量子行为粒子群优化算法在几何约束问题上的应用

Application of the Quantum Particle Swarm Optimization Approach in the Geometric Constraint Problems

几何约束问题可以等价为求解非线性方程组问题,同时也可以将几何约束问题转化为一个优化问题来求解.受经典粒子群优化算法和量子动力学启发,提出一种新的算法——量子行为粒子群优化算法(QPSO)来求解几何约束问题.在QPSO模型里,粒子的状态不再通过位置和速度来决定,而是通过一个波函数来确定.这种算法的主要优点就是可以在感兴趣的问题上保持种群的多样性.实验结果表明,该方法可以提高几何约束求解的效率和收敛性.

Geometric constraint problem is equivalent to the problem of solving a set of nonlinear equations,and the constraint problem can be transformed into an optimization problem.Inspired by the classical PSO method and quantum mechanics theory,this paper presents a novel quantum-behaved PSO（QPSO） to solve geometric constraint problems.In the QPSO model,the state of a particle is depicted by a wave function instead of position and velocity.The advantage of the algorithm is that it can maintain the diversity of the population in the interested problems.The experimental result shows that the algorithm can improve efficiency and convergence of the geometric constraint solutions.