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Optimal routing and transmission strategies for UAV reconnaissance missions with detection threats

Riley Badenbroek, Relinde Jurrius, Lander Verlinde

TL;DR

This work models UAV reconnaissance as joint routing and transmission decisions on a weighted graph with edge survival $q_{ij}$ and vertex transmission probability $p_i$, aiming to maximize the expected transmitted information $\mathbb{E}[X]$ under detection threats. It proves NP-completeness, provides a MILP formulation with linearized survival and value terms, and develops a genetic algorithm to efficiently search for high-quality strategies; it further generalizes to multiple drones. Key findings show MILP solves small instances quickly but scales poorly, while the GA—especially with full mutation strategies—consistently reaches near-optimal solutions and scales better, with multi-drone coordination yielding substantial gains. The results demonstrate practical planning tools for autonomous reconnaissance under adversarial threats and lay groundwork for extending to larger teams and more complex threat models.

Abstract

We consider an autonomous reconnaissance mission where an Unmanned Aerial Vehicle (UAV) has to visit several points of interest and communicate the intel back to the base. At every point of interest, the UAV has the option to either send back all available info, or continue to the next point of interest and communicate at a later stage. Both choices have a chance of detection, meaning the mission fails. We wish to maximize the expected amount of information gathered by the mission. This is modelled by a routing problem in a weighted graph. We show that the problem is NP-complete, discuss an ILP formulation, and use a genetic algorithm to find good solutions for up to ten points of interest.

Optimal routing and transmission strategies for UAV reconnaissance missions with detection threats

TL;DR

This work models UAV reconnaissance as joint routing and transmission decisions on a weighted graph with edge survival and vertex transmission probability , aiming to maximize the expected transmitted information under detection threats. It proves NP-completeness, provides a MILP formulation with linearized survival and value terms, and develops a genetic algorithm to efficiently search for high-quality strategies; it further generalizes to multiple drones. Key findings show MILP solves small instances quickly but scales poorly, while the GA—especially with full mutation strategies—consistently reaches near-optimal solutions and scales better, with multi-drone coordination yielding substantial gains. The results demonstrate practical planning tools for autonomous reconnaissance under adversarial threats and lay groundwork for extending to larger teams and more complex threat models.

Abstract

We consider an autonomous reconnaissance mission where an Unmanned Aerial Vehicle (UAV) has to visit several points of interest and communicate the intel back to the base. At every point of interest, the UAV has the option to either send back all available info, or continue to the next point of interest and communicate at a later stage. Both choices have a chance of detection, meaning the mission fails. We wish to maximize the expected amount of information gathered by the mission. This is modelled by a routing problem in a weighted graph. We show that the problem is NP-complete, discuss an ILP formulation, and use a genetic algorithm to find good solutions for up to ten points of interest.

Paper Structure

This paper contains 23 sections, 4 theorems, 44 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Our Contribution
  4. Mathematical exploration of the problem
  5. An example of a reconnaissance mission
  6. NP-completeness
  7. Mixed-integer linear problem formulation for the autonomous reconnaissance problem
  8. Moving the drone
  9. Observing information
  10. Sending information
  11. Survival probability
  12. Expected transmission value
  13. Final model
  14. Performance
  15. Genetic algorithm
  16. ...and 8 more sections

Key Result

Theorem 1

The reconnaissance problem on the undirected connected graph $G = (V, E)$ has an optimal solution consisting of at most $|V|^2-1$ time periods.

Figures (5)

  • Figure 1: Example of a graph with send and crossing probabilities.
  • Figure 2: Overview of a time period in the mixed-integer linear programming problem.
  • Figure 3: Overview of how to construct a new generation. First order the current generation from best to worst. Then discard the worst genes in the generation. This corresponds to the red part. Copy the best genes -- the green part -- directly in the new generation. The rest of the genes in the new generation is made of crossovers of genes that are either in the green part or the grey part of the previous generation.
  • Figure 4: Four runs of the genetic algorithm for $K_{10}$. The $x$-axis shows the generation, the $y$-axis the best expected value. There is only one run that finds the optimal strategy.
  • Figure 5: Four runs of the genetic algorithm with mutation. The $x$-axis shows the generation, the $y$-axis the best expected value.

Theorems & Definitions (8)

  • Theorem 1
  • proof
  • Proposition 2
  • proof
  • Proposition 3
  • proof
  • Theorem 4
  • proof