Application of Improved Differential Evolution Algorithm in Solving Equations

Abstract

The problem of finding roots of equations has always been an important research problem in the fields of scientific and engineering calculations. For the standard differential evolution algorithm cannot balance the convergence speed and the accuracy of the solution, an improved differential evolution algorithm is proposed. First, the one-half rule is introduced in the mutation process, that is, half of the individuals perform differential evolutionary mutation, and the other half perform evolutionary strategy reorganization, which increases the diversity of the population and avoids premature convergence of the algorithm; Second, set up an adaptive mutation operator and a crossover operator to prevent the algorithm from falling into the local optimum and improve the accuracy of the solution. Finally, classical high-order algebraic equations and nonlinear equations are selected for testing, and compared with other algorithms. The results show that the improved algorithm has higher solution accuracy and robustness, and has a faster convergence speed. It has outstanding effects in finding roots of equations, and provides an effective method for engineering and scientific calculations.