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A Quantum Computing Based Numerical Method for Solving Mixed-Integer Optimal Control Problems

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Abstract

Mixed-integer optimal control problems (MIOCPs) usually play important roles in many real-world engineering applications. However, the MIOCP is a typical NP-hard problem with considerable computational complexity, resulting in slow convergence or premature convergence by most current heuristic optimization algorithms. Accordingly, this study proposes a new and effective hybrid algorithm based on quantum computing theory to solve the MIOCP. The algorithm consists of two parts: (i) Quantum Annealing (QA) specializes in solving integer optimization with high efficiency owing to the unique annealing process based on quantum tunneling, and (ii) Double-Elite Quantum Ant Colony Algorithm (DEQACA) which adopts double-elite coevolutionary mechanism to enhance global searching is developed for the optimization of continuous decisions. The hybrid QA/DEQACA algorithm integrates the strengths of such algorithms to better balance the exploration and exploitation abilities. The overall evolution performs to seek out the optimal mixed-integer decisions by interactive parallel computing of the QA and the DEQACA. Simulation results on benchmark functions and practical engineering optimization problems verify that the proposed numerical method is more excel at achieving promising results than other two state-of-the-art heuristics.

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Correspondence to Shurong Li.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 61573378 and the BUPT Excellent Ph.D. Students Foundation under Grant No. CX2019113.

This paper was recommended for publication by Editor WU Wenyuan.

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Liu, Z., Li, S. A Quantum Computing Based Numerical Method for Solving Mixed-Integer Optimal Control Problems. J Syst Sci Complex 34, 2428–2469 (2021). https://doi.org/10.1007/s11424-020-9278-6

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  • DOI: https://doi.org/10.1007/s11424-020-9278-6

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