模糊机会约束规划的混沌量子蚁群算法及收敛性  

Solving Fuzzy Chance-constrained Programming Using Chaos Quantum ACO Algorithm and Its Convergence

作　　者：薛晗[1] 金敏[2] 马宏绪[1] 

机构地区：[1]国防科学技术大学机电工程与自动化学院,长沙410073 [2]湖南大学软件学院,长沙410000

出　　处：《系统仿真学报》2009年第20期6462-6468,共7页Journal of System Simulation

基　　金：国家863计划(2007AA041603);国家自然科学基金(60475035);湖南省科学技术厅重大科技专项计划(2007FJ1806);国防科技大学预研项目(CX07-03-01);国防科技大学优秀研究生创新资助(B070302)

摘　　要：模糊机会约束规划因其非线性、非凸性及模糊性,对经典的优化理论提出了极大的挑战。设计了一种基于模糊模拟的混沌量子蚁群算法,为解决复杂的模糊机会约束规划问题提供了有力的工具。算法中每只蚂蚁携带一组表示蚂蚁当前位置信息的量子比特,采用随机干扰离散量子交叉,进行高斯量子变异,为量子旋转门更新设计基于梯度的转角计算方法。在每次迭代的当前全局最优解附近使用混沌量子搜索,搜索范围随迭代次数而逐渐减小,因而在初期能防止陷入局部最优,后期能提高搜索精度。证明了该蚁群算法的收敛性。数值案例研究验证了该算法的有效性、稳定性及准确性。Fuzzy Chance Constrained Programming （FCCP） poses significant computational challenges due to its non-linear, non-convex, and stochastic nature. A fuzzy simulation based chaos quantum ant colony optimization algorithm （CQACO） was designed for solving the FCCP problem. Each ant carries a group of quantum bits which represent its position. The algorithm uses random interferential discrete quantum crossover and gauss quantum mutation, and designs new method of computing rotation angle for quantum rotation gates based on grads. The chaos quantum search algorithm searches the space around the best-so-far ant, and the radius of the searching area is decreased as the algorithm goes on, which helps avoid dropping into the local optima in the beginning and improve the accuracy of the generated solutions in the end. A proof of convergence for CQACO algorithms is developed. A numerical example shows the potential applications of the fuzzy programming as well as the efficiency, stability and accuracy of the proposed algorithm.

关 键 词：蚁群算法 模糊机会约束规划 量子计算 混沌 模糊模拟 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] O224[自动化与计算机技术—控制科学与工程]