In recent years much work has been don; on modelling the growth of malignant tumours with a view to predicting their development and optimizing the effect of chemotherapy on their alleviation. One approach has been to treat the tumour as a non‐linear system and the drug treatment as a control strategy. This has led to the use of calculus of variations and optimization techniques to produce optimal and sub‐optimal drug regimes. This paper uses the Gompertz equation as a model of tumour growth and attempts to minimize final tumour size in the presence of drug constraints. The optimization technique is novel in that it uses the genetic algorithm method to devise optimal drug regimes where individual regimes are encoded as ‘chromosomes’ and evolution is simulated in order to improve treatment strategies.