We consider the cluster-restricted maximum weight clique problem (CRCP), a variation of the well-known maximum weight clique problem. While CRCP itself is mathematically interesting, our motivation to study the problem primarily comes from its application in the area of Satellite Image Acquisition Scheduling. Earth observing satellites revolve around the earth in specific orbits and takes images of prescribed areas requested by the clients. Not every region can be fully acquired in a single satellite pass. This necessitates the division of the region into multiple strips. There might be several image acquisition opportunities for each strip as the satellites have agility in their rolling angles. Then the Satellite Image Acquisition Scheduling Problem (SIASP) is to select the opportunities to acquire as many images as possible, without repetition, within a planning horizon while considering the image priorities and energy constraints. SIASP has a piecewise linear objective function to favor the completion of an image acquisition request and try to avoid partial acquisition of many requests. Extensive experimental study is provided on randomly generated instances based on the predicted statistics given by MDA, Richmond, Canada. These experiments are intended as a preliminary investigation on image acquisition scheduling for the Canadian RADARSAT Constellation Mission (RCM), a constellation of three satellites, which is planned to be launched in 2018.SIASP can be modeled as a CRCP with piecewise linear objective function. We provide integer programming (IP) formulations for CRCP with linear and piecewise linear objective function. We also suggest heuristic (metaheuristic) algorithms that exploit the power of modern IP solvers such as CPLEX. Experimental results using the heuristic algorithms on DIMACS and BOSHLIB benchmark instances for the clique problem are reported. Finally, an exact algorithm for CRCP along with some theoretical analysis is presented.
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