Optimal Search Plan for a Moving Target

Fuzzy Optimal Search Plan for N-Dimensional Randomly Moving Target

International Journal of Computational Methods ◽

10.1142/s0219876216500389 ◽

2016 ◽

Vol 13 (06) ◽

pp. 1650038 ◽

Cited By ~ 12

Author(s):

Mohamed Abd Allah El-Hadidy

Keyword(s):

Target Position ◽

Expected Value ◽

Numerical Results ◽

Search Model ◽

Moving Target ◽

Optimal Search ◽

Search Plan

This paper presents a search model that finds [Formula: see text]-dimensional randomly moving target in which any information of the target position is not available to the searchers. There exist [Formula: see text]-searchers, starting the searching process from the origin. Rather than finding the conditions that make the expected value of the first meeting time between one of the searchers and the target is finite, this work shows the existence of the fuzzy optimal search plan that minimizes the expected value of the first meeting time. The effectiveness of this method is illustrated by using an example with numerical results.

Download Full-text

THE OPTIMAL SEARCH PLAN FOR A MOVING TARGET MINIMIZING THE EXPECTED RISK

Journal of the Operations Research Society of Japan ◽

10.15807/jorsj.31.294 ◽

1988 ◽

Vol 31 (3) ◽

pp. 294-321 ◽

Cited By ~ 11

Author(s):

Koji Iida ◽

Ryusuke Hozaki

Keyword(s):

Moving Target ◽

Optimal Search ◽

Search Plan

Download Full-text

Optimal Search for a Moving Target

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964800003764 ◽

1995 ◽

Vol 9 (2) ◽

pp. 159-182 ◽

Cited By ~ 13

Author(s):

I. M. MacPhee ◽

B. P. Jordan

Keyword(s):

Markov Chain ◽

Optimal Policy ◽

Average Cost ◽

Large Range ◽

Moving Target ◽

Optimal Search ◽

Threshold Probability

Consider the problem of searching for a leprechaun that moves randomly between two sites. The movement is modelled with a two-state Markov chain. One of the sites is searched at each time t = 1,2,…, until the leprechaun is found. Associated with each search of site i is an overlook probability αi and a cost Ci Our aim is to determine the policy that will find the leprechaun with the minimal average cost. Let p denote the probability that the leprechaun is at site 1. Ross conjectured that an optimal policy can be defined in terms of a threshold probability P* such that site 1 is searched if and only if p ≥ P*. We show this conjecture to be correct (i) when α1 = α2 and C1 = C2, (ii) for general Ci when the overlook probabilities α, are small, and (iii) for general αi and Ci for a large range of transition laws for the movement. We also derive some properties of the optimal policy for the problem on n sites in the no-overlook case and for the case where each site has the same αi, and Ci.

Download Full-text