基于PSO算法的SOR最优松弛因子选取研究

Study on Selecting SOR Optimal Relaxation Factor with Particle Swarm Optimization

目前选取逐次超松弛迭代法(SOR)最优松弛因子的基本思路是:在区间(0,2)上,根据确定的分割策略,选取分割点的值作为松弛因子来计算相应的SOR迭代次数,将小于预设的SOR迭代次数阈值的松弛因子作为最优解返回,例如二分比较法、黄金分割法、逐步搜索法等,其缺陷在于不易找到全局最优松弛因子且对参数依赖较大。为克服传统策略解决该问题的不足,受粒子群优化算法及其在不同场景成功应用的启发,提出利用基本粒子群优化算法(bPSO)、简化粒子群优化算法(sPSO)、带极值扰动粒子群优化算法(tPSO)和带极值扰动的简化粒子群优化算法(tsPSO)来搜索SOR迭代法最优松弛因子。通过对两个不同的线性方程组的实证测试,验证了四种算法在选取SOR最优松弛因子问题上的有效性。

At present,the basic idea of selecting SOR optimal relaxation factor is as follows:in the interval(0,2),the value of a split point is selected as the relaxation factor to calculate the corresponding SOR iteration number,and the relaxation factor less than the preset SOR iteration threshold is returned as the optimal solution,such as dichotomous comparison method,golden section method,stepwise search method,and so on.However,this strategy is hard to find the global optimal one and heavily depends on parameter setting.In order to solve the problem above,inspired by the particle swarm optimization and its successful application in different scenes,we propose to use the basic particle swarm optimization(bPSO),the simple particle swarm optimization(sPSO),the extremum disturbed particle swarm optimization(tPSO)and the extremum disturbed and simple particle swarm optimization(tsPSO)for finding SOR optimal relaxation factor.By testing the two different linear equations,we verify the validity of four algorithms in selecting SOR optimal relaxation factor.