Research on Solving Mathematical Programming Problems Based on Intelligent Optimization Algorithms

This paper studies the solution methods of mathematical programming problems based on intelligent optimization algorithms, focusing on the application and performance of GA and PSO in complex mathematical programming. First, a hybrid intelligent algorithm that integrates the characteristics of genetic algorithm and particle swarm optimization is designed. By optimizing the coding structure, selection strategy and crossover mutation operator, the global search ability and convergence speed of the algorithm are improved. Secondly, a mathematical model suitable for integer programming and nonlinear programming is constructed, and experimental verification of problems of different scales is carried out in combination with the simulation platform. Experiments show that in typical test functions and actual application scenarios, the improved algorithm improves the solution accuracy by 15.3% and shortens the convergence time by 18.7<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">%</sup> compared with the traditional method. The simulation results prove the effectiveness and robustness of the improved algorithm through quantitative data analysis, especially in solving high-dimensional nonlinear problems. The research in this paper not only expands the application of intelligent optimization algorithms in the field of mathematical programming, but also provides a theoretical basis and practical reference for solving actual engineering optimization problems.