# A Metaheuristic Optimization Algorithm for Task Clustering in Collaborative Multi-Cluster Systems

## TL;DR

This paper introduces a new optimization algorithm for grouping tasks in 3D environments for UAV swarms, improving performance and efficiency.

## Contribution

A dual-modal metaheuristic algorithm, DPM-Kmeans, is proposed for 3D task clustering with improved convergence and solution quality.

## Key findings

- DPM-Kmeans outperforms traditional methods by 2–10% in clustering metrics like SSE, SC, and DB.
- The algorithm shows superior convergence speed and robustness in large-scale 3D scenarios.
- The hybrid initialization strategy enhances initial solution diversity and environmental adaptability.

## Abstract

To address the task-grouping problem for air–ground integrated Unmanned Aerial Vehicle (UAV) swarm missions in three-dimensional (3D) environments, this study proposes a data-preprocessing and hybrid initialization clustering method based on 3D spatial features. A dual-modal prototype meta-heuristic optimization model, Dual-Prototype Metaheuristic K-Means (DPM-Kmeans), is constructed accordingly. First, to overcome spatial information loss in high-dimensional task allocation