Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 1 2 2020 09 01 Heuristic artificial bee colony algorithm for solving the Homicidal Chauffeur differential game 153 163 3819 10.22060/ajmc.2019.16949.1025 EN Zahra Yazdaniyan Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran M. Shamsi Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran Maria Do Rosario De Pinho Department of Electrical and Computer Engineering, SYSTEC, Faculdade de Engenharia, Universidade do Porto, 4200-465, Porto, Portugal Z. Foroozandeh Department of Electrical and Computer Engineering, SYSTEC, Faculdade de Engenharia, Universidade do Porto, 4200-465, Porto, Portugal Journal Article 2019 08 21 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 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 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. https://ajmc.aut.ac.ir/article_3819_eb1848290d5a7de9c9ccabc67fefa211.pdf