TY - JOUR
A2 - Wang, Yuping
AU - Li, Hecheng
AU - Fang, Lei
PY - 2012
DA - 2012/10/17
TI - An Evolutionary Algorithm for Solving Bilevel Programming Problems Using Duality Conditions
SP - 471952
VL - 2012
AB - Bilevel programming is characterized by two optimization problems located at different levels, in which the constraint region of the upper level problem is implicitly determined by the lower level problem. This paper is focused on a class of bilevel programming with a linear lower level problem and presents a new algorithm for solving this kind of problems by combiningan evolutionary algorithm with the duality principle. First, by using the prime-dual conditions of the lower level problem, the original problem is transformed into a single-level nonlinearprogramming problem. In addition, for the dual problem of the lower level, the feasible bases are taken as individuals in population. For each individual, the values of dual variables canbe obtained by taking the dual problem into account, thus simplifying the single-level problem. Finally, the simplified problem is solved, and the objective value is taken as the fitness of theindividual. Besides, when nonconvex functions are involved in the upper level, a coevolutionary scheme is incorporated to obtain global optima. In the computational experiment, 10 problems,smaller or larger-scale, are solved, and the results show that the proposed algorithm is efficient and robust.
SN - 1024-123X
UR - https://doi.org/10.1155/2012/471952
DO - 10.1155/2012/471952
JF - Mathematical Problems in Engineering
PB - Hindawi Publishing Corporation
KW -
ER -