Discounted MEAN bound for the optimal searcher path problem with non-uniform travel times

Abstract

We consider an extension of the optimal searcher path problem (OSP), where a searcher moving through a discretised environment may now need to spend a nonuniform amount of time travelling from one region to another before being able to search it for the presence of a moving target. In constraining not only where but when the search of each cell can take place, the problem more appropriately models the search of environments which cannot be easily partitioned into equally-sized cells. An existing OSP bounding method in literature, the MEAN bound, is generalised to provide bounds for solving the new problem in a branch and bound framework. The main contribution of this paper is an enhancement, Discounted MEAN (DMEAN), which greatly tightens the bound for the new and existing problems alike with almost no additional computation. We test the new algorithm against existing OSP bounding methods and show it leads to faster solution times for moving target search problems.

Path optimization for the resource‐constrained searcher

“…Hence, the glimpse detection probability during time period t depends on the previous and current waypoints for the searcher. This is a generalization of earlier models where the glimpse detection probability depends only on v and t [25,17]. Our model accounts for the fact that moving from some waypoint to a new waypoint may result in a lower glimpse detection probability than if the searcher already was loitering at the latter waypoint.…”

“…Bounds on the optimal value of the problem are obtained by replacing the probability of detection with, effectively, the expected number of detections [8,25,17]. Bounds are also obtained by assuming that the searcher can divide its effort among multiple cells each time period [11].…”

“…These studies as well as more recent ones [11,18,8,25,17] focus on the development of specialized branch-and-bound algorithms for finding an optimal path for the searcher. In these algorithms, a path is a sequence of cells that the searcher will visit and branching corresponds to extending a subpath by one more cell.…”

“…We combine the methodology for solving the path-and time-constrained search problem with the line of research on the resource-constrained shortest-path problem. Specifically, we merge the algorithms in [17] and [6], and develop a specialized branch-and-bound algorithm for RCSP. The resulting algorithm utilizes a new bounding technique, applies several network reduction procedures, exhibits promising behavior in computational tests, and appears to be easier to implement efficiently than the algorithm in [17].…”

The eye and the fist: Optimizing search and interdiction

“…The field of classical search theory, addressing the problem of optimal search for static or mobile targets, has been extensively studied for over seven decades, since the groundbreaking research of Koopman [4], through the seminal works of Washburn [5] and Stone [6], to the recent surge in publications; for example see [7][8][9][10][11][12][13][14][15][16][17][18][19]. The problem of coordinating search and interception-the topic of this paper-is more involved.…”