Time constrained optimization

The optimization problem constrained by the expected time allowed to search for an optimal solution is considered in this paper. The work is motivated from the observation that finding a best or reasonably good solution within a time frame is often a primary concern in practice. In the paper, we propose a mathematical formulation for the problem and derive the optimal sequential sampling policies for the problem formulated assuming that the partitioned random search approaches are applied. The results are in general consistent with the experimental results from the early research on the partitioned random search for optimization