COMPUTATIONAL METHODS THROUGH GENETIC ALGORITHMS FOR OBTAINING STACKELBERG SOLUTIONS TO TWO-LEVEL INTEGER PROGRAMMING PROBLEMS
Ichiro Nishizaki, Masatoshi Sakawa · Cybernetics & Systems · 2005
In this article, we present a method for obtaining Stackelberg solutions to two-level integer problems through genetic algorithms, which have received much attention as a promising computational method for complex problems. Assuming that there exist the upper- and the lower-bounds constraints with respect to integer variables, we employ a zero-one bit string as an individual in our artificial genetic systems. It is required that each individual satisfies the constraints of the given problem and a response of the lower level decision maker with respect to a decision that the upper level decision maker is rational. Therefore, individuals not satisfying the two conditions are penalized in the artificial genetic systems. To demonstrate the feasibility and efficiency of the proposed methods, computational experiments are carried out and comparisons between the Moore and Bard method based on the branch-and-bound techniques and the proposed methods are provided.