Determination of an optimal control strategy for drug administration in tumor treatment using multi-objective optimization differential evolution

• To formulate and to solve a multi-objective optimal control problem applied to treatment of tumors.
• To minimize the cancerous cells concentration and the drug concentration.
• The results demonstrated that an optimal protocol can be obtained considering both objectives.

The mathematical modeling of physical and biologic systems represents an interesting alternative to study the behavior of these phenomena. In this context, the development of mathematical models to simulate the dynamic behavior of tumors is configured as an important theme in the current days. Among the advantages resulting from using these models is their application to optimization and inverse problem approaches. Traditionally, the formulated Optimal Control Problem (OCP) has the objective of minimizing the size of tumor cells by the end of the treatment. In this case an important aspect is not considered, namely, the optimal concentrations of drugs may affect the patients' health significantly. In this sense, the present work has the objective of obtaining an optimal protocol for drug administration to patients with cancer, through the minimization of both the cancerous cells concentration and the prescribed drug concentration. The resolution of this multi-objective problem is obtained through the Multi-objective Optimization Differential Evolution (MODE) algorithm. The Pareto's Curve obtained supplies a set of optimal protocols from which an optimal strategy for drug administration can be chosen, according to a given criterion.