Differential Evolution Algorithm for Unconstrained Continuous Variable Global Optimization

This article presents the Differential Evolution (DE) algorithm as a global optimization method designed for solving various unconstrained continuous variable problems, including linear programming, nonlinear programming, and non-smooth optimization challenges. Implemented efficiently in MATLAB, the algorithm operates through a population-based search paradigm that mimics biological evolution processes. The core mechanism involves three key operations: mutation (creating donor vectors by combining differential vectors), crossover (generating trial vectors by mixing target and donor vectors), and selection (retaining superior solutions based on fitness comparisons). In practical implementations, users can customize critical parameters such as population size (NP), scaling factor (F), and crossover rate (CR) to adapt to specific problem characteristics. The MATLAB implementation typically utilizes vectorized operations for mutation strategies like "rand/1/bin" and employs logical indexing for efficient selection processes. This algorithm serves as a robust tool for addressing complex optimization scenarios where traditional gradient-based methods may struggle with non-convex or discontinuous objective functions.