Optimization of Chemotherapy Using Hybrid Optimal Control and Swarm Intelligence

Abstract

This study aimed to minimize the tumor cell population using minimal medicine for chemotherapy treatment, while maintaining the effector-immune cell population at a healthy threshold. Therefore, a mathematical model was developed in the form of ordinary differential equations (ODE), and the solution to the Multi-Objective Optimal Control Problem (MOOCP) was obtained using Multi-Objective Optimization algorithms. In this study, the interaction of the tumor cell and effector cell populations with chemotherapy was investigated using Pure MOOCP and Hybrid MOOCP methods. The handling of constraints and the Pontryagin Maximum Principle (PMP) differ among these methods. Swarm Intelligence (SI) and Evolutionary Algorithms (EA) were used to process the results of these methods. The numerical outcomes of SI and EA are displayed via the Pareto Optimal Front. In addition, the solutions from these algorithms were further analyzed using the Hypervolume Indicator. The findings of this study demonstrate that the Hybrid Method outperforms Pure MOOCP via Multi-Objective Differential Evolution (MODE). MODE produces a point on the Pareto Optimal Front with a minimal distance to the origin, where the distance represents the best solution.

Keywords

• Multi-objective optimal control problem
• Pontryagin maximum principle
• swarm intelligence
• evolutionary algorithms