A Genetic Algorithm for Solving Weak Nonlinear Bilevel Programming Problems

The weak bilevel programming problem is characterized by the decision-making process that the follower has nonunique solutions and reacts to the leader by providing the worst one. We are concerned with a class of weak nonlinear bilevel programming problems in which the follower is linear with respect to all follower's variables. At first, the original problem is transformed into a nonlinear program via the prime-dual principle. In addition, the leader variable values are encoded as individuals, whereas the values of other variables can be obtained by solving a linear programming (LP). Further, the leader's objective value of the original bilevel programming is taken as the fitness of individuals. Based on these schemes, a genetic algorithm is presented for solving this class of weak bilevel programming problems, and an example is solved to illustrate that the method is feasible and efficient.