Solving Bilevel Programming Models Using Genetic Algorithm to Obtain Optimal Solutions

Bilevel programming models represent hierarchical optimization problems typically comprising two interdependent levels: upper-level decision-making and lower-level feedback. These models find extensive applications in resource allocation, transportation planning, and other fields, though their nested structure introduces significant computational complexity.

Genetic Algorithm (GA), as a heuristic search method, mimics natural selection and genetic mechanisms to identify optimal solutions, making it particularly suitable for handling nonlinear, non-convex complex optimization problems. In bilevel programming, GA can be implemented through hierarchical approaches:

Upper-level Genetic Encoding: Upper-level decision variables are encoded as chromosomes, where each individual represents a potential solution Lower-level Response Solving: For each upper-level solution, an independent optimization process runs at the lower level (potentially integrated with other algorithms) Fitness Evaluation: Chromosome quality is assessed based on comprehensive performance metrics from both levels Iterative Evolution: Solution quality gradually improves through selection, crossover, and mutation operations

Key considerations for MATLAB implementation include: - Utilizing parallel computing to accelerate independent lower-level problem solving - Designing appropriate constraint handling mechanisms to ensure solution feasibility - Maintaining sufficiently large upper-level population sizes to cover decision spaces - Implementing elitism strategies to preserve high-quality solutions

Although computationally intensive, this bilevel genetic algorithm effectively addresses complex hierarchical optimization problems that traditional methods struggle to solve. By adjusting parameters like selection pressure and mutation probability, practitioners can balance solution accuracy and computational efficiency. For large-scale engineering applications, surrogate models can be incorporated to reduce computational costs.