Genetic Algorithm Toolbox Functions and Practical Example Explanation

This tutorial demonstrates MATLAB's Genetic Algorithm Toolbox functions through a practical optimization case. The problem requires minimizing the function f(x1,x2) = -20*exp(-0.2*sqrt(0.5*(x1^2+x2^2))) - exp(0.5*(cos(2πx1)+cos(2πx2))) + 22.71282 within the bounded domain -5≤Xi≤5 for i=1,2. Genetic algorithms represent optimization techniques inspired by natural evolution processes, utilizing selection, crossover, and mutation operations to converge toward optimal solutions. This explanation details how to implement this minimization problem using MATLAB's Global Optimization Toolbox, specifically focusing on ga() function configuration. Key implementation aspects include: defining the objective function using function handles, setting boundary constraints via lb and ub vectors, configuring algorithm parameters (population size, generations, crossover rate), and interpreting convergence plots. The tutorial will demonstrate proper fitness function formatting, constraint handling, and result visualization techniques essential for effective genetic algorithm application in mathematical optimization scenarios. The solution approach involves encoding decision variables as chromosomes, implementing fitness evaluation through vectorized operations, and utilizing MATLAB's built-in operators for efficient evolutionary computation. Special attention will be given to penalty methods for constraint satisfaction and convergence criteria specification for termination conditions.