Studies on the Optimal Search Plan

ISBN-13: 9780387977393 / Angielski / Miękka / 1992 / 130 str.

Koji Iida

Opis

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.

Spis treści

Short Survey of Search Theory.- Attributes of Search Models.- Outline of Chapters.- 1. Optimal Search Plan for a Stationary Target Minimizing the Expected Risk.- 1.1. Introduction.- 1.2. Optimal Search Plan.- 1.2.1. Optimal Distribution of Searching Effort.- 1.2.2. Optimal Stopping Time of the Search.- 1.3. Two-Box Problem.- 2. Optimal Search Plan for a Moving Target.- 2.1. Introduction.- 2.2. Optimal Search Plan Maximizing the Detection Probability.- 2.3. Optimal Search Plan Minimizing the Expected Risk.- 2.3.1. Optimal Distribution of Searching Effort.- 2.3.2. Optimal Stopping Time of the Search.- 2.3.3. A Numerical Example.- 2.4. Optimal Search Plan for a Target with Conditionally Deterministic Motion.- 3. Optimal Whereabouts Search Plan Minimizing the Expected Risk.- 3.1. Introduction.- 3.2. Optimal Whereabouts Search Plan for an Appeared Target.- 3.2.1. Optimal Distribution of Searching Effort.- 3.2.2. Optimal Stopping Time of the Search.- 3.2.3. Optimal Box to Be Guessed.- 3.3. Optimal Whereabouts Search Plan for a Mortal Target.- 3.4. Numerical Examples.- 4. Optimal Investigating Search Plan for Contacts in Two-Stage Search.- 4.1. Introduction.- 4.2. Optimal Investigating Search Plan.- 4.2.1. Optimal Selection of Contacts for Investigation and Optimal Stopping Time.- 4.2.2. Properties of the Optimal Investigating Search Plan.- 4.3. Numerical Examples.- 5. Forestalling Detection in Two-Sided Search.- 5.1. Introduction.- 5.2. Forestalling Detection in Broad Search.- 5.3. Forestalling Detection in Barrier Search.- Author Index.