Experiment · Space mechanics · Lunar logistics

European Space Agency, Luna Tomato Logistics: 400 transfers from the Earth to the Moon

This experiment addresses a logistics problem between the Earth and the Moon: carry “tomatoes” from 400 Earth orbits, through 400 lunar orbits, to 400 destinations, choosing the assignment of each tomato and the trajectory of each transfer so that the delivered mass is as large as possible. The referee is the Optimize platform of the European Space Agency (ESA), which evaluates every solution with its official simulator. Outcome: 506,077.456 kg delivered, the best score among 103 entries as read on 11 Oct 2026. The solution was submitted on 7 Oct 2026, after the close of the competition (30 June 2026): the ranking is a post-competition ranking.

1. The problem

ESA offers a logistics challenge between the Earth and the Moon: 400 Earth departure orbits, 400 lunar arrival orbits and 400 destinations. A solution is a set of 400 triplets (Earth orbit, lunar orbit, destination) in which each orbit and each destination appears exactly once, each triplet coming with the trajectory that links its Earth orbit to its lunar orbit. The score is the sum of the delivered masses, to be maximised.

A trajectory starts from a state on the Earth orbit, receives a velocity impulse, flies a 1st arc, receives a 2nd impulse, flies a 2nd arc, receives a 3rd impulse, and must then be on the required lunar orbit: semi-major axis (in units of the Earth–Moon distance), eccentricity and inclination must match those of that orbit to within 10⁻⁶, which is about 384 m on the semi-major axis. The flight is computed in a four-body model, Earth, Moon and Sun (the bicircular model); it must not pass within 99 km of the Earth’s surface or 30 km of the Moon’s.

The velocity cost ΔV of the transfer, the sum of the norms of the three impulses, gives the mass of tomatoes through the rocket equation: m = 5,000 · exp(−ΔV / (311 · g₀)) − 500 kg, with g₀ = 9.80665 m/s². The mass delivered at the destination is capped by (200 − Δt) · c, where Δt is the flight duration in days and c the coefficient of ESA’s LTL table for the pair (lunar orbit, destination). The submitted vector has 8,400 values, 21 per triplet. The challenge offers three problems (matching-i, matching-ii, trajectory-matching); this page covers trajectory-matching, the one that requires the trajectories.

2. Verification protocol

The result is a vector of 8,400 numbers, submitted to the Optimize platform. The platform evaluates it with the official simulator of the problem, published by ESA (Python code in the pygmo format, propagation with the heyoka library, orbital elements with pykep), and derives the score from it; a solution that violates a constraint receives a score of zero. The figures on this page are those of the ranking as read on the date given.

The referee and the problem

The Optimize platform is developed by ESA’s Advanced Concepts Team, which organises SpOC 4 with the GECCO conference. The esa/SpOC4 repository publishes, in the folder “Challenge 1 Luna Tomato Logistics”, the three files of the instance (Earth_orbits.txt, Moon_orbits.txt, LTL.txt); the page reads these files and their fingerprints are given in section 5. The bicircular model is described in the literature (Simó, Gómez, Jorba and Masdemont, 1995); two-impulse Earth–Moon transfers in a four-body model were studied by Topputo (Celestial Mechanics and Dynamical Astronomy, 117, 2013). Competition submissions closed on 30 June 2026; the portal stayed open afterwards.

3. The problem statement in pictures

The figures in this section illustrate the problem as posed: they are drawn from the files published by ESA, not from the solution. The main figure shows the shape of the 400 Earth departure orbits, with their actual semi-major axis and eccentricity (semi-major axis from 6,545 to 42,924 km, eccentricity up to 0.74); the colour is the inclination. The files give neither the orientation nor the phase of the orbits: here they are aligned, for readability. The grey disc is the Earth; 41 of them, reaching up to 43,000 km, are high orbits; the others are low and tight around it.

The arrivals are 400 lunar orbits, smaller (semi-major axis from 1,838 to 5,314 km, eccentricity up to 0.65); the second figure shows them in the same way, the first frames the low Earth orbits up close. Then the rocket equation of the statement: the more velocity a transfer costs, the less tomato mass remains, down to zero at about 7,023 m/s. Last, ESA’s LTL table: the coefficient c of the delivery cap for each pair (lunar orbit, destination), averaged in blocks of 16 × 16; 11% of the 160,000 coefficients are zero or nearly zero, and the mean is 8.44.

The elements of the instance

Each cell is an orbit or a destination of the instance. Orbits are coloured by inclination (from violet, 0°, to cyan, 90°); destinations by the mean coefficient c of their column in the LTL table. This map describes the problem statement. The parameters of the instance are in esa_luna_tomato_instance.json.

4. Result

The submitted solution delivers 506,077.456 kg in total, through 400 triplets. As read on 11 Oct 2026, the platform’s ranking has 103 entries, 91 with a non-zero score. The best score of the competition period, up to the close of 30 June 2026, was 500,236.503 kg; the submitted solution and the 2nd entry both come after that close.

5. What is checked, and by whom

• The referee (ESA). The official simulator of the Optimize platform evaluates the submitted vector and publishes the score, 506,077.456 kg as read on the date given. This evaluation establishes the ranking.
• Check with the official code (7 Oct 2026). The code of the problem, downloaded from the platform and run offline with pykep 2.6.4 and heyoka 7.13.2, returns −506,077.4559769009 for this vector. The 400 rows have Earth orbits, lunar orbits and destinations that are all distinct, and the instance files have the same fingerprints as those of the public repository.
• Independent check (11 Oct 2026). The physics was rewritten, orbital elements and the bicircular model integrated with an 8th-order Dormand–Prince integrator, without the official packages. The check recovers the sum of 506,077.4559769 kg, confirms that each orbit and each destination is used once, that the 400 departure and arrival states respect the required orbits to the 10⁻⁶ tolerance and that no trajectory enters the forbidden zones. This is an internal check; ESA’s simulator remains the referee.
• Fingerprint of the submitted file. The sha256 below is that of the file sent to the platform. It fixes the result: any file presented later as the submission can be compared with this fingerprint.

Instance files (esa/SpOC4 repository, folder “Challenge 1 Luna Tomato Logistics”), sha256: Earth_orbits.txt 6c048d808bfca820d3742a1077993568faa3fbfb42a954cdb41f5d0952b49e53
Moon_orbits.txt 03a75b4911945288690eee021b02b87ffffb6ab1c2810e6bd438beb5ce8efad0
LTL.txt c30bd4caed25e841bdc54d4a703f58de905403a98dd529c9755117eafd2a9108

6. What this question models

ESA presents the challenge as the design of a transport network that brings loads from Earth orbits to lunar destinations (README of the esa/SpOC4 repository). This type of question models logistics between the Earth and the Moon, three-dimensional assignment under constraints (each departure, each arrival and each destination exactly once), and the coupling of a combinatorial choice with a trajectory computation, where the cost of each assignment depends on orbital mechanics. The experiment contributes a complete plan of 400 transfers, evaluated by the referee’s simulator.

My AI project in the service of my research

This challenge is not an end in itself: it is a test bench for my research on a certifiable embedded AI. My AI project, whose inner workings remain confidential, lets me reach 506,077.456 kg delivered through 400 transfers, constraints met, with the best score in the ranking as read. The certificate and the referee vouch for it: it is not my explanation you need to believe, it is the result, which can be checked again. This is the best known result at the date given, not a proven optimum.