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A group of satellites, with either homogeneous or heterogeneous orbitalcharacteristics and/or hardware specifications, can undertake a reconfigurationprocess due to variations in operations pertaining to Earth observationmissions. This paper investigates the problem of optimizing a satelliteconstellation reconfiguration process against two competing mission objectives:(i) the maximization of the total coverage reward and (ii) the minimization ofthe total cost of the transfer. The decision variables for the reconfigurationprocess include the design of the new configuration and the assignment ofsatellites from one configuration to another. We present a novel bi-objectiveinteger linear programming formulation that combines constellation design andtransfer problems. The formulation lends itself to the use of genericmixed-integer linear programming (MILP) methods such as the branch-and-boundalgorithm for the computation of provably-optimal solutions; however, theseapproaches become computationally prohibitive even for moderately-sizedinstances. In response to this challenge, this paper proposes a Lagrangianrelaxation-based heuristic method that leverages the assignment problemstructure embedded in the problem. The results from the computationalexperiments attest to the near-optimality of the Lagrangian heuristic solutionsand a significant improvement in the computational runtime compared to acommercial MILP solver.

Regional Constellation Reconfiguration Problem: Integer Linear Programming Formulation and Lagrangian Heuristic Method