Multi-Sine Cosine Algorithm for Solving Nonlinear Bilevel Programming Problems

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.