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

TL;DR

This paper formulates a satellite constellation reconfiguration problem as a bi-objective integer linear program and introduces a Lagrangian heuristic to efficiently find near-optimal solutions, balancing coverage and cost.

Contribution

It presents a novel bi-objective ILP formulation for satellite reconfiguration and proposes a Lagrangian heuristic that improves computational efficiency over traditional MILP methods.

Findings

Lagrangian heuristic achieves near-optimal solutions.

Significant reduction in computational time compared to MILP solvers.

Effective balancing of coverage maximization and transfer cost minimization.

Abstract

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.