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Heuristic artificial bee colony algorithm for solving the Homicidal Chauffeur differential game | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 3، دوره 1، شماره 2، آذر 2020، صفحه 153-163 اصل مقاله (610.28 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2019.16949.1025 | ||
| نویسندگان | ||
| Zahra Yazdaniyan1؛ M. Shamsi* 1؛ Maria do Rosario de Pinho2؛ Z. Foroozandeh2 | ||
| 1Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran | ||
| 2Department of Electrical and Computer Engineering, SYSTEC, Faculdade de Engenharia, Universidade do Porto, 4200-465, Porto, Portugal | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Differential game؛ Saddle point solution؛ Artificial bee colony؛ Bilevel optimal control | ||
| مراجع | ||
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