QUEST – A new quadratic decision model for the multi-satellite scheduling problem

Abstract

Demand for earth observation satellite imagery is pervasive and increasing rapidly across multiple domains, highlighting the key problem to optimally schedule satellite image acquisition/collection, subject to ground and on-board constraints. Despite the variety of reported approaches to solving the NP-hard multi-satellite scheduling problem (m-SatSP), serious limitations still prevail, largely overlooking problem structure exploitation and/or domain knowledge. Assuming a few constraints, problem modelling—or scope—is often confined to a simple trailing satellite constellation composition perspective and tends to conveniently oversimplify footprint coverage intricacies. As a result, adequate problem task decomposition properly reflecting complex kinematic behaviour for an ad hoc satellite constellation remains elusive. Known approaches also fail to provide valuable solution optimality gap estimations to objectively qualify best computed solution and/or to control run-time execution in solving hard problem instances. In this paper, a novel approach to solving the single objective static m-SatSP is proposed. It is based on network flow optimization using mathematical programming. Unlike previous methods, QUEST (QUadratically constrainEd program Solver Technology) relies on a sound alternative approximate objective function and, the exploitation of exact problem-solving techniques. Derived from domain knowledge and problem structure considerations, QUEST generalizes problem modelling to successfully handle virtual constellation, avoiding unsuitable utilization of traditional area coverage decomposition scheme. The proposed decision model concurrently captures coverage approximation, imaging success uncertainty and quality for a variety of tasks. It also includes new and optional constraints while embracing an acceptable upper bound on collection value. A QUEST variant alternatively relying on “delayed reward” to bridge promising search regions on move selection, further shows optimality gap reduction and provides additional speedup. Computational results prove QUEST to be cost-effective and to outperform some recent baseline methods derived from best-known m-SatSP procedures. It comparatively demonstrates measurable collection and run-time gains, and provides a tight upper bound on the optimal solution of hard problems.