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

Articles in Press

Document Type : Research Article

Authors

• Mitra Salimi ¹
• Akbar Hashemi Borzabadi ²
• Seyed hamed Hashemi mehne ³
• Aghileh Heydari ¹

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

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

³ Khayyam Institute, Tehran, Iran.

10.22067/ijnao.2024.86859.1389

Abstract

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).

Keywords

• Parallel algorithm
• Neighborhood descent algorithm
• Optimal control problem

Main Subjects

• Control and Optimization

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