Research on Mathematical Modeling and Solution Method of Complex System Based on Multi-Objective Optimization Algorithm

Complex systems, due to their intrinsic nonlinearity, strong coupling and multi-objective characteristics, make mathematical modeling and solving an important challenge in theoretical research and practical applications. Multi-objective optimization algorithms, as an important tool for solving such problems, have received extensive attention and in-depth research in recent years. With the development of modern system synergization and integration, the resource interaction between systems and between systems and the environment is more and more frequent, and the systems are more and more systematized and networked. The system design method based on MBSE faces the challenges of interdisciplinarity and interdisciplinarity, and it is necessary to extend the system design method based on MBSE to the structural design of the system to cope with the demand of the structural design of the system under the complex scenarios, and systematically expounds the modeling method of multi-objective optimization problem; in view of the limitations of the classical multi-objective optimization algorithm in solving the problems of the complex system, the optimization algorithm with stronger adaptability and efficiency is designed and improved, and experimentally verified. In view of the limitations of classical multi-objective optimization algorithms in solving complex system problems, an optimization algorithm with stronger adaptability and efficiency is designed and improved, and its superior performance in terms of convergence and diversity is verified through experiments. The results show that the improved optimization algorithm is not only able to effectively deal with the multi-objective conflict problem of complex systems, but also has significant improvement in the model solving efficiency and solution quality. This paper provides new theoretical support and technical means for mathematical modeling and solving of complex systems, and points out the direction for further research in related fields.