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.

混合整数最佳控制问题（MIOCP）通常在许多实际工程应用中扮演重要角色。但是，MIOCP是典型的NP难题，具有相当大的计算复杂性，导致大多数当前的启发式优化算法收敛缓慢或收敛过早。因此，本研究提出了一种基于量子计算理论的新型有效混合算法来解决MIOCP问题。该算法由两部分组成：（i）量子退火（QA）由于基于量子隧穿的独特退火过程而专门解决高效率整数优化；以及（ii）采用了双精英量子蚁群算法（DEQACA）开发了用于增强全局搜索的双精英协同进化机制，以优化连续决策。QA / DEQACA混合算法整合了此类算法的优势，以更好地平衡勘探和开发能力。通过对QA和DEQACA进行交互式并行计算，整体进化可以找出最佳的混合整数决策。在基准函数和实际工程优化问题上的仿真结果证明，与其他两种最新的启发式方法相比，所提出的数值方法在实现有希望的结果方面更加出色。