An optimal drug delivery policy for cancer chemotherapy is determined by direct search optimization based on random numbers and region contraction, so that the size of a cancerous tumour is minimized at the end of a given time interval. Due to the large number of state constraints and the threshold function in the state equation, direct search optimization appears to be most appropriate. However, because of the high dimensionality, a sequence of computer runs was necessary to establish the optimal control policy. The results from a previous run were used to establish the conditions for the following run. The results were thus improved from one run to the next until the global optimal control policy was established. The results obtained are significantly better than have been previously reported for this problem, and show the difficulties that may be encountered in the optimization of high-dimensional nonlinear systems.