Optimization Using Genetic Algorithm to Find Minimum Solution for Multivariate Function (Griewank Function)

When solving the minimization problem for multivariate functions (such as the Griewank Function), genetic algorithms can be effectively employed for optimization. Genetic algorithms simulate biological evolution processes through operations like selection, crossover, and mutation to iteratively improve solution quality. The implementation typically involves key components: population initialization with random candidate solutions, fitness evaluation using the Griewank function formula (which contains cosine terms creating numerous local minima), tournament selection for parent selection, crossover operators (like simulated binary crossover) to combine solutions, and mutation operators (such as polynomial mutation) to maintain diversity. For the Griewank function minimization, the algorithm parameters would include population size (typically 50-200 individuals), crossover probability (0.7-0.9), and mutation probability (0.01-0.1). This approach systematically explores the complex search space characterized by the Griewank function's high-dimensional landscape with frequent local minima, ultimately converging toward the global minimum at zero. While demonstrated here for the Griewank function, this methodology can be extended to various similar function optimization problems including Rosenbrock, Rastrigin, and other benchmark functions commonly used in optimization research.