%0 Journal Article
%T Heuristic artificial bee colony algorithm for solving the Homicidal Chauffeur differential game
%J AUT Journal of Mathematics and Computing
%I Amirkabir University of Technology
%Z 2783-2449
%A Yazdaniyan, Zahra
%A Shamsi, M.
%A de Pinho, Maria do Rosario
%A Foroozandeh, Z.
%D 2020
%\ 09/01/2020
%V 1
%N 2
%P 153-163
%! Heuristic artificial bee colony algorithm for solving the Homicidal Chauffeur differential game
%K Differential game
%K Saddle point solution
%K Artificial bee colony
%K Bilevel optimal control
%R 10.22060/ajmc.2019.16949.1025
%X 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.
%U https://ajmc.aut.ac.ir/article_3819_d7bf45bb8b6003cc03fb68a78cdb6ff7.pdf