# Parametric Optimization of VLM Panel Discretization Using Bio-Inspired Crayfish and Aquila Algorithms Coupled with Hybrid RSM-Based Ensemble Machine Learning Surrogate Models: A Case Study

## TL;DR

This paper introduces a bio-inspired optimization framework to improve the accuracy of aerodynamic predictions using the Vortex Lattice Method by optimizing panel discretization strategies.

## Contribution

A novel hybrid response surface methodology and ensemble machine learning models are combined with bio-inspired algorithms to optimize VLM panel discretization.

## Key findings

- Optimally clustered discretization improved aerodynamic prediction accuracy by 33% compared to uniform distribution.
- Trailing-edge clustering dominated accuracy at low angles of attack, while tip clustering became more influential at higher angles.
- Aquila algorithm showed higher solution consistency, while Crayfish converged faster but with greater dispersion.

## Abstract

Fast and reliable aerodynamic predictions are crucial in the early phases of aircraft design, where a quick assessment of various configurations is required. In this context, the Vortex Lattice Method (VLM) is widely adopted due to its computational efficiency; however, its predictive accuracy is highly sensitive to panel discretization strategies, which are often determined heuristically. This study proposes a bio-inspired optimization framework for VLM panel discretization and evaluates it through a systematic case study on a representative wing geometry. A grid-convergence analysis was initially carried out to ensure solution independence across various spanwise-to-chordwise panel ratios. Subsequently, a novel Hybrid Response Surface Methodology (HRSM), integrating Box–Behnken and Central Composite experimental designs, was employed to enable a more comprehensive exploration of the factor space while quantifying the effects of clustering parameters at the leading-edge, trailing-edge, root, and tip regions of the wing. The HRSM dataset was further utilized to train Ensemble Machine-Learning surrogate models, which were coupled with bio-inspired Crayfish and Aquila optimization algorithms, alongside a classical Genetic Algorithm (GA) as a performance benchmark, to identify the optimal discretization strategy and to enable a comparative assessment of their convergence behavior and robustness against the numerical noise of the ensemble-based landscape. Compared to base (i.e., uniform) panel distribution, the optimally clustered discretization enhanced overall aerodynamic prediction accuracy by approximately 33%, particularly at low angles of attack, while maintaining robust performance at higher angles. Both algorithms converged to similar minima; however, the Aquila algorithm achieved higher solution consistency, whereas the Crayfish algorithm exhibited greater dispersion despite faster convergence, revealing a multimodal optimization landscape. The variance decomposition revealed that trailing-edge clustering dominated aerodynamic accuracy at low angles of attack, contributing up to 90% of the total variance, whereas tip clustering became increasingly influential at higher angles, exceeding 30%, highlighting the need for adaptive discretization strategies to ensure reliable VLM-based aerodynamic analyses.