求解优化问题的混合PSO-Solver算法

融合了粒子群算法(PSO) 和Solver 加载宏，形成混合PSO-Solver算法进行优化问题的求解。PSO作为全局搜索算法首先给出问题的全局可行解，Solver则是基于梯度信息的局部搜索工具，对粒子群算法得出的解再进行改进，二者互相结合，既加快了全局搜索的速度，又有效地避免了陷入局部最优。算法用VBA语言进行编程，简单且易于实现。通过对无约束优化问题和约束优化问题的求解，以及和标准PSO、其他一些混合算法的比较表明，PSO-Solver算法能够有效地提高求解过程的收敛速度和解的精确性。

Hybrid PSO-Solver algorithm for solving optimization problems

Combined Particle Swarm Optimization (PSO) and Solver add-in, this paper proposed a hybrid PSO-Solver algorithm to solve the optimization problems. As a global search algorithm, PSO looks for the global feasible solution, and Solver is a local search tool based on gradient information, which refines the solution obtained by PSO. The hybrid algorithm could speed up the global search, as well as avoid getting into local minima. VBA was used to code, which is simple and easily conducted. Results of solving some unconstrained and constrained examples, compared to the standard PSO and other heuristic algorithms, show that this hybrid PSO-Solver algorithm can improve the speed of convergence and the accuracy of solutions significantly.