Path optimization for the resource-constrained searcher

Naval Research Logistics, 1996

The search theory open literature has paid little, if any, attention to the multiple-searcher, moving-target search problem. We develop an optimal branch-and-bound procedure and six heuristics for solving constrained-path problems with multiple searchers. Our optimal procedure outperforms existing approaches when used with only a single searcher. For more than one searcher, the time needed to guarantee an optimal solution is prohibitive. Our heuristics represent a wide variety of approaches: One solves partial problems optimally, two use paths based on maximizing the expected number of detections, two are genetic algorithm implementations, and one is local search with random restarts. A heuristic based on the expected number of detections obtains solutions within 2% of the best known for each one-, two-, and three-searcher test problem considered. For one-and two-searcher problems, the same heuristic's solution time is less than that of other heuristics. For threesearcher problems, a genetic algorithm implementation obtains the best-known solution in as little as 20% ofother heuristic solution times. 0 1996 John Wiley & Sons, Inc. The constrained-path, moving-target search problem [ 6 , 15, 161 has the following characteristics: 0 A single searcher and target move among a finite set of cells in discrete time. 0 The searcher and target occupy only one cell each time period. 0 Each time period, the searcher moves from its current cell to one of a specified 0 The target moves among cells according to a specified stochastic process. 0 If the target occupies the searched cell, the random search formula determines the probability of detection-otherwise the detection probability is zero. 0 The target's probability distribution is Bayesian updated for nondetection each time period.

2012

Discrete static open-loop target search path planning is known to be a NP (non-deterministic polynomial) -Hard problem, and problem-solving methods proposed so far rely on heuristics with no way to properly assess solution quality for practical size problems. Departing from traditional nonlinear model frameworks, a new integer linear programming (ILP) exact formulation and an approximate problem-solving method are proposed to near-optimally solve the discrete static search path planning problem involving a team of homogeneous agents. Applied to a search and rescue setting, the approach takes advantage of objective function separability to efficiently maximize probability of success. A network representation is exploited to simplify modeling, reduce constraint specification and speed-up problem-solving. The proposed ILP approach rapidly yields near-optimal solutions for realistic problems using parallel processing CPLEX technology, while providing for the first time a robust upper bound on solution quality through Lagrangean programming relaxation. Problems with large time horizons may be efficiently solved through multiple fast subproblem optimizations over receding horizons. Computational results clearly show the value of the approach over various problem instances while comparing performance to a myopic heuristic.

Naval Research Logistics, 1995

A search is conducted for a target moving in discrete time among a finite number of cells according to a known Markov process. The searcher must choose one cell in which to search in each time period. The set ofcells available for search depends upon the cell chosen in the last time period. The problem is to find a search path, i.e., a sequence of search cells, that either maximizes the probability ofdetection or minimizes the mean number oftime penods required for detection. The search problem is modelled as a partially observable Markov decision process and several approximate solutions procedures are proposed. 0 search for efficient approximate solution procedures. Washburn [ 15 ] generalized Brown's algorithm to find approximate solutions when there are no path constraints. Stewart [ 121 used branch-and-bound methods and Brown's algorithm to obtain approximate solutions when both discrete effort and path constraints are allowed. Eagle and Yee [ 51 extended Stewart's work and obtained a branch-and-bound method that gives optimal solutions. An alternative approach for finding optimal solutions, suggested by Smallwood and Sondik [lo] and extended by Eagle [4], is to model the problem as a partially observable Markov decision process. This is the approach investigated here. Monahan's survey article [ 81 outlines the properties of partially observable Markov decision processes, and Lovejoy [ 71 describes the algorithms used to solve them. The difficulty with using this approach is that value iteration, which is the usual solution algorithm, takes too long and needs too much storage for some large problems. Lovejoy [ 61 attempts to overcome this difficulty by developing bounds on the iterates that are easier to calculate. Our objective is the same. We describe easy-to-calculate starting values for value iteration, as well as a pruning procedure similar to Lovejoy's bounds but developed independently.

The procedure presented within, considers the problem of calculating flight time for unmanned aerial vehicles (UAVs) while incorporating a subset of important flight dynamics characteristics in an operational field, which contains obstacles. These flight time calculations are parameter inputs in mission planning and dynamic reassignment problems. The addition of pseudonodes and the addition of penalties into the associated edge weights are the basis for how the network generation procedure includes flight dynamics. The procedure includes a method for handling pop-up targets or obstacles in a dynamic reassignment problem. To guarantee that the optimal path includes flight dynamics, a selective Dijkstra's algorithm computes the shortest path. A complex mission plan consisting of thirty targets and three obstacles is the largest test scenario of nine developed scenarios. Our network generation procedure along with the shortest path calculations of all 992-node pairs of interest solves in approximately one second. This procedure allows for the fast computation needed to generate parameters for use in a dynamic domain such as mission planning and dynamic reassignment algorithms.

Proceedings of the 12th International Conference on Information Fusion, 2009

In this paper, the problem of path planning for a ground search unit looking for an object of unknown location is considered. As in the classical optimal searcher path problem, the probability of finding the search object is the main criterion of optimality and the search unit is constrained by the environment topology that influences its choices for a navigable path as well as its detection capabilities. This paper proposes an extension to the classical optimal searcher path problem in discrete time and space by integrating inter-region visibility as an additional criterion. This new formulation allows a refinement in the discretization of the space in which a ground search unit evolves. A general mixed-integer programming model is proposed, and experimental results with a moving object in grid environments are discussed.

European Journal of Operational Research, 2008

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.

2006

This paper presents the 3D shortest path searching algorithms in the volumes with O(N) of time and memory space complexities based on the nuclear fission chain reactions scheme, where N is the number of voxels in the grid space. Furthermore, the proposed algorithm is extended to the 3D shortest path searching for multiple pairs based on the concept of the aircraft domain to avoid collision and chasing algorithm in the volumes with the time complexity of O(qN) and O(N 2 /a), respectively, where q is the number of aircraft and a is the relative speed ratio of chaser to target. The concept of these algorithms can be applied to GIS (Geographic Information System), search and interception for aircrafts, and cruise missile interception system.

Naval Research Logistics (NRL), 2010

We consider a discrete time-and-space route-optimization problem across a finite time horizon in which multiple searchers seek to detect one or more probabilistically moving targets. The paper formulates a novel convex mixed-integer nonlinear program for this problem that generalizes earlier models to situations with multiple targets, searcher deconfliction, and target-and location-dependent search effectiveness. We present two solution approaches, one based on the cutting-plane method and the other on linearization. These approaches result in the first practical exact algorithms for solving this important problem, which arises broadly in military, rescue, law enforcement, and border patrol operations. The cutting-plane approach solves many realistically sized problem instances in a few minutes, while existing branch-and-bound algorithms fail. A specialized cut improves solution time by 50% in difficult problem instances. The approach based on linearization, which is applicable in important special cases, may further reduce solution time with one or two orders of magnitude. The solution time for the cutting-plane approach tends to remain constant as the number of searchers grows. In part, then, we overcome the difficulty that earlier solution methods have with many searchers.

Military Operations Research, 2009

We formulate and solve aircraft-routing problems that arise when planning missions for military aircraft that are subject to ground-based threats such as surface-to-air missiles. We use a constrained-shortest path (CSP) model that discretizes the relevant airspace into a grid of vertices representing potential waypoints, and connects vertices with directed edges to represent potential flight segments. The model is flexible: It can route any type of manned or unmanned aircraft; it can incorporate any number of threats; and it can incorporate, in the objective function or as side constraints, numerous mission-specific metrics such as risk, fuel consumption, and flight time. We apply a new algorithm for solving the CSP problem and present computational results for the routing of a high-altitude F/A-18 strike group, and the routing of a medium-altitude unmanned aerial vehicle. The objectives minimize risk from ground-based threats while constraints limit fuel consumption and/or flight time. Run times to achieve a near-optimal solution range from fractions of a second to 80 seconds on a personal computer. We also demonstrate that our methods easily extend to handle turn-radius constraints and round-trip routing.

International Journal of Aerospace Engineering, 2017

A path planning strategy for a search and coverage mission for a small UAV that maximizes the area covered based on stored energy and maneuverability constraints is presented. The proposed formulation has a high level of autonomy, without requiring an exact choice of optimization parameters, and is appropriate for real-time implementation. The computed trajectory maximizes spatial coverage while closely satisfying terminal constraints on the position of the vehicle and minimizing the time of flight. Comparisons of this formulation to a path planning algorithm based on those with time constraint show equivalent coverage performance but improvement in prediction of overall mission duration and accuracy of the terminal position of the vehicle.