A discrete optimisation approach for target path planning whilst evading sensors

In this paper we deal with a practical problem that arises in military situations. The problem is to plan a path for one (or more) agents to reach a target without being detected by enemy sensors. Agents are not passive, rather they can (within limits) initiate actions which aid evasion, namely knockout (completely disable sensors) and confusion (reduce sensor detection probabilities). Agent actions are path dependent and time limited. Here by path dependent we mean that an agent needs to be sufficiently close to a sensor to knock it out. By time limited we mean that a limit is imposed on how long a sensor is knocked out or confused before it reverts back to its original operating state. The approach adopted breaks the continuous space in which agents move into a discrete space. This enables the problem to be represented (formulated) mathematically as a zero-one integer program with linear constraints. The advantage of representing the problem in this manner is that powerful commercial software optimisation packages exist to solve the problem to proven global optimality. Computational results are presented for a number of randomly generated test problems.