Designing Active Tether-Net Systems for Space Debris Capture with Graph-Learning-Aided Mixed-Combinatorial Optimization

2026-05-27

AI Summary

This study addresses the challenging mixed combinatorial nonlinear optimization problem arising in active tether-net systems for capturing large non-cooperative space debris, where continuous, integer, and categorical variables are tightly coupled. To tackle this issue, the authors propose a unified joint optimization framework based on graph neural networks (GNNs). By modeling system morphology, actuator configuration, and control parameters within a single formulation, the method leverages GNNs to provide structured representations of discrete combinatorial variables, thereby eliminating spurious correlations introduced by conventional encoding schemes. This transformation recasts the original mixed-variable problem into a purely continuous nonlinear programming problem. The resulting formulation is solved efficiently via particle swarm optimization combined with gradient-based fine-tuning, achieving significantly accelerated convergence without compromising solution quality. This work pioneers the integration of graph learning into tether-net system design for space applications, offering a novel and efficient paradigm for complex mixed-variable optimization challenges.

Abstract

Active tether-net systems are a promising solution for capturing large non-cooperative targets, such as space debris, by deploying a flexible net manipulated by maneuverable units (MUs). However, concurrent systematic explorations of design and control choices of the tether-net system to understand its full potential remain limited, partly due to the complex, constrained, nonlinear optimization problem that it presents -- one that involves a mixture of continuous, integer and categorical variables, with the latter two arising from net connectivity and component choices, respectively. Classical binary encoding methods are often ineffective for solving highly nonlinear and multimodal Mixed Combinatorial Nonlinear Programmings (MCNLPs) in engineering design, while integer coding approaches can introduce spurious relations among combinations. Given the graph-structured characteristics of the combinatorial space, this paper adopts and extends a new graph-learning-aided optimization approach to solve this MCNLP problem. Here, a Graph Neural Network (GNN) is trained to score (as output) and thereof recommend candidate combinations represented as nodes in a graph, with the continuous variable vector portion of a candidate design given as input. As a result, the MCNLP optimization reduces to an NLP, which can be solved using standard solvers. While this reduction approach is agnostic to the choice of the NLP solver, here a state-of-the-art Particle Swarm Optimization (PSO) algorithm with gradient-based fine-tuning is used as the solver. Demonstrated on the problem of concurrently designing the morphology of the net, choice of mass and thrusters in the MUs and aiming points used by the controller of the tether-net system, the GNN-based recommender is shown to provide significantly faster convergence to similar optimal solutions, compared to direct solution of the MCNLP problem.

Problem

• space debris capture
• mixed-combinatorial optimization
• active tether-net systems
• nonlinear programming
• graph-structured optimization

Innovation

• Graph Neural Network
• Mixed Combinatorial Optimization
• Space Debris Capture
• Tether-Net System
• Particle Swarm Optimization