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.
Funder
National Natural Science Foundation of China
QingHai Department of Science and Technology
Jiangsu Key Laboratory for the Research and Utilization of Plant Resources
Publisher
Public Library of Science (PLoS)
Reference55 articles.
1. Practical Bilevel Optimization
2. Bilevel Programming Approaches to Production Planning for Multiple Products with Short Life Cycles;XD Zhu;4OR Quarterly Journal of the Belgian: French and Italian Operations Research Societies,2019
3. A Bilevel Model for Participation of a Storage System in Energy and Reserve Markets;E Nasrolahpour;IEEE Transactions on Sustainable Energy,2018
4. A Bilevel Optimisation Approach to Obtain Optimal Cost Functions for Human Arm Movements;M Ulbrich;Numerical Algebra: Control and Optimisation (NACO),2017
5. Monitoring Mechanisms in New Product Development with Risk-Averse Project Manager;K Yang;Journal of Intelligent Manufacturing,2017
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. A Review on Evolutionary Multiform Transfer Optimization;2024 IEEE Congress on Evolutionary Computation (CEC);2024-06-30
2. Multiobjective Bilevel Optimization: A Survey of the State-of-the-Art;IEEE Transactions on Systems, Man, and Cybernetics: Systems;2023-09