Multi-objective Particle Swarm Optimization Algorithm

The Multi-objective Particle Swarm Optimization (MOPSO) algorithm is designed to solve multi-objective optimization problems. Using two objective functions as an example, each objective has its own optimization goals and constraint conditions. The algorithm operates by simulating particle swarm behavior in solution space, continuously updating particle positions and velocities through iterative processes to identify a set of Pareto-optimal solutions. Key implementation components include: velocity updates using cognitive and social components, position updates based on velocity vectors, and non-dominated sorting for maintaining archive solutions. During each iteration, MOPSO employs crowding distance computation to preserve diversity and leader selection mechanisms to guide particles toward promising regions. This approach enables comprehensive exploration of the solution space and identifies balanced trade-offs between conflicting objectives. The algorithm's core functions involve fitness evaluation, dominance checking, and archive maintenance, making it particularly valuable for engineering applications requiring multi-criteria decision-making.