Optimal drug regimens in cancer chemotherapy: a multi-objective approach.

In this paper, based on two mathematical models, a set of optimal anticancer drug regimens is designed. Two important difficulties in treating cancers with chemotherapy are drug resistance and toxicity. They were considered in our treatment design; a compartmental model was extended to appropriately describe drug resistance and two constraints were imposed on the value of the anticancer drug dynamics to avoid toxicity. Indeed, we optimized two objective functions simultaneously in order to minimize the size of the tumor as well as the side effects of the anticancer drug on the patient's body. Operating the described task, a bi-objective optimization problem was defined and solved by an evolutionary method. This optimization led to a set of optimal drug regimens, which can be used in several chemotherapy treatments. Numerical simulations were given to illustrate the flexibility of the method.