Finding Extrema Using Genetic Algorithms

Please examine carefully my implementation of a genetic algorithm program that solves for the extremum of f(x) = x*sin(10π*x) + 2.0, where x is constrained to the interval from -1 to 2. The algorithm's objective is to find the optimal solution through genetic optimization processes, utilizing key operations including chromosome encoding, fitness evaluation, selection, crossover, and mutation. Genetic algorithms simulate natural evolutionary processes by mimicking genetic crossover, mutation, and selection mechanisms to iteratively improve solution quality. In this implementation, I've employed real-value encoding for chromosome representation and incorporated tournament selection with simulated binary crossover (SBX) and polynomial mutation operations. The fitness function directly evaluates f(x) values, while maintaining population diversity through elitism preservation. This program demonstrates core genetic algorithm concepts and can be adapted to similar optimization problems, with particular attention to handling the trigonometric function's multiple local extrema within the specified domain. The code structure includes initialization routines for generating the initial population, fitness evaluation functions, and iterative optimization loops that terminate upon reaching convergence criteria or maximum generations. This approach effectively balances exploration and exploitation to locate global optima in complex search spaces.