Function Optimization Using Penalty Function-Based Particle Swarm Algorithm

Since the mid-1950s when bionics was established, many scholars have started developing new algorithms inspired by biological systems to address complex optimization problems. Bionics is a scientific discipline that studies biological principles and applies them to engineering and technological domains. Through in-depth research on biological evolution mechanisms, scholars have proposed various simulated evolutionary algorithms suitable for real-world complex optimization problems, including Simulated Annealing (SA), Seeker Optimization Algorithm (SOA), Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO), and Genetic Algorithms (GA).

Notable examples include Genetic Algorithm (GA) developed by Professor J.H. Holland and colleagues at the University of Michigan, Evolution Strategy by Rechenberg, and Evolutionary Programming by Fogel. Genetic Algorithms, Evolution Strategy, and Evolutionary Programming share certain similarities as they all originate from Darwin's theory of evolution. Among these, Genetic Algorithm has been most thoroughly researched, possesses the most mature theoretical foundation, and has the widest range of applications.

Particle Swarm Optimization (PSO) represents an interdisciplinary field that combines multiple disciplines. As an optimization algorithm, PSO simulates the optimal foraging behavior of bird flocks. The algorithm typically involves initializing a population of particles with random positions and velocities, then iteratively updating their positions based on personal best experiences and global best solutions. This attracts numerous researchers from various fields including mathematics, computer science, biology, and physics to study and improve it using different technical approaches. Particle Swarm Optimization has promising application prospects in numerous domains such as industry, transportation, chemical engineering, energy, agriculture, national defense, engineering, and communications. Therefore, research on PSO holds significant importance.

In summary, the study of bionic algorithms has become a prominent research area, with their wide applicability and significant effectiveness being widely recognized. Consequently, we have reason to believe that bionic algorithms will see broader applications and more in-depth research in future developments.