Orthogonal genetic algorithm for solving quadratic bilevel programming problems

A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker (KKT) conditions. To cope with the complementarity constraints, a binary encoding scheme is adopted for KKT multipliers, and then the complementarity slackness problem is simplified to successive quadratic programming problems, which can be solved by many algorithms available. Based on 0-1 binary encoding, an orthogonal genetic algorithm, in which the orthogonal experimental design with both two-level orthogonal array and factor analysis is used as crossover operator, is proposed. Numerical experiments on 10 benchmark examples show that the orthogonal genetic algorithm can find global optimal solutions of quadratic bilevel programming problems with high accuracy in a small number of iterations.