Differential Evolution Optimization Algorithm Program with Code Implementation

In this document, we present a comprehensive differential evolution (DE) optimization algorithm program example designed for solving various optimization problems, including but not limited to function optimization. First, we introduce the fundamental concepts and principles of the differential evolution algorithm to establish a clear understanding of the program's operational mechanics. Key algorithmic components such as mutation strategies (e.g., DE/rand/1), crossover operations, and selection mechanisms will be explained with corresponding code snippets. Next, we systematically break down the program structure, covering input/output specifications, algorithm parameter configuration (population size, scaling factor, crossover rate), population initialization methods, and core evolutionary operations implemented through vectorized computations. Finally, we demonstrate practical usage examples showcasing how to adapt the program for different optimization problem types, along with guidance on tuning algorithm parameters (e.g., F and CR values) for performance enhancement. Code annotations will highlight critical functions like mutation vector generation and boundary constraint handling.