Two Classical Metaheuristics: Differential Evolution and Particle Swarm Optimization

This chapter introduces two foundational population-based metaheuristic algorithms: Differential Evolution (DE) and Particle Swarm Optimization (PSO). Metaheuristics, which rely on stochastic processes, are effective for solving complex nonlinear optimization problems. DE and PSO are widely recognized for their simplicity, efficiency, and robustness across various application domains, including engineering and finance. The chapter begins with an overview of metaheuristics and their advantages, such as diversity maintenance and knowledge sharing among search agents. It then delves into the operational mechanisms of DE, detailing its mutation, crossover, and selection processes, along with multiple mutation strategies. A complete pseudocode and MATLAB implementation are provided. Subsequently, the chapter explores PSO, focusing on the social behavior-inspired movement of particles, the role of personal and global best positions, and the influence of inertia weight strategies. By the end of the chapter, readers gain a comprehensive understanding of the theoretical foundations, algorithmic structures, and practical implementation aspects of DE and PSO, equipping them to apply these methods to a wide range of optimization problems.