Brahe constellation access optimization

This standalone tutorial is part of the public fcmaes-rust repository. It combines the native Rust optimizers in fcmaes-core with Brahe 1.7.0, an MIT-licensed Rust astrodynamics and mission-analysis library.

The example is deliberately a real simulation objective rather than a mathematical test function:

10 design variables
    ↓
four Keplerian satellite propagators
    ↓
Brahe access search: 6 stations × 4 satellites × 24 hours
    ↓
merge overlapping contacts, reject passes shorter than 3 minutes
    ↓
BiteOpt retry or constrained MODE

Brahe’s KSAT station data is embedded in the dependency, so no station file or network request is required at runtime. The model also installs a zero-valued static Earth-orientation provider. That choice makes optimization runs offline and repeatable; replace it with current EOP data before treating the access times as operational predictions.

Design

The four satellites share altitude and inclination. Each has independent RAAN and mean anomaly:

x = [
    altitude_km,
    inclination_deg,
    raan_1, raan_2, raan_3, raan_4,
    mean_anomaly_1, mean_anomaly_2, mean_anomaly_3, mean_anomaly_4
]

The fixed epoch is 2025-01-01 00:00 UTC. Eccentricity is 0.001 and argument of perigee is 0°. The default network selects Svalbard, Fairbanks, Singapore, Hartebeesthoek, Cordoba, and Troll from Brahe’s embedded KSAT dataset.

An access requires at least 10° elevation. Brahe searches on a 60-second grid and refines boundaries to 0.25 seconds. Windows shorter than 180 seconds are reported but excluded from all objectives and constraints. Since a retained window spans at least three grid steps, the grid cannot step entirely over it.

Overlapping satellite windows at one station are merged. Thus simultaneous visibility of two satellites is one continuous contact opportunity, and contact duration is not double counted.

Optimization formulations

The scalar BiteOpt retry objective is minimized:

score =
    worst_station_gap_hours
    + 10 × missing_required_passes
    + 4.5 × normalized_altitude
    + circular_RAAN_spread

All undesirable terms are positive penalties. The altitude term ranges from zero at 450 km to 4.5 at 900 km.

Constrained MODE independently minimizes:

1. worst communication gap over all stations;
2. negative total network contact duration;
3. normalized_altitude + 0.5 × circular_RAAN_spread.

MODE also receives one explicit feasibility constraint:

missing_required_passes <= 0

The required number is two merged, accepted contact opportunities per station per 24 hours, scaled up for longer horizons. Bounds enforce the prescribed LEO altitude range, and the three-minute rule is enforced by filtering.

The printed Pareto quality is a higher-is-better summary used only to select one representative for reporting:

quality =
    total_contact_hours
    / ((1 + worst_gap_hours) × (1 + launch_complexity))

MODE itself still optimizes the uncollapsed three-objective vector.

MAP-Elites is retained as a separate architecture view. Shared altitude and circular RAAN spread are behavior descriptors; the feasible scalar constellation score determines quality inside each cell. Candidates missing the required station passes cannot enter the archive. The resulting portfolio answers which contact design is best at different altitude/plane-spread architectures, while MODE continues to expose the gap/contact/launch trade-off.

Parallelism without oversubscription

Both layers can parallelize, so the CLI makes ownership explicit:

• --parallel outer is the default. fcmaes runs independent retry optimizers or MODE candidate evaluations on --workers threads. Every Brahe access search is serial.
• --parallel inner gives fcmaes one objective worker and configures Brahe to process the 24 station/satellite pairs on --workers threads.

No mode allows both pools to expand at once. For this workload, outer parallelism is preferable because candidate evaluations are independent and numerous.

The built-in benchmark evaluates exactly the same fixed candidate vectors in both modes and verifies identical scores:

cd tutorials/brahe-constellation
cargo run --release -- \
  --mode benchmark --workers 24 --benchmark-candidates 512 --seed 42

Recorded on 2026-07-24 on an AMD Ryzen 9 9950X:

The maximum score difference was exactly zero. Outer parallelism was 1.20× faster for this six-station, four-satellite problem. This is a single-machine measurement, not a general Brahe benchmark; the balance can change with a larger station network or fewer optimizer candidates.

Run

A substantial 24-worker run:

cd tutorials/brahe-constellation
cargo run --release -- \
  --mode all --workers 24 --parallel outer \
  --evaluations 500 --retries 24 \
  --mo-evaluations 8192 --popsize 256 --seed 42 \
  --qd-evaluations 4096 --qd-capacity 400 --qd-chunk-size 128 \
  --numerical-validation

--evaluations is the budget of each BiteOpt retry. MODE rounds --mo-evaluations up to a complete population. Numerical validation runs only after optimization.

