Benchmarking global optimization techniques for unmanned aerial vehicle path planning

TL;DR

This work investigates using UAV path planning as a benchmark for global optimization by generating 56 realistic problem instances and comparing 12 diverse optimization methods across varying dimensionalities and budgets. It combines a terrain/threat generator with a four-component objective (path length, safety, altitude, and smoothness) and analyzes instance novelty with Exploratory Landscape Analysis. The empirical results consistently favor evolutionary algorithms such as EA4eig, APGSK, and ELSHADE, though performance varies with budget and dimension, underscoring a meaningful variable-dimension aspect. The paper provides a reproducible UAV benchmark and discusses implications for future benchmarking platforms and variable-dimension optimization methods.

Abstract

The Unmanned Aerial Vehicle (UAV) path planning problem is a complex optimization problem in the field of robotics. In this paper, we investigate the possible utilization of this problem in benchmarking global optimization methods. We devise a problem instance generator and pick 56 representative instances, which we compare to established benchmarking suits through Exploratory Landscape Analysis to show their uniqueness. For the computational comparison, we select twelve well-performing global optimization techniques from both subfields of stochastic algorithms (evolutionary computation methods) and deterministic algorithms (Dividing RECTangles, or DIRECT-type methods). The experiments were conducted in settings with varying dimensionality and computational budgets. The results were analyzed through several criteria (number of best-found solutions, mean relative error, Friedman ranks) and utilized established statistical tests. The best-ranking methods for the UAV problems were almost universally the top-performing evolutionary techniques from recent competitions on numerical optimization at the Institute of Electrical and Electronics Engineers Congress on Evolutionary Computation. Lastly, we discussed the variable dimension characteristics of the studied UAV problems that remain still largely under-investigated.

Figures (11)

• Figure 1: General scheme of the adopted approach.
• Figure 2: A Side view of four generated terrains with 900 pixels. The black rectangle/circle resembles the start/goal points respectively. The red cylinders represent the threats that the UAV must avoid.
• Figure 3: Different scenarios considered in the penalty function $T_k$ for UAV passing a line segment from point $P_{ij}$ to $P_{i,j+1}$. The red circle represents the area of collision with penalty $J_{\text{pen}}$, while the yellow circle indicates the surrounding dangerous zone.
• Figure 4: UAV’s turning angle and climbing angle. The dark green points denote the waypoints $P_{ij}$, with their projection on the terrain colored light green, and the projection on the horizontal plane represented by black points $P'_{ij}$. $P"_{i,j+1}$ is the projection of $P_{i,j+1}$ onto a horizontal plane at an altitude of $z_{i,j}$. The red circle represents a potential threat $T_k$.
• Figure 5: Visualization of the ELA features using different dimension reduction techniques.