Common Algorithms for Solving Bilevel Programming Problems

The article mentions that common algorithms for solving bilevel programming problems include vertex enumeration algorithms, direct search methods, descent methods, and non-numerical optimization methods (such as simulated annealing algorithms, genetic algorithms, etc.). The genetic algorithm implementation follows this workflow: first, upper-level decision variables are encoded (typically using binary or real-number representations) and substituted into the lower-level programming model. By solving the lower-level model's decision variables, we obtain fitness values for the upper-level model (often through objective function evaluation). Subsequently, genetic operations including crossover (combining parent solutions), mutation (introducing random variations), and selection (preserving high-fitness individuals) are performed. This evolutionary process continues through multiple generations until convergence criteria are met, ultimately yielding the optimal solution. This method provides an effective approach for solving complex bilevel programming problems, particularly useful when traditional gradient-based methods face limitations.