A Mixed-Encoding Genetic Algorithm for Nonlinear Bilevel Programming Problems
Hecheng Li, Yuping Wang · 2009
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.