It is critical in many system-engineering problems (such as surveillance, environmental monitoring, and cooperative task performance) to optimally allocate resources in the presence of limited resources. Static coverage problem is an important class of the resource allocation problems that focuses on covering an area of interest so that the activities in the area of interest can be detected/monitored with higher probability. In many practical settings (primarily due to financial constraints) a system designer has to allocate resources in multiple stages. In each stage, the system designer can assign a fixed number of resources (agents). In the multi-stage formulation, the agents locations for the next stage are dependent on all the agents location in the previous stages. Such multi-stage static coverage problems are non-trivial to solve. In this paper, we propose a robust and efficient sequential sampling algorithm to solve the multi-stage static coverage problem in the presence of probabilistic resource intensity allocation maps (RIAMs). The agents locations are determined by formulating this problem as an optimization problem in the successive stage . Three different objective functions are compared and discussed from the aspects of decreasing L2 difference and Sequential Minimum Energy Design (SMED). It is shown that utilizing SMED objective function leads to a better approximation of the RIAMs. Two heuristic algorithms, i.e. cuckoo search, and pattern search, are used as optimization algorithms. Numerical functions and real-life applications are provided to demonstrate the robustness and efficiency of the proposed approach.

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