Bilevel optimization based on iterative approximation of multiple mappings

Ankur Sinha*, Zhichao Lu, Kalyanmoy Deb, Pekka Malo

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

10 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)151-185
Number of pages35
JournalJournal of Heuristics
Volume26
Issue number2
Early online date24 Sep 2019
DOIs
Publication statusPublished - 1 Apr 2020
MoE publication typeA1 Journal article-refereed

Keywords

  • Bilevel optimization
  • Evolutionary algorithms
  • Mathematical programming
  • Stackelberg games

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