The multi-factor evolutionary algorithm (MFEA) is mainly studied and improved. The mixed probability distribution of the offspring population optimized by the maximum mean difference method (MMD) is used as the metric criterion of the algorithm. MFEA-MMD is improved on the basis of the Random Mating Probability matrix (RMP) of MFEA-II algorithm to avoid the influence of negative transfer most common in multi-factor evolutionary algorithms to the greatest extent. The convergence rate of the MFEA-MMD is faster than that of MFEA-II. The operation speed of the algorithm is 29% higher than that of MFEA-II, and the degree of knowledge transfer between tasks is 35% higher than that of MFEA-II.

Tumor metastasis is an important link in the process of tumor development, and it is also one of the main reasons for cancer deterioration and treatment failure. Taking tumor metastasis as the background, a study is conducted on the generative model of tumor lymphatics based on the interaction between tumor and extracellular matrix (ECM). First, mathematical language is used to sort out the biological principles of tumor lymphangiogenesis, and then assumptions made and mathematical models established and qualitative analysis carried out. The proof of the uniqueness of the existence of local solutions of the model is mainly carried out by means of approximation methods, the qualitative theory of partial differential equations and Banach's immovable point theorem, as well as the uniqueness of the existence of the overall solution of the model with the help of the regularity estimate of the local solution and the embedding inequality. Finally, the difference numerical method is used to carry out numerical simulation to illustrate the reliability and accuracy of the model. This research is of great significance for in-depth understanding the mechanism of tumor metastasis, guiding cancer treatment, and promoting related research.

In this study, a multi-scale mathematical model of the tumor immune microenvironment was developed, combined with experimental data from mouse models to investigate the regulatory mechanisms of combined therapy using the prostaglandin E2 receptor 4 (EP4) antagonist MF-766 and anti-programmed cell death protein 1 (anti-PD-1) on tumor immune microenvironment and tumor growth. The model quantitatively analyzed the dynamic changes in immunosuppressive cells, effector immune cells, and cytokines, revealing the synergistic effects of the combined therapy in reducing the concentration of myeloid-derived suppressor cells (MDSCs) and enhancing the function of effector immune cells. Experimental validation demonstrated that the model accurately described the dynamic changes in tumor volume and the immunomodulatory effects of the drugs. Furthermore, it revealed the nonlinear impact of drug dosage and dosing intervals on therapeutic efficacy. The simulation results not only deepened the understanding of the mechanisms of tumor metastasis but also provided a theoretical foundation for optimizing the dosage and dosing strategies of immunotherapy. This study lays a solid groundwork for the design and advancement of precision medicine.