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.

Eugene Kagan, Department of Applied Mathematics and Computer Science, Weizmann Institute of Science, Israel

Irad Ben-Gal, Department of Industrial Engineering, Tel-Aviv University, Israel

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.

List of figures xi

Preface xv

Notation and terms xvii

1 Introduction 1

1.1 Motivation and applications 4

1.2 General description of the search problem 5

1.3 Solution approaches in the literature 7

1.4 Methods of local search 11

1.5 Objectives and structure of the book 14

References 15

2 Problem of search for static and moving targets 19

2.1 Methods of search and screening 20

2.1.1 General definitions and notation 20

2.1.2 Target location density for a Markovian search 24

2.1.3 The search-planning problem 30

2.2 Group-testing search 55

2.2.1 General definitions and notation 56

2.2.2 Combinatorial group-testing search for static targets 63

2.2.3 Search with unknown number of targets and erroneous observations 71

2.2.4 Basic information theory search with known location probabilities 84

2.3 Path planning and search over graphs 108

2.3.1 General BF* and A* algorithms 109

2.3.2 Real-time search and learning real-time A* algorithm 122

2.3.3 Moving target search and the fringe-retrieving A* algorithm 131

2.4 Summary 140

References 140

3 Models of search and decision making 145

3.1 Model of search based on MDP 146

3.1.1 General definitions 146

3.1.2 Search with probabilistic and informational decision rules 152

3.2 Partially observable MDP model and dynamic programming approach 161

3.2.1 MDP with uncertain observations 162

3.2.2 Simple Pollock model of search 166

3.2.3 Ross model with single-point observations 174

3.3 Models of moving target search with constrained paths 179

3.3.1 Eagle model with finite and infinite horizons 180

3.3.2 Branch-and-bound procedure of constrained search with single searcher 184

3.3.3 Constrained path search with multiple searchers 189

3.4 Game theory models of search 192

3.4.1 Game theory model of search and screening 192

3.4.2 Probabilistic pursuit-evasion games 201

3.4.3 Pursuit-evasion games on graphs 206

3.5 Summary 214

References 215

4 Methods of information theory search 218

4.1 Entropy and informational distances between partitions 219

4.2 Static target search: Informational LRTA* algorithm 227

4.2.1 Informational LRTA* algorithm and its properties 228

4.2.2 Group-testing search using the ILRTA* algorithm 234

4.2.3 Search by the ILRTA* algorithm with multiple searchers 244

4.3 Moving target search: Informational moving target search algorithm 254

4…