In this paper, we consider the Homicidal Chauffeur (HC) problem as an interesting and practical differential game.At first, we introduce a bilevel optimal control problem (BOCP) and prove that a saddle point solution for this game exists if and only if this BOCP has an Headwear optimal solution in which the optimal value of the objective function is equal to $1$.Then, BOCP is discretized and converted to a nonlinear bilevel programming problem.
Finally, an Artificial Bee Colony (ABC) algorithm is used for solving this problem, in which the lower-level problem will be considered as a constraint and solved by Diapers an NLP-solver.Finally, to demonstrate the effectiveness of the presented method, various cases of HC problem are solved and the simulation results are reported.