A Mixed-Encoding Genetic Algorithm for Nonlinear Bilevel Programming Problems

For nonlinear bi-level programming problems in which the follower´s problem is linear, the paper develops a genetic algorithm based on a mixed encoding technique. At first, each individual consists of two parts, the first part is the leader´s variable values using real-encoding, whereas the second one is the sequence number of basic variables of the follower´s programming, which are some integers. Then, a new fitness function is given, in which the optimality conditions of linear programming are incorporated into penalty term to guarantee the optimality of the follower´s problem is satisfied. At last, based on the characteristic of individuals, new crossover and mutation operators are designed. The numerical results illustrate that the proposed algorithm is efficient and stable.