Finding the Minimum Value of f(x)=x²-22x+30 Using Standard Genetic Algorithm

This implementation demonstrates how to use standard genetic algorithm in MATLAB to find the minimum value of the function f(x)=x²-22x+30, where x is constrained to the interval [0,31]. The algorithm utilizes key genetic operations including selection, crossover, and mutation to evolve a population of candidate solutions toward the optimal value. The MATLAB code implements a complete genetic algorithm workflow: initial population generation, fitness evaluation using the quadratic function, tournament selection for parent selection, single-point crossover for offspring creation, and bit-flip mutation to maintain diversity. The algorithm continues through multiple generations until convergence criteria are met. Full source code and optimization results are provided below, showing how the genetic algorithm effectively locates the global minimum of this quadratic function. This approach demonstrates the application of evolutionary computation for mathematical optimization problems, providing both the optimal solution value and the corresponding x-coordinate that minimizes the function. The implementation includes proper parameter settings such as population size, crossover rate, mutation rate, and termination conditions, ensuring efficient convergence to the optimal solution while exploring the defined search space comprehensively.