Piled-slab searches

This paper deals with the conflict between simplicity and optimality in searching for a stationary target whose location is distributed in two dimensions, thus continuing an analysis that was begun in World War II. The search is assumed to be of the ‘piled-slab’ type, where each slab consists of a uniform search of some simple region. The measure of simplicity is the number of regions (smaller is simpler). If each of a fixed number of elliptical regions is searched randomly, we find the optimal region size and the optimal division of effort between regions. Rectangular regions are also considered, as are problems where the regional searches are according to the inverse-cube law, instead of random search. There is a strong tendency for optimal inverse-cube law searches to consist of a single slab. We also consider problems where the amount of effort for each region is optimized myopically, with no consideration for the search of future regions.