A Novel Differential Evolution Algorithm with K-Means and Simplex Search Method for Absolute Value Equations

In this paper, we propose a feasible method for solving the NP-hard absolute value equation (AVE) Ax -- |x| = b, which has 2ⁿ-solutions. The method mixes differential evolution, K-Means and Simplex Search Method together and achieves an effective balance of exploration and exploitation, denotes SKDE. SKDE execute k-means to gain 2n subgroups from initial individuals. perform DE operation to obtain a candidate solution of each subgroup, manipulate simplex search method to harvest 2n optimal solutions. Numerical results show that KSDE can quickly get as many solutions to the absolute value equation as possile.