Formulation and Analysis for Integrated Spacecraft Routing and Trajectory Design Problem

Euihyeon Choi; Koki Ho

arxiv: 2604.18826 · v1 · submitted 2026-04-20 · 🧮 math.OC

Formulation and Analysis for Integrated Spacecraft Routing and Trajectory Design Problem

Euihyeon Choi , Koki Ho This is my paper

Pith reviewed 2026-05-10 03:35 UTC · model grok-4.3

classification 🧮 math.OC

keywords spacecraft routingtrajectory optimizationmixed-integer programmingcolumn generationsatellite servicingpropellant replenishmentgeosynchronous orbit

0 comments

The pith

Two formulations for integrated spacecraft routing and trajectory optimization reveal distinct trade-offs in optimality, speed, and reliability.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops methods to plan spacecraft missions where routing decisions and detailed trajectories are optimized together, including options for refueling along the way. One method uses variables on individual arcs and alternates between mixed-integer linear programming for routing and nonlinear optimization for trajectories. The other uses variables on full paths and applies column generation to find good routes efficiently. Experiments on a geosynchronous satellite servicing mission measure how the approaches differ in the quality of solutions found, the time taken, and how often they avoid failures or useless outcomes. Readers interested in space logistics would care because these planning tools directly affect whether complex servicing missions can be scheduled and executed at acceptable cost.

Core claim

The paper introduces an arc-based formulation that employs an iterative decoupling scheme alternating between mixed-integer linear programming and sequential nonlinear trajectory optimization, and a path-based formulation that defines variables on paths and uses column generation together with a labeling algorithm. A geosynchronous satellite servicing case study together with numerical experiments quantifies the trade-offs between the two in terms of solution optimality, computational time, and robustness against non-converging or trivial solutions.

What carries the argument

Arc-based formulation with iterative decoupling between mixed-integer linear programming and nonlinear trajectory optimization; path-based formulation with column generation and labeling algorithm for route identification.

If this is right

Mission planners can select the arc-based method when solution quality is paramount and the path-based method when faster computation is needed.
Partial en-route propellant replenishment can be incorporated into routing decisions without separating routing from trajectory design.
Numerical benchmarks provide guidance on expected run times and solution gaps for similar servicing scenarios.
Robustness metrics help identify problem sizes where one formulation is more likely to produce usable results.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Hybrid solvers that switch between the two formulations based on instance size could combine their strengths.
The observed robustness issues point to a need for improved warm-starting techniques for the nonlinear subproblems.
Similar integrated routing-trajectory models could be tested on low-Earth orbit constellations or asteroid rendezvous missions.

Load-bearing premise

Nonlinear trajectory optimization subproblems can be solved reliably and the iterative decoupling scheme converges to useful solutions without excessive computational cost or trivial outcomes.

What would settle it

A set of test instances where the nonlinear solver fails to converge for a large fraction of subproblems or the overall procedure repeatedly returns trivial routes would show the formulations are not yet practical for real missions.

read the original abstract

This paper studies the integrated spacecraft routing and trajectory optimization problem for satellite servicing missions involving partial en-route propellant replenishment. Unlike terrestrial routing problems, spacecraft operate in a dynamic environment, and we need to optimize the spacecraft routing over a network with nonlinear and time-dependent trajectory costs. In this paper, we tackle this problem using two different formulations. The first formulation, referred to as the arc-based formulation, defines variables based on arcs and employs an iterative decoupling scheme that alternates between mixed-integer linear programming and sequential nonlinear trajectory optimization. The second formulation, referred to as the path-based formulation, defines variables based on paths/routes and leverages column generation and a labeling algorithm to accelerate the identification of promising routes. Through a geosynchronous satellite servicing case study and numerical experiments, we quantify the computational trade-offs between these two formulations in terms of the solution optimality, computational time, and robustness against non-converging or trivial solutions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper adapts standard MILP routing techniques to spacecraft with nonlinear trajectory costs and partial refueling, then compares an arc-based iterative scheme against a path-based column-generation version on one GEO servicing instance.

read the letter

The core contribution is the pair of formulations that fold realistic flight costs and en-route propellant options into a routing model. The arc-based version alternates a mixed-integer linear program with sequential nonlinear trajectory solves; the path-based version uses column generation plus a labeling routine to generate promising routes without enumerating everything. Both are written out clearly enough that a reader can implement the basics from the text. The numerical section then runs both on the same geosynchronous satellite-servicing example and reports the usual metrics: optimality gap, wall-clock time, and how often each method lands on non-convergent or trivial solutions. That direct head-to-head is the part that could actually help someone deciding which decomposition to try on a similar problem. The main soft spot is that the results rest on a single instance and on the assumption that the nonlinear subproblems can be solved reliably and cheaply each iteration. If those subproblems become expensive or fail to converge on other orbits or vehicle models, the reported trade-offs will shift. The paper does not explore that sensitivity, so the robustness claim is narrower than it first appears. This is useful reading for people who already work on space logistics or on vehicle-routing problems with expensive continuous costs. A practitioner who needs to decide between decomposition strategies for a mission-planning tool would get concrete numbers to start from. It is worth sending to referees; the formulations are reproducible from the write-up and the comparison addresses a real engineering question even if the evidence base is still narrow.

Referee Report

0 major / 2 minor

Summary. The paper studies the integrated spacecraft routing and trajectory optimization problem for satellite servicing missions with partial en-route propellant replenishment. It presents an arc-based formulation that uses an iterative decoupling scheme alternating between mixed-integer linear programming and sequential nonlinear trajectory optimization, and a path-based formulation that employs column generation together with a labeling algorithm. The two approaches are compared on a geosynchronous satellite servicing case study, with numerical experiments quantifying trade-offs in solution optimality, computational time, and robustness against non-converging or trivial solutions.

Significance. If the reported numerical results hold, the work supplies concrete guidance on selecting between decomposition strategies for hybrid discrete-continuous optimization problems that arise in space logistics. The explicit quantification of robustness metrics directly addresses a practical concern for mission planners. The manuscript is strengthened by the provision of the two complete mathematical programs, the labeling algorithm, and the focused case-study evaluation.

minor comments (2)

The abstract outlines the methods and evaluation approach but does not report any quantitative results (e.g., relative optimality gaps or run-time ratios) from the geosynchronous case study; adding one or two such figures would allow readers to gauge the claimed trade-offs immediately.
Section describing the labeling algorithm: a compact pseudocode listing would improve clarity and reproducibility of the column-generation procedure.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our work on arc-based and path-based formulations for the integrated spacecraft routing and trajectory optimization problem, including the recognition of its practical guidance on decomposition strategies and robustness metrics. The recommendation for minor revision is noted.

Circularity Check

0 steps flagged

No significant circularity detected in formulations or claims

full rationale

The paper presents two distinct optimization formulations (arc-based with iterative MILP-NLP decoupling, path-based with column generation and labeling) for the integrated routing-trajectory problem. These are derived from standard mixed-integer and nonlinear programming techniques without any reduction of a claimed result to its own fitted inputs or self-referential definitions. No load-bearing self-citations, uniqueness theorems from prior author work, or ansatzes smuggled via citation appear in the text. The geosynchronous case study supplies direct numerical measurements of optimality, runtime, and robustness, keeping the central quantification externally grounded rather than tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract; the work implicitly relies on standard assumptions from trajectory optimization and mixed-integer programming but introduces no new free parameters or entities in the provided summary.

pith-pipeline@v0.9.0 · 5453 in / 1030 out tokens · 33094 ms · 2026-05-10T03:35:22.413892+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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