An Exact Algorithm for Multi-Task Large-Scale Inter-Satellite Routing Problem with Time Windows and Capacity Constraints

Abstract

In the context of a low-orbit mega constellation network, we consider the large-scale inter-satellite routing problem with time windows and capacity constraints (ISRPTWC) with the goal of minimizing the total consumption cost, including transmission, resource consumption, and other environmentally impacted costs. Initially, we develop an integer linear programming model for ISRPTWC. However, a difficult issue when solving ISRPTWC is how to deal with complex time window constraints and how to reduce congestion and meet transmission capacity. Along this line, we construct a three-dimensional time-space state network aiming to comprehensively enumerate the satellite network state at any moment in time and a task transmission route at any given time and further propose a time-discretized multi-commodity network flow model for the ISRPTWC. Then, we adopt a dynamic programming algorithm to solve the single-task ISRPTWC. By utilizing a Lagrangian relaxation algorithm, the primal multi-task routing problem is decomposed into a sequence of single-task routing subproblems, with Lagrangian multipliers for individual task route nodes and links being updated by a subgradient method. Notably, we devise a novel idea for constructing the upper bound of the ISRPTWC. Finally, a case study using illustrative and real-world mega constellation networks is performed to demonstrate the effectiveness of the proposed algorithm.