基于梯度投影法与随机优化算法的约束优化方法

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。

Constrained optimization based on gradient projection method and stochastic optimization algorithm

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.