An improved uniform design-based genetic algorithm for multi-objective bilevel convex programming

Abstract

Bilevel programming problems have a nested structure in which two optimisation programming problems are involved, one is the constraints of the other. Among bilevel programming problems, multiobjective bilevel programming problems are applicable but seldom studied. In this paper, a multi-objective bilevel convex programming is considered. To deal with this problem effectively, the lower level is transformed into a single optimisation problem by multiplying by a weighted vector. The vector is generated by scheme of uniform design. By designing a pattern of encoding, initial population generation, uniform design-based crossover, mutation, selection operator and fitness function, an improved uniform design-based genetic algorithm is proposed. Numerical experiments are implemented to test the efficiency of the proposed algorithm with the known results.