Nonlinear Integer Programming Problems with Genetic Algorithm Implementation

In mathematics and computer science, nonlinear integer programming represents a significant research domain focused on identifying optimal solutions under specific constraints to maximize or minimize objective functions. Genetic algorithms provide an effective computational approach for solving such problems by simulating biological evolutionary processes to search for optimal solutions within population sets. MATLAB implementations leverage genetic algorithm programming to enhance computational efficiency and solution accuracy through key functions like population initialization, fitness evaluation, crossover operations, and mutation mechanisms. The algorithm typically involves encoding integer variables as chromosomes, applying selection pressure based on fitness scores, and employing genetic operators to evolve solutions across generations. Practical implementation includes constraint handling techniques, termination criteria configuration, and parameter tuning for convergence optimization, making it particularly suitable for complex nonlinear problems where traditional methods face limitations.