The search for an alerted moving target

We investigate a two-sided, multi-stage search problem where a continuous search effort is made by one or more search units to detect a moving target in a continuous target space, under noisy detection conditions. A specific example of this problem is hunting for an enemy submarine by naval forces. So far, this problem has not been solved, because of the difficulty of predicting the target's behaviour. In finding promising routes for the search units, a heuristic has been developed. To obtain these routes, at every decision moment in time an optimal point to go to must be determined. This amounts to finding at every decision moment an optimum of a function that changes over time.