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An evolutionary algorithm based on approximation method and related techniques for solving bilevel programming

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Summary
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This study introduces an evolutionary algorithm with surrogate models to solve complex hierarchical optimization problems. The novel approach effectively finds optimal solutions for bilevel programming problems.

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Area of Science:

  • Engineering
  • Economic Management
  • Operations Research

Background:

  • Optimization models in engineering and economic management often feature multiple decision-making levels, termed multi-level or hierarchical optimization problems.
  • Bilevel programming problems (BLPP) specifically address optimization scenarios with two hierarchical decision-making levels.

Purpose of the Study:

  • To develop an effective evolutionary algorithm for solving complex nonlinear bilevel programming problems.
  • To enhance the efficiency and accuracy of optimization algorithms in hierarchical decision-making contexts.

Main Methods:

  • An evolutionary algorithm is designed, incorporating a surrogate model for approximation and correlation coefficients for screening.
  • The isodata method groups the initial population, and correlation coefficients are determined based on objective function ranks.
  • A novel crossover operator utilizing spherical search diversifies offspring generation.

Main Results:

  • The surrogate model approximates solutions for the follower's problem, with population screening guided by correlation coefficients.
  • Simulation experiments validated the algorithm's capability to effectively find optimal solutions for bilevel programming problems.

Conclusions:

  • The proposed evolutionary algorithm with surrogate modeling and correlation coefficients offers an effective method for tackling complex nonlinear bilevel programming problems.
  • The integration of isodata grouping, rank-based correlation coefficients, and spherical search crossover enhances the optimization process.