Reinforcement learning techniques offer a very powerful method of finding solutions in unpredictable problem environments where human supervision is not possible. However, in many real world situations, the state space needed to represent the solutions becomes so large that using these methods becomes infeasible. Often the vast majority of these states are not valuable in finding the optimal solution. This work introduces a novel method of using linear programming to identify and represent the small area of the state space that is most likely to lead to a near-optimal solution, significantly reducing the memory requirements and time needed to arrive at a solution. An empirical study is provided to show the validity of this method with respect to a specific problem in vehicle dispatching. This study demonstrates that, in problems that are too large for a traditional reinforcement learning agent, this new approach yields solutions that are a significant improvement over other nonlearning methods. In addition, this new method is shown to be robust to changing conditions both during training and execution. Finally, some areas of future work are outlined to introduce how this new approach might be applied to additional problems and environments.

This thesis concerns solutions to problems that arise in optimizing fixed interval scheduling under situations of uncertainty such as when there are random delays in job process times. These problems can be solved by using a vertex coloring with random edges and problems can be formulated using integer linear, quadratic and stochastic programming. In this thesis is propo- sed a new integer linear formulation. Under certain conditions there is proved its equivalence with stochastic formulation, where is maximized the schedule reliability. Moreover, we modified the proposed formulation to obtain bet- ter corresponding to real life situations. In a numerical study we compared computational time of individual formulations. It turns out that the propo- sed formulation is able to solve scheduling problems considerably faster than other formulations. 1