Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24491220200901Heuristic artificial bee colony algorithm for solving the Homicidal Chauffeur differential game153163381910.22060/ajmc.2019.16949.1025ENZahraYazdaniyanDepartment of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran,
IranM.ShamsiDepartment of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran,
IranMaria Do RosarioDe PinhoDepartment of Electrical and Computer Engineering, SYSTEC, Faculdade de Engenharia, Universidade do Porto, 4200-465, Porto,
PortugalZ.ForoozandehDepartment of Electrical and Computer Engineering, SYSTEC, Faculdade de Engenharia, Universidade do Porto, 4200-465, Porto, PortugalJournal Article20190821In 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_d7bf45bb8b6003cc03fb68a78cdb6ff7.pdf