A quick functional run:

cargo run --release -- \
  --mode both --workers 4 --parallel outer \
  --evaluations 12 --retries 2 \
  --mo-evaluations 8 --popsize 4 --no-output

Run only the QD architecture search:

cargo run --release -- \
  --mode qd --workers 24 --parallel outer \
  --qd-evaluations 4096 --qd-capacity 400 \
  --qd-chunk-size 128 --seed 42

QD requires --parallel outer; the CLI refuses nested Brahe/fcmaes pools.

Evaluate the baseline without optimization:

cargo run --release -- --mode simulate --workers 16

Replay a design by passing ten comma-separated values:

cargo run --release -- \
  --mode simulate --numerical-validation \
  --x 702.086836885,88.660434130,296.042491414,172.978771112,227.690703019,181.241523928,329.014897384,148.678143359,241.988590149,297.782016936

Use --provider and --stations to select another embedded network. Run cargo run --release -- --help for all options.

Recorded 24-worker optimization

The following deterministic smoke run uses the full 24-hour model:

cargo run --release -- \
  --mode both --workers 24 --parallel outer \
  --evaluations 50 --retries 24 \
  --mo-evaluations 512 --popsize 64 --seed 42

Every design in the table satisfies the per-station pass constraint. BiteOpt minimizes the scalar’s strong altitude and RAAN-spread costs; MODE exposes the trade-off and finds a representative with 32.9% more contact and a 38.3% shorter worst gap than the baseline. Its final population contained 64 nondominated feasible points in this small run.

The MODE representative is:

[702.086836885, 88.660434130,
 296.042491414, 172.978771112, 227.690703019, 181.241523928,
 329.014897384, 148.678143359, 241.988590149, 297.782016936]

Optional finalist validation replaces two-body Keplerian motion with Brahe’s numerical propagator and a 20×20 EGM2008 gravity field. For that representative it predicted a 2.790-hour worst gap and 22.561 contact-hours: changes of -0.049 hour and +0.450 hour respectively. The numerical module is not used during optimization because it is slower and Brahe currently documents that API as experimental.

These are functional results from one optimizer seed, not repeated-seed performance statistics.

MAP-Elites pilot and campaign

Brahe passed the conditional QD pilot. Altitude and circular plane spread are direct architecture choices with physical bounds, so the archive does not duplicate MODE’s objective axes. The 512-evaluation pilot occupied 94 of 100 niches with no descriptor clipping.

The publication campaign used 24 outer fcmaes workers, serial Brahe access calculations, a 400-cell archive, chunks of 128 and 4,096 evaluations for each of three optimizer seeds:

The near-complete coverage shows that the architecture space is reachable; it does not imply all cells have equally strong access performance. MODE remains the correct artifact for selecting among the three explicit mission objectives. Raw statistics are in results/publication/qd-summary.csv.

Output

Unless --no-output is supplied, the command writes:

• results/report.html: self-contained station map, access timeline, and optimization progress;
• results/access_windows.csv: accepted and rejected raw Brahe windows;
• results/stations.csv: station coordinates and aggregated metrics;
• results/design.csv: the selected design;
• results/pareto.csv: feasible nondominated MODE designs;
• results/convergence.csv: incumbent scalar proxy or MODE quality.
• results/qd_archive.csv: occupied architecture niches and their designs;
• results/run.json: schema-v1 run configuration and artifact references.

Open results/report.html directly in a browser; it has no external assets.

Accuracy and scope

This is a simulation-optimization example, not an operational mission-design tool. It deliberately omits antenna scheduling, simultaneous-link capacity, frequency compatibility, occultation beyond the elevation constraint, launch vehicle plane-change modeling, collision avoidance, and station outages. Static zero EOP data is reproducible but not appropriate for precise pass timing. The numerical finalist uses gravity perturbations but no drag, solar radiation pressure, or third bodies.

For higher fidelity, initialize current EOP data, add spacecraft-specific force models and constraints, validate several Pareto finalists, and keep that expensive stage separate from the fast search.

Test

cargo test
cargo clippy --all-targets -- -D warnings

The tests cover bounds, interval merging, circular plane spread, embedded station loading, deterministic access evaluation, constraint output, and invalid configuration. The QD adapter test checks feasible architecture descriptors and archive option validation.

References

• Brahe source and MIT license
• Brahe ground-station datasets
• Brahe access computation
• Brahe maximum-communications-gap example
• Brahe thread-pool configuration
• Brahe numerical propagation