Abstract
In this paper, multi-sine cosine algorithm (MSCA) is presented to solve nonlinear bilevel programming problems (NBLPPs); where three different populations (completely separate from one another) of sine cosine algorithm (SCA) are used. The first population is used to solve the upper level problem, while the second one is used to solve the lower level problem. In addition, the Kuhn—Tucker conditions are used to transform the bilevel programming problem to constrained optimization problem. This constrained optimization problem is solved by the third population of SCA and if the objective function value equal to zero, the obtained solution from solving the upper and lower levels is feasible. The heuristic algorithm didn’t used only to get the feasible solution because this requires a lot of time and efforts, so we used Kuhn—Tucker conditions to get the feasible solution quickly. Finally, the computational experiments using 14 benchmark problems, taken from the literature demonstrate the effectiveness of the proposed algorithm to solve NBLPPs.
Highlights
Many practical problems such as engineering design, management, economic policy and traffic problems, can be formulated as nonlinear bilevel programming problems (NBLPP)
The 14 benchmark problems have been optimized and solved, using new evolutionary algorithms (NEA), by Wang et al [19] and the combining particle swarm optimization with chaos searching technique (PSO-CST), by Wan et al [35]. Their results are comparable with the present optimization results that obtained by multi-sine cosine algorithm (MSCA)
The proposed algorithm MSCA is better than the other methods that solve the NBLPPs, where it gives the leader the ability to choose the appropriate solution from many feasible solutions
Summary
Many practical problems such as engineering design, management, economic policy and traffic problems, can be formulated as nonlinear bilevel programming problems (NBLPP). It has been studied and received increasing attention in the literatures. The NBLPP is a nested optimization problem with two levels (namely the upper and lower level) in a hierarchy order. The decision maker at the upper level (the leader) firstly optimizes his/her objective function independently. After the leader picks his/her decision, the decision maker at the lower level (the follower) makes his/her decision. The leaders’ decision is directly influenced by the decision of the follower. Reference books on NBLPPs and related issues have emerged in [4,5]
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