Particle Swarm Optimization for Solving the Knapsack Problem

In this assignment, I implemented Particle Swarm Optimization (PSO) to solve the Knapsack Problem. PSO is a metaheuristic optimization algorithm that simulates collective behaviors observed in bird flocks and fish schools to address complex optimization challenges. The MATLAB source code I developed implements key PSO components including: - Particle position and velocity initialization representing potential solutions - Fitness function evaluation based on knapsack constraints and objective values - Personal best (pbest) and global best (gbest) tracking mechanisms - Velocity update equations incorporating cognitive and social components - Position update logic with boundary handling for valid solutions The accompanying technical report provides comprehensive documentation of: - Problem formulation for the binary knapsack optimization - PSO parameter tuning strategies (inertia weight, acceleration coefficients) - Convergence analysis and performance metrics - Comparative evaluation of solution quality and computational efficiency The report further examines PSO's advantages in global search capability and implementation simplicity, while addressing limitations such as premature convergence. Additional discussions explore PSO's applicability to other combinatorial optimization problems. Through this project, I gained deeper insights into metaheuristic optimization techniques and enhanced my MATLAB programming skills, particularly in algorithm implementation and performance analysis for complex problem domains.