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Afsharirad, Maria. (1404). Novel Schemes for Approximate Solutions of Optimal Control Problems via a Hybrid Evolutionary and Clustering Algorithm. فصلنامه علمی زیست فناوری گیاهان زراعی, 10(2), 255-271. doi: 10.30473/coam.2025.74474.1306
Maria Afsharirad. "Novel Schemes for Approximate Solutions of Optimal Control Problems via a Hybrid Evolutionary and Clustering Algorithm". فصلنامه علمی زیست فناوری گیاهان زراعی, 10, 2, 1404, 255-271. doi: 10.30473/coam.2025.74474.1306
Afsharirad, Maria. (1404). 'Novel Schemes for Approximate Solutions of Optimal Control Problems via a Hybrid Evolutionary and Clustering Algorithm', فصلنامه علمی زیست فناوری گیاهان زراعی, 10(2), pp. 255-271. doi: 10.30473/coam.2025.74474.1306
Afsharirad, Maria. Novel Schemes for Approximate Solutions of Optimal Control Problems via a Hybrid Evolutionary and Clustering Algorithm. فصلنامه علمی زیست فناوری گیاهان زراعی, 1404; 10(2): 255-271. doi: 10.30473/coam.2025.74474.1306

Novel Schemes for Approximate Solutions of Optimal Control Problems via a Hybrid Evolutionary and Clustering Algorithm

Control and Optimization in Applied Mathematics
مقاله 10، دوره 10، شماره 2 - شماره پیاپی 20، مهر 2025، صفحه 255-271    اصل مقاله (778.49 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.30473/coam.2025.74474.1306
نویسنده
Maria Afsharirad*
Department of Applied Mathematics‎, ‎University of Science and Technology of Mazandaran‎, ‎Behshahr‎, ‎Iran‎.
چکیده
This paper presents a hybrid scheme for solving optimal control problems‎. ‎Discretizing the time interval and assuming a constant control value on each sub-interval transforms the optimal control problem into an assignment problem‎. ‎To cluster feasible solutions, a novel method is proposed in this paper, which applies metaheuristic algorithms—specifically, genetic algorithms and particle swarm optimization—to generate a large number of solutions. ‎Subsequently‎, ‎the K-means clustering method is employed to classify these solutions into clusters‎. ‎Enhancing the median of each cluster‎, ‎using metaheuristic techniques, ultimately results in improved medians‎. ‎The best median from the final iteration of the algorithm serves as an acceptable solution for the optimal control problem‎. ‎In some cases‎, ‎it even succeeds in discovering a new best solution‎.

تازه های تحقیق
  • A hybrid optimization framework is introduced for optimal control that integrates time discretization, clustering, and metaheuristics.
  • A two-stage approach uses genetic algorithms (GA) and particle swarm optimization (PSO) to generate diverse feasible solution populations for the control problem.
  • The solution quality is enhanced by applying GA crossover and PSO directional updates to refine candidates within and across clusters.
  • The optimal control problem is reformulated as selecting the best representative solution from clustered populations via a K-means-based P-median mechanism, improving tractability and performance.
  • The method is validated on multiple optimal control problems, exploring three cluster counts and two time-interval discretizations, with several instances achieving superior results compared to existing literature.
کلیدواژه‌ها
Clustering‎؛ ‎K-means algorithm‎؛ ‎Optimal control problem؛ ‎Genetic algorithm‎؛ ‎ ‎Particle swarm optimization
مراجع

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