The M-States Search Problem For The Lost Markovian Targets: Analysis

This paper presents more analysis about the M-States search problem for the lost Markovian targets which is detailed in El-Hadidy (Asia-Pac. J. Oper. Res. 33(3):1650019 (30 pages), 2016). At each fixed number of time intervals, the search effort is a random variable with a normal distribution. More than minimizing the undetection probability of the targets at time interval i, we seek for the optimal distribution of the search effort by maximizing the discounted effort reward search. We present some special cases of one Markovian and hidden target. An experimental results for a Markovian, hidden target are obtained and compared in the cases of applying and without applying the discounted effort reward search.[End abstract] (-- removed HTML
Many scientists have been provided more different kinds of search plan fit the nature of the search area. Sometimes we search for the targets in difficult terrain areas on the surface of the ground or in the deep of the sea. Specialists in this field interested in dividing those areas to a set of identical or different states in order to increase the probability of detection or minimize the search effort. The nature of the search area is control in the form of the cells. Hong et al. [1-2] divided the area into hexagonal cells. They proposed an approximation algorithm for the optimal search path. This algorithm optimizes an approximate path to compute detection probability by using the conditional probabilities. Then, finding the maximum detection probability search path. Song and Teneketizs [3] determined the optimal search strategies with multiple sensors that maximize the total probability of successful search where the target is hidden in one of a finite set of different cells. Teamah et al. [4] divided the search region into square cells. They minimized the probability of undetection and the searching effort (is bounded by a normal distribution) by using multiple searchers. They studied some special cases when the target is hidden in one of M-identical cells and when the effort is
The related targets either located in one of a finite set of different states or moved through them according to discrete state and time stochastic process (discrete-time Markovian targets). This situation occurs when the located targets is very important such as searching for the spider landmines (see, https://www.youtube.com/watch?v=XH0n6I0qMZA) and when they are moving such as two related submarines on the ocean. The effort must be divided among the states to find the targets. This search effort at each fixed number of time intervals is a random variable has a normal distribution. Our purpose here is to obtain the optimal distribution of effort that makes the discounted effort reward of finding the targets, is maximum. This made the probability of undetection and the cost of finding the target, are minimum. The rest of the paper is organized as follows. Section 2 discuss the problem and provide the optimal values of the minimum search effort and the maximum probability of detection. Section 3 gives special cases of one Markovian and hidden target. Section 4 presents simulation example with numerical results for a Markovian and hidden target. These results are compared in the cases of applying and without applying the discounted effort reward search. This comparsion can be shown the effectiveness of this solution. Finally, section