Optimal Search For Moving Targets

This book begins with a review of basic results in optimal search for a stationary target. It then develops the theory of optimal search for a moving target, providing algorithms for computing optimal plans and examples of their use. Next it develops methods for computing optimal search plans involving multiple targets and multiple searchers with realistic operational constraints on search movement. These results assume that the target does not react to the search. In the final chapter there is a brief overview of mostly military problems where the target tries to avoid being found as well as rescue or rendezvous problems where the target and the searcher cooperate. Larry Stone wrote his definitive book Theory of Optimal Search in 1975, dealing almost exclusively with the stationary target search problem. Since then the theory has advanced to encompass search for targets that move even as the search proceeds, and computers have developed sufficient capability to employ the improved theory. In this book, Stone joins Royset and Washburn to document and explain this expanded theory of search. The problem of how to search for moving targets arises every day in military, rescue, law enforcement, and border patrol operations.

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 of cells 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 maximizes the probability of detecting the target in a fixed number of time periods. Closely following earlier work by Theodor Stewart, a branch-and-bound procedure is developed which finds optimal search paths. This procedure is tested and appears to be more efficient than existing dynamic programming solution methods. Keywords: Moving targets; Target detection; Searching.

Presents a probabilistic and information-theoretic framework for a search for static or moving targets in discrete time and space. Probabilistic Search for Tracking Targets uses an information-theoretic scheme to present a unified approach for known search methods to allow the development of new algorithms of search. The book addresses search methods under different constraints and assumptions, such as search uncertainty under incomplete information, probabilistic search scheme, observation errors, group testing, search games, distribution of search efforts, single and multiple targets and search agents, as well as online or offline search schemes. The proposed approach is associated with path planning techniques, optimal search algorithms, Markov decision models, decision trees, stochastic local search, artificial intelligence and heuristic information-seeking methods. Furthermore, this book presents novel methods of search for static and moving targets along with practical algorithms of partitioning and search and screening. Probabilistic Search for Tracking Targets includes complete material for undergraduate and graduate courses in modern applications of probabilistic search, decision-making and group testing, and provides several directions for further research in the search theory. The authors: Provide a generalized information-theoretic approach to the problem of real-time search for both static and moving targets over a discrete space. Present a theoretical framework, which covers known information-theoretic algorithms of search, and forms a basis for development and analysis of different algorithms of search over probabilistic space. Use numerous examples of group testing, search and path planning algorithms to illustrate direct implementation in the form of running routines. Consider a relation of the suggested approach with known search theories and methods such as search and screening theory, search games, Markov decision process models of search, data mining methods, coding theory and decision trees. Discuss relevant search applications, such as quality-control search for nonconforming units in a batch or a military search for a hidden target. Provide an accompanying website featuring the algorithms discussed throughout the book, along with practical implementations procedures.

On the solution of an optimal search problem with an exponential detection function. Covers one- and two-sided detection problems by furnishing continuous and discret time strategies; examines two-sided search strategies with solutions in hide and seek games in many discrete and continuous bounded

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Search theory is concerned with the location of a 'target' given imprecise information concerning its location. The subject has a variety of applications such as locating missing people in wilderness or at sea, searching for mineral deposits, medical diagnosis, and searching for malfunctions in industrial processes. This volume is concerned with search strategies which are optimal in the sense that they minimize the 'risk' or cost of a search where this may be measured in factors such as time or money. Consequently, the author discusses a range of mathematical techniques including non-linear programming, fractional programming, dynamic programming, the calculus of variation, and the Pontryagin maximum principle from optimal control theory. Many numerical examples are presented in order to illustrate the effectiveness of particular techniques. As a result, this book will provide all researchers in search theory with an up-to-date account of this important area of operations research.

This paper focuses on the problem of regional cooperative search using multiple unmanned aerial vehicles (UAVs) for targets that have the ability to perceive and evade. When UAVs search for moving targets in a mission area, the targets can perceive the positions and flight direction of UAVs within certain limits and take corresponding evasive actions, which makes the search more challenging than traditional search problems. To address this problem, we first define a detailed motion model for such targets and design various search information maps and their update methods to describe the environmental information based on the prediction of moving targets and the search results of UAVs. We then establish a multi-UAV search path planning optimization model based on the model predictive control, which includes various newly designed objective functions of search benefits and costs. We propose a priority-encoded improved genetic algorithm with a fine-adjustment mechanism to solve this model. The simulation results show that the proposed method can effectively improve the cooperative search efficiency, and more targets can be found at a much faster rate compared to traditional search methods.