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Evolutionary algorithm using surrogate models for solving bilevel multiobjective programming problems.

Yuhui Liu1, Hecheng Li2, Hong Li3

  • 1School of Computer Science and Technology, Qinghai Normal University, Xining, China.

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|December 17, 2020
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Summary
This summary is machine-generated.

This study introduces an efficient evolutionary algorithm using surrogate models to solve complex bilevel multiobjective programming problems (BMPP). The approach effectively handles hierarchical structures and multiple objectives, significantly reducing computational cost.

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Area of Science:

  • Operations Research
  • Computational Optimization
  • Decision Sciences

Background:

  • Bilevel multiobjective programming problems (BMPP) are computationally challenging due to their inherent hierarchical structure and multiple objectives.
  • Existing methods struggle with the significant computational cost of finding non-dominated solutions for these strongly NP-hard problems.
  • Few studies have effectively addressed the complexity of solving BMPPs.

Purpose of the Study:

  • To develop an efficient evolutionary algorithm for solving bilevel multiobjective programming problems (BMPP).
  • To reduce the computational burden associated with finding optimal solutions in hierarchical, multi-objective optimization scenarios.
  • To enhance the discovery of non-dominated solutions at both leader and follower levels.

Main Methods:

  • A dynamic weighted sum method transforms the follower's multi-objective problems into single-objective ones.
  • Adaptive surrogate optimization models approximate follower's optimal solutions for each leader's variable setting.
  • The proposed techniques are integrated into MOEA/D, incorporating a heuristic crossover operator using gradient information.

Main Results:

  • The developed algorithm successfully obtains non-dominated solutions for the leader in bilevel multiobjective programming problems.
  • Simulation results on linear and nonlinear cases demonstrate the algorithm's efficiency.
  • The surrogate-assisted approach significantly reduces the computational cost compared to traditional methods.

Conclusions:

  • The proposed evolutionary algorithm with surrogate optimization models provides an efficient method for solving complex BMPPs.
  • The integration of dynamic weighting, surrogate models, and heuristic operators enhances solution quality and computational efficiency.
  • This approach offers a viable solution for tackling challenging hierarchical and multi-objective optimization problems.