为设计高效稳定的演化算法,将方程求根的不动点迭代思想引入到优化领域,通过将演化算法的寻优过程看作为在迭代框架下方程不动点的逐步显示化过程,设计出一种基于数学模型的演化新算法,即不动点演化算法(fixed point evolution algorithm,FPEA).该算法的繁殖算子是由Aitken加速的不动点迭代模型导出的二次多项式,其整体框架继承传统演化算法(如差分演化算法)基于种群的迭代模式.试验结果表明:在基准函数集CEC2014、CEC2019上,本文算法的最优值平均排名在所有比较算法中排名第1;在4个工程约束设计问题上,FPEA与CSA、GPE等多个算法相比,能以较少的计算开销获得最高的求解精度.
文章针对实Hilbert空间中的单调变分不等式和不动点连续映射的凸可行性问题,提出了一种非单调步长算法来求解。该算法利用可行集的信息构造特殊半空间,以及结合外梯度方法构造半空间。每次向两个半空间作投影。同时结合惯性加速技巧与Mann迭代方法,在一定条件下,建立了所提算法的弱收敛性定理。最后,我们进行了一些计算测试,以证明所提算法的效率和优点,并与现有算法进行了比较。This paper presents a new inertial subgradient extragradient algorithm designed to solve variational inequalities and fixed point problems in real Hilbert spaces. Integrating the Mann iteration method with the subgradient extragradient approach and employing inertial acceleration techniques, the algorithm constructs a half-space using subgradient information and projects onto it. Step lengths are determined via a line search procedure, eliminating the need to compute the Lipschitz constant of the mapping. The algorithm’s weak convergence is established under assumptions like the pseudo-nonexpansiveness of the mappings. Finally, Numerical experiments additionally illustrate the algorithm’s advantages over existing approaches in the literature.
