---
title: "Constellation Optimization | Truman DeWalch"
description: "Multi-objective evolutionary optimization for satellite constellation design"
url: "https://trumandewalch.dev/research/constellation-optimization"
route: "/research/constellation-optimization"
---

Dissertation Component

# Constellation Optimization

Multi-objective evolutionary algorithms for deployer satellite constellation design

**Timeline:** 2024 – Present

**Algorithms:** R-NSDE, NSGA-II, SMS-EMOA, MOPSO

**Status:** Active

Deployer constellation on Walker planes versus conjunction coverage.

## Summary

- Multi-objective design of debris remediation constellations.
- Forward-only V3 pipeline with interpolated event catalogues.
- Explores trade-offs among delta-v, dust mass, and success rate.

## Overview

Designing an effective debris remediation constellation requires balancing competing objectives: maximize the fraction of conjunction events that can be feasibly remediated while minimizing total delta-v budgets and required dust mass. This is a challenging **multi-objective optimization problem** with a complex, nonlinear objective landscape shaped by orbital mechanics and stochastic debris encounters.

I developed a **V3 optimization pipeline** that uses forward-only propagation and pre-computed event catalogues to enable efficient exploration of the design space. The system supports multiple constellation topologies and uses adaptive evaluation policies to balance accuracy against computational cost.

## Design Space

The optimizer works with convenient parameterizations that avoid singularities in orbital elements:

### Walker Constellation

**Parameters:** altitude (km), inclination (°)

Classic Walker-delta/star pattern with configurable satellites per plane. Randomized anomalies avoid singular gradients.

### Flower Constellation

**Parameters:** scale, eccentricity, inclination, ω, Ω, M

6D harmonic flower patterns with altitude derived as a = s·R_E + R_E + 160 km. Perigee guard ensures a(1−e) ≥ R_E + 200 km.

### Dual Walker

**Parameters:** alt₁, alt₂, inc₁, inc₂

Two Walker-like shells at different altitudes and inclinations for improved coverage diversity.

## Evaluation Pipeline

The V3 pipeline achieves fast evaluation through several key optimizations that enable evolutionary algorithms to explore thousands of candidate designs:

- **Interpolated Event Catalogues:** Target states are pre-sampled into state tables and interpolated at runtime, eliminating expensive repeated propagation
- **Forward-Only Propagation:** Constellation satellites are propagated once per event to an intercept epoch late in the response timeline (default: 2 hours before conjunction). The minimum lead time constraint below governs how much warning is required before that intercept; the intercept epoch itself is the final approach point
- **Rust Batch Evaluator:** Native backend supports fast batch evaluation with vectorized processing
- **Adaptive Policies:** BetaPolicy uses credible interval convergence to stop evaluation early when success rate is confidently estimated

## Objectives & Constraints

Minimize

### Total Delta-V

Sum of deployment and phasing maneuver costs

Minimize

### Dust Mass

Required mass for momentum transfer

Maximize

### Success Rate

Fraction of events with feasible remediation

**Subject to:** max deployment Δv ≤ 0.5 km/s, max phasing Δv ≤ 0.1 km/s, minimum lead time ≥ 20 hours, perigee radius ≥ R_E + 200 km

## Key Results

01

### Rust-backed

Batch evaluation workflow for optimization studies

02

### 1,000 events

Events in reproducible conjunction bank

The optimizer produces Pareto fronts that are being used to explore trade-offs across the design space. Early runs suggest lower-altitude constellations tend to require less delta-v while reaching fewer events, with higher-altitude designs trading increased fuel for broader reach. Characterizing these trends is ongoing work.

## Publication

### "Stochastic Optimization Techniques for the Design of Just-In-Time Collision Avoidance Constellations"

DeWalch, T., Fitzgerald, R.

AIAA SciTech 2026

Presents the V3 forward-only evaluation pipeline, constellation parameterizations, adaptive stopping policies, and Pareto analysis of the debris remediation trade space.

## Tools & Technologies

Python 3.14 · Rust · R-NSDE · NSGA-II · SMS-EMOA · MOPSO · NumPy · Numba · maturin · Parallel Computing

[← Back to selected work](https://trumandewalch.dev/#projects)