By C. D Olds

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**Example text**

By the same token, define the cost of the search as C = K × T. 1 of constrained search, it is required to find the strategy w* specifying the observation numbers κ* (aj,T) such that the probability p(w*,T) is maximal and the cost is constrained as © 2015 by Taylor & Francis Group, LLC C ( w*, T ) ≤ C. 48) κ * (a j , T ) t (a j ) , j =2 m ∑ where n j are integer valued functions, which define the numbers of observations of the areas a j, j = 1, 2,…, m, given the available cost. 1. Finally, assume that the probability of detecting the target in the area a j, j = 1, 2,…, m, does not depend on the observation number; in other words, similarly to the sequential search, the observations do not add information about the target’s location and are defined as 1 − ε j = φ(a j, 1), where ε j is an overlook probability of nondetecting the target in the area aj given that it is somewhere in aj.

X Since q(w, t) is the probability of nondetecting the target, the probability of detecting the target during the period [0, t] using the strategy w is defined as p ( w, t ) = 1− q ( w, t ) . 4) t ∫ w ( x, τ) dτ applied in the point x up to the 0 q ( w, T ) = u ( x ) exp −κ ( x, T ) d x and p ( w, T ) = 1 − q ( w, T ) . 5) x Additional condition, which represents a “conversation” of search efforts, is specified as follows: T © 2015 by Taylor & Francis Group, LLC ∫κ ( x, T ) dx = ∫K ( t ) dt. 6) 11 Methods of Optimal Search and Screening Thus, according to the goal of the searcher, it is required to find such search strategy w that maximizes the probability p(w, t) or minimizes the probability q(w, t) of nondetecting the target.

Using the detection function φ, the probability of detecting the target during the period 0,t ) using the search strategy w is defines as follows: ∫ t ∫ p ( w, t ) = u ( x ) ϕ ( x, κ ) d x, κ ( x, t ) = w ( x, τ ) dτ. 9) 0 Let W be a set of all possible search strategies w over the domain X given the target’s probability distribution u ( x ) , x ∈ X. Then, according to the goal of the searcher, it is required to find a search strategy w* ∈ W such that the probability p(w*, T) is maximal over all strategies w ∈ W.