The Keplerian Traveling Salesperson Problem

TL;DR

This paper introduces the Keplerian TSP, a new variant modeling interplanetary mission planning with orbital target motion, and provides formalization, benchmarks, and solution methods for it.

Contribution

It formalizes the Keplerian TSP, creates a benchmark suite, and develops ILP-based and heuristic solution approaches for this complex space logistics problem.

Findings

Benchmark suite enables standardized study of KTSP.

ILP and heuristic methods effectively solve KTSP instances.

Time-unfolding reformulation makes the problem accessible to discrete optimization.

Abstract

We address a fundamental challenge in space mission design and space logistics: planning interplanetary trajectories for missions that must rendezvous with multiple bodies. Such mission occur, for instance, in active debris removal, in-orbit servicing, or asteroid belt exploration. We model these problems as a variant of the Traveling salesperson problem (TSP), which we term the Keplerian TSP (KTSP). Unlike the well-studied TSP, the KTSP accounts for the motion of orbital targets, leading to time-dependent and asymmetric transfer costs that capture key real-world effects in astrodynamics. We provide a rigorous formalization of the KTSP and release a benchmark suite to support its study. Central to our approach is a time-unfolding technique that reformulates the continuous problem as a discrete optimization task in a time-expanded network. This representation makes the benchmark accessible to researchers in discrete optimization even without prior knowledge of celestial mechanics. We also develop an alternative encoding as an integer linear program using Interval-based Dynamic Discretization Discovery to handle the time-dependent nature of transfers. We leverage state-of-the-art ILP solvers to solve the KTSP instances, accompanied by a detailed computational study that highlights their strengths and limitations. We complement these exact methods with an initial solution heuristic, an improvement heuristic, and preprocessing routines that preserve optimality.