  A group of satellites, with either homogeneous or heterogeneous orbital
characteristics and/or hardware specifications, can undertake a reconfiguration
process due to variations in operations pertaining to Earth observation
missions. This paper investigates the problem of optimizing a satellite
constellation reconfiguration process against two competing mission objectives:
(i) the maximization of the total coverage reward and (ii) the minimization of
the total cost of the transfer. The decision variables for the reconfiguration
process include the design of the new configuration and the assignment of
satellites from one configuration to another. We present a novel bi-objective
integer linear programming formulation that combines constellation design and
transfer problems. The formulation lends itself to the use of generic
mixed-integer linear programming (MILP) methods such as the branch-and-bound
algorithm for the computation of provably-optimal solutions; however, these
approaches become computationally prohibitive even for moderately-sized
instances. In response to this challenge, this paper proposes a Lagrangian
relaxation-based heuristic method that leverages the assignment problem
structure embedded in the problem. The results from the computational
experiments attest to the near-optimality of the Lagrangian heuristic solutions
and a significant improvement in the computational runtime compared to a
commercial MILP solver.
