the effective hull of a nonconvex multidimensional set. A theoretical analysis of LPM is presented, and experimental results are given for the applied problem of constructing control rules for a cascade of reservoirs, which is reduced to a complicated MOO problem with scalarizing functions having numerous local extrema.

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ACKNOWLEDGMENTS

We are deeply grateful to G.K. Kamenev for his critical remarks and helpful advice.

Funding

This work was supported in part by the Russian Foundation for Basic Research, project no. 17-29-05108 ofi_m.

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Correspondence to A. V. Lotov.

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Translated by I. Ruzanova

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Lotov, A.V., Ryabikov, A.I. Launch Pad Method in Multiextremal Multiobjective Optimization Problems. Comput. Math. and Math. Phys. 59, 2041–2056 (2019). https://doi.org/10.1134/S0965542519120145

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  • DOI: https://doi.org/10.1134/S0965542519120145

Keywords:

  • nonlinear multiobjective optimization
  • Pareto frontier
  • Edgeworth–Pareto hull
  • effective hull of a nonconvex set
  • approximation of Edgeworth–Pareto hull
  • approximation of the effective hull of a multidimensional set