APPLICATION OF DIRECT SEARCH OPTIMIZATION TO OPTIMAL-CONTROL PROBLEMS

Application of the direct search optimization procedure as proposed by LUUS and JAAKOLA [1], using randomly chosen numbers and systematic se arch region contraction, is investigated for the optimal control of fo ur widely different problems. The dimensionality by itself does riot a ppear to be an obstacle for the Luus-Jaakola (LJ) direct search proced ure in obtaining convergence to the immediate vicinity of the optimum, as illustrated by a system having 30 state variables and 30 control v ariables, even when a relatively small number of random points are use d. The effect of the number of random points used in the search is fur ther investigated by considering two highly nonlinear chemical enginee ring optimization problems. In the presence of state constraints speci al considerations may be necessary as illustrated by the problem of op timal drug scheduling in cancer chemotherapy, where better results tha n previously reported in literature are obtained.