针对演化算法在求解带平衡约束的圆形布局问题上所出现的早熟现象,提出一种有利于保持种群多样性的多量子态量子进化算法,并结合高效的定位定序启发式方法进行求解.为了高效优化布局顺序,在量子进化算法的基础上:引入多量子态编码和基于平均收敛概率的收敛标准以提高求解速度；引入基于禁忌策略和启发信息的观测方法,使其所得到的n进制解为互不相同的整数串,同时保证优先布局质量大、半径大的小圆；引入动态量子进化策略,有效地引导种群向最优个体进化.在定位规则中引入定位概率函数提高解的精度,数值实验结果表明,该算法能够有效求解带平衡约束的圆形布局问题.%To solve the prematurity of evolutionary algorithm on the equilibrium constrained circles packing problem, the Multi-Quantum States Quantum-Inspired Evolutionary Algorithm (MQSQIEA) proposed in this paper was beneficial to keeping the population diversity, which combined the heuristics based on the order-based positioning technique. The layout sequence was optimized efficiently by MQSQIEA. The solving speed was improved by the multi-quantum states coding and the convergence criterion based on the average convergence probability. The observation method based on the taboo strategy and heuristic information was introduced to obtain the n-ary solution with different integers and ensure the priority to place circles with large mass and long radius. The dynamic quantum evolutionary strategy was applied to guide the population to evolve towards the best individual. The positioning probability function introduced to the positioning rule was employed to improve the solution quality. The numerical experimental results show that the proposed method can effectively solve the circular packing problem with equilibrium constraints.
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