Neural Network Genetic Algorithm for Extreme Value Optimization

Finding extremum points of nonlinear functions through optimization algorithms represents a crucial challenge in computational mathematics and engineering. In mathematical modeling and engineering applications, identifying maximum or minimum values of functions is essential for solving complex optimization problems. Various optimization techniques—such as gradient descent, genetic algorithms, and simulated annealing—can effectively locate extreme values of nonlinear functions. The selection of appropriate algorithms and parameter tuning significantly impacts the accuracy of extremum identification, requiring careful consideration during implementation. Genetic algorithms, for instance, employ population-based search mechanisms with crossover and mutation operations to explore solution spaces, while gradient-based methods utilize derivative information for iterative convergence. Through continuous refinement of algorithm design and parameter optimization, we can enhance both efficiency and precision in locating extremum points of nonlinear functions. Key implementation considerations include fitness function design for genetic algorithms and learning rate selection for gradient-based methods.