Approximately optimal one-dimensional search policies in which search costs vary through time
✍ Scribed by Brian Gluss
- Publisher
- John Wiley and Sons
- Year
- 1961
- Tongue
- English
- Weight
- 290 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0894-069X
No coin nor oath required. For personal study only.
✦ Synopsis
Consider a model in which there a r e N neighboring cells in one of which there i s an object that it i s required to find.
abilities of the object being in cells 1, . . . , N a r e p l , . . . , pN respectively, and the costs of examination of these cells a r e t l , . . . , tN respectively; the search policy i s considered to be optimal when the statistical expectation of the total cost of the search i s minimized. For the case in which the ti's a r e constant throughout the search, an optimal policy solution has previously been found by Bellman and by Smith. In the present paper it i s assumed that the costs comprise a travel cost dependent upon the distance from the last cell examined, in addition to a fixed examination cost: initially, assuming that the searcher i s next to cell 1, t i = i t t , where t i s constant; and from then onwards, assuming that the jth cell has just been examined, t i = 1 i -j I + t. An optimal search strategy i s found in the case where the pi's a r e all equal, and approximately optimal strategies in the case where pi i s proportional to i. where complete searches occur at successive intervals of time, and hence the enemy objects a r e thinned out the nearer they come to the defense base.
The a priori prob-
The latter case has application to defense situations * * *