Function Optimization Algorithm Based on Genetic Algorithm and Nonlinear Programming

When addressing optimization problems, we employ a dual-algorithm strategy combining genetic algorithms (GA) and nonlinear programming (NLP). Genetic algorithms perform global searching through population-based evolutionary operations (selection, crossover, mutation), while nonlinear programming algorithms conduct precise local optimization using gradient-based methods. By integrating these two approaches, we obtain globally optimal solutions with balanced exploration and exploitation capabilities. Key implementation aspects include: - Genetic Algorithm Component: Initializes a population of candidate solutions, evaluates fitness functions, and evolves solutions through generations using genetic operators. Termination criteria typically involve maximum generations or convergence thresholds. - Nonlinear Programming Component: Refines promising solutions from GA using techniques like sequential quadratic programming (SQP) or interior-point methods, leveraging derivative information for rapid local convergence. Notably, both algorithms operate through iterative improvement mechanisms. These hybrid optimization techniques have proven effective across industrial design, financial modeling, scientific research, and technological applications. When selecting algorithms, professionals must evaluate problem characteristics (multimodality, constraints, dimensionality) and algorithm properties (global convergence rate, local precision, computational overhead) to determine the optimal strategy for specific scenarios.