Evolutionary algorithm using surrogate models for solving bilevel multiobjective programming problems

Yuhui Liu, Hecheng Li and Hong Li

PLOS ONE, 2020, vol. 15, issue 12, 1-31

Abstract: A bilevel programming problem with multiple objectives at the leader’s and/or follower’s levels, known as a bilevel multiobjective programming problem (BMPP), is extraordinarily hard as this problem accumulates the computational complexity of both hierarchical structures and multiobjective optimisation. As a strongly NP-hard problem, the BMPP incurs a significant computational cost in obtaining non-dominated solutions at both levels, and few studies have addressed this issue. In this study, an evolutionary algorithm is developed using surrogate optimisation models to solve such problems. First, a dynamic weighted sum method is adopted to address the follower’s multiple objective cases, in which the follower’s problem is categorised into several single-objective ones. Next, for each the leader’s variable values, the optimal solutions to the transformed follower’s programs can be approximated by adaptively improved surrogate models instead of solving the follower’s problems. Finally, these techniques are embedded in MOEA/D, by which the leader’s non-dominated solutions can be obtained. In addition, a heuristic crossover operator is designed using gradient information in the evolutionary procedure. The proposed algorithm is executed on some computational examples including linear and nonlinear cases, and the simulation results demonstrate the efficiency of the approach.

Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0243926 (text/html)
https://journals.plos.org/plosone/article/file?id= ... 43926&type=printable (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0243926

DOI: 10.1371/journal.pone.0243926

Access Statistics for this article

More articles in PLOS ONE from Public Library of Science
Bibliographic data for series maintained by plosone ().