Background: This study explores the dynamics of a mathematical model, utilizing ordinary differential equations (ODE), to depict the interplay between cancer cells and effector cells under chemotherapy. The stability of the equilibrium points in the model is analysed using the Jacobian matrix and eigenvalues. Additionally, bifurcation analysis is conducted to determine the optimal values for the control parameters.
Objective: To evaluate the performance of the model and control strategies, benchmarking simulations are performed using the PlatEMO platform.
Methods: The Pure Multi-objective Optimal Control Problem (PMOCP) and the Hybrid Multi-objective Optimal Control Problem (HMOCP) are two different forms of optimal control problems that are solved using revolutionary metaheuristic optimisation algorithms. The utilization of the Hypervolume (HV) performance indicator allows for the comparison of various metaheuristic optimization algorithms in their efficacy for solving the PMOCP and HMOCP.
Results: Results indicate that the MOPSO algorithm excels in solving the HMOCP, with M-MOPSO outperforming for PMOCP in HV analysis.
Conclusion: Despite not directly addressing immediate clinical concerns, these findings indicates that the stability shifts at critical thresholds may impact treatment efficacy.
Keywords: Multi-objective optimal control problem; bifurcation analysis; metaheuristic optimization algorithms; stability analysis.