Bilevel optimization based on iterative approximation of multiple mappings

Ankur Sinha (), Zhichao Lu, Kalyanmoy Deb and Pekka Malo
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Ankur Sinha: Indian Institute of Management
Zhichao Lu: Michigan State University
Kalyanmoy Deb: Michigan State University
Pekka Malo: Aalto University School of Economics

Journal of Heuristics, 2020, vol. 26, issue 2, No 1, 185 pages

Abstract: Abstract A large number of application problems involve two levels of optimization, where one optimization task is nested inside the other. These problems are known as bilevel optimization problems and have been studied by both classical optimization community and evolutionary optimization community. Most of the solution procedures proposed until now are either computationally very expensive or applicable to only small classes of bilevel optimization problems adhering to mathematically simplifying assumptions. In this paper, we propose an evolutionary optimization method that tries to reduce the computational expense by iteratively approximating two important mappings in bilevel optimization; namely, the lower level rational reaction mapping and the lower level optimal value function mapping. The algorithm has been tested on a large number of test problems and comparisons have been performed with other algorithms. The results show the performance gain to be quite significant. To the best knowledge of the authors, a combined theory-based and population-based solution procedure utilizing mappings has not been suggested yet for bilevel problems.

Keywords: Bilevel optimization; Evolutionary algorithms; Stackelberg games; Mathematical programming (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10732-019-09426-9

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