A parallel hybrid variable neighborhood descent algorithm for non-linear optimal control problems

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 29 مرداد 1403

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.86859.1389

نویسندگان

Mitra Salimi¹؛ Akbar Hashemi Borzabadi^{* 2}؛ Seyed hamed Hashemi mehne³؛ Aghileh Heydari⁴

¹Department of Mathematics, Payam Noor University, Tehran, Iran.

²Department of Applied Mathematics, University of Science and Technology of Mazandaran, Behshahr, Iran.

³Khayyam Institute, Tehran, Iran.

⁴Department of Mathematics, Payam Noor University, Tehran, Iran.

چکیده

In this paper, a numerical method for solving bounded continuous-time nonlinear optimal control problems (NOCP) that is based on a variable neighborhood descent algorithm (VND) is proposed. First, an improved VND that uses efficient neighborhood interchange, is applied to the discrete form of NOCP. Then, to improve the efficiency of the algorithm for practical and large-scale problems, the parallel processing approach is implemented. It performs the required complex computations in parallel. The resulting parallel algorithm is applied to a benchmark of nine practical problems such as the Van Der Pol Problem (VDP) and Chemical Reactor Problem (CRP). For large-scale problems, the parallel hybrid variable neighborhood descent algorithm (PHVND) is capable of obtaining optimal control values effectively. Our experimentation shows that PHVND outperforms the best-known heuristics in terms of solution quality and computational effort. In addition, computational results indicate that PHVND produces superior results compared to Particle swarm optimization (PSO) or genetic algorithm (GA).

کلیدواژه‌ها

Parallel algorithm؛ Neighborhood descent algorithm؛ Optimal control problem