基于梯度投影法与随机优化算法的约束优化方法  

Constrained optimization based on gradient projection method and stochastic optimization algorithm

作　　者：张华军[1] 赵金[1] 罗慧[1] 解相朋[1] 

机构地区：[1]华中科技大学自动化学院,武汉430074

出　　处：《控制与决策》2014年第10期1777-1782,共6页Control and Decision

基　　金：国家自然科学基金项目(61273174;61034006;60874047)

摘　　要：针对带有线性等式和不等式约束的无确定函数形式的约束优化问题,提出一种利用梯度投影法与遗传算法、同时扰动随机逼近等随机算法相结合的优化方法.该方法利用遗传算法进行全局搜索,利用同时扰动随机逼近算法进行局部搜索,算法在每次进化时根据线性约束计算父个体处的梯度投影方向,以产生新个体,从而能够严格保证新个体满足全部约束条件.将上述约束优化算法应用于典型约束优化问题,其仿真结果表明了所提出算法的可行性和收敛性.For the optimization problem with the unspecific function, linear equality and inequality constraints, a method which combines gradient projection method with stochastic approximation algorithm is proposed. The proposed method uses genetic algorithm（GA） to search the optimal solution overall the feasible region, and uses simultaneous perturbation stochastic approximation algorithm（SPSA） to search the optimal solution at the local region. During the search process, the proposed method generates a new individual along the gradient projection direction which is calculated according to linear equality and inequality constraints at father individual location, which ensures the new individual satisfy all constraints strictly. The proposed method is applied to three typical optimization problems, and the simulation results show the feasibility and convergence of the proposed method.

关 键 词：约束优化 梯度投影 遗传算法 同时扰动随机逼近 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]