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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.

Inhaltsverzeichnis

Frontmatter

Introduction

Abstract
Search theory, one of the oldest areas of operations research, has continuously provided powerful support for planning efficient search operations in real-world applications. The aim of the searcher is to efficiently find the target in his search operations, and analysts are asked to offer theoretical bases for optimal planning of the search. The search theory makes many valuable contributions to the study of the optimal solutions of search problems by applying optimization techniques, such as nonlinear programming, fractional programming, dynamic programming, calculus of variations, and the maximum principle of optimal control theory. We begin by providing a short survey of search theory.
Kōji Iida

Chapter 1. Optimal Search Plan for a Stationary Target Minimizing the Expected Risk

Abstract
In this chapter, we investigate an optimal search plan for a stationary target that minimizes the expected risk with a definite amount of continuous searching effort per unit time.
Kōji Iida

Chapter 2. Optimal Search Plan for a Moving Target

Abstract
In this chapter, we investigate an optimal search plan for a moving target that maximizes the detection probability of the target or minimizes the expected risk.
Kōji Iida

Chapter 3. Optimal Whereabouts Search Plan Minimizing the Expected Risk

Abstract
Imagine a search-and-rescue situation in which it is known that a lost party in a mountain can survive no longer than T units of time in the environment. If the searcher finds the party in some subarea up to T, the rescue can be effected immediately. If the party is not found until T, the rescue effort is assigned to some subarea; really it is a bet. The rescue will be successful if the lost party is in fact in the subarea. In analyzing this and similar situations, we will consider the following search model.
Kōji Iida

Chapter 4. Optimal Investigating Search Plan for Contacts in Two-Stage Search

Abstract
In the previous sections, we have investigated the optimal search plan in various search situations without considering the possibility of false contacts. In this chapter, a noisy search model will be dealt with. In the noisy search, the detection device of the searcher sometimes gives false alarms of the target, and hence the second stage of search is needed to ascertain whether the detection is true or not. The first- and the second-stage search are called the broad search and the investigating search, respectively.
Kōji Iida

Chapter 5. Forestalling Detection in Two-Sided Search

Abstract
In this chapter, we will investigate a forestalling detection problem in a two-sided search situation. At present, studies of the two-sided search problem are classified into two types, the hide-and-search problem and the evasion-and-search problem. In the hide-and-search problem, the target hides itself, selecting a point in the target space and stays there inactive during the search. A searcher wants to find the target efficiently, whereas the target does want not to be found. Usually, the game theoretical approach is taken and the optimal strategies for both sides are sought. The works of Neuts (1963), Johnson (1964), Danskin (1968), and Gittins and Roberts (1979) are the studies of this category. In the evasion-and-search problem, the target is assumed to be able to evade the searcher, observing the searcher’s current position during the search. The problem is formulated as a sequential multistage search game. Norris (1962), Sakaguchi (1973), Washburn (1980b), and Nakai (1986a) investigated this problem. Nakai (1986b) considered a search game in which two searchers compete with each other in detecting a stationary and unconscious target.
Kōji Iida

Backmatter

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