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目的针对传统量子遗传算法无法充分利用种群中未成熟个体信息的不足,提出了基于交互更新模式的量子遗传算法(IUMQGA)并应用于几何约束求解中。方法几何约束问题的约束方程组可转化为优化模型,因此约束求解问题可以转化为优化问题。采用将遗传算法与量子理论相结合的量子遗传算法,使用双串量子染色体结构,使用交互更新策略将遗传算法中的交叉操作利用量子门变换来实现,根据不同情况采用不同的交互更新策略。这里的交互,指的是两个个体进行信息交换的过程,该过程用以产生新的个体。这不仅增加了个体间信息的交换而且充分利用了种群中未成熟个体的信息,提高了算法的收敛速度。结果通过非线性方程实例和几何约束实例测试并与其他方法比较表明,基于交互更新模式的量子遗传算法求解几何约束问题具有更好的求解精度和求解速率。双圆外公切线问题实例中,IUMQGA算法比QGA算法稳定;单圆填充问题和双圆外公切线问题实例中,通过实验求得各变量的最优值与其相应的精确值的误差在1E-2以下。结论采用交互更新模式的量子遗传算法可以很好地求解几何约束问题。
Aim To solve the problem that traditional quantum genetic algorithm can not make full use of the information of immature individuals in population, a quantum genetic algorithm (IUMQGA) based on interactive update mode is proposed and applied to geometric constraint solving. Method Constraint equations constrained by geometric constraints can be transformed into optimization models, so constrained solving problems can be transformed into optimization problems. The quantum genetic algorithm which combines genetic algorithm and quantum theory is used. By using double-string quantum chromosome structure, the cross-operation in genetic algorithm is realized by quantum door transformation using the interactive updating strategy. Different interactive updating strategies are adopted according to different situations. The interaction here refers to the process of exchanging information between two individuals, which is used to generate new individuals. This not only increases the exchange of information between individuals but also makes full use of the information of immature individuals in the population, which improves the convergence rate of the algorithm. The results are tested by examples of nonlinear equations and geometric constraints and compared with other methods. The results show that the quantum genetic algorithm based on the interactive update mode has better solving precision and solving rate for solving geometric constraint problems. In the case of the tangent of the double circle, the IUMQGA algorithm is more stable than the QGA algorithm. In the case of the single-circle filling problem and the double-circle male-line tangent problem, the error between the optimal value of each variable and its corresponding exact value is less than 1E-2 . Conclusion The quantum genetic algorithm using the interactive update model can solve the problem of geometric constraints well.