Research on nonlinear optimization problem solving and model performance improvement based on adaptive genetic algorithm

Nonlinear optimization problems exist widely in many fields, and its complex structure and nonlinear objective function make it difficult for traditional optimization methods to work. Adaptive Genetic Algorithm (AGA) can effectively balance global search and local search capabilities by dynamically adjusting key parameters such as crossover rate and mutation rate, and avoid falling into local optimal solution. This paper first introduces the design of AGA, including real number coding, fitness function design, adaptive crossover and mutation operation and roulette wheel selection method. The performance of AGA is compared with traditional GA and particle swarm optimization (PSO) through the experimental verification of Rastrigin function. The results show that AGA is significantly superior to other algorithms in global search ability and stability, but there is some computational overhead. In order to further improve the performance of the model, this paper optimizes the parameter range through grid search, dynamically adjusts the mutation intensity, and embeds local search strategy. The improved AGA shows faster convergence speed and higher solution accuracy on high-dimensional problems. The research results show that AGA can effectively balance exploration and development through dynamic parameter adjustment, significantly improve the global search ability and stability, and provide an efficient method for solving complex nonlinear optimization problems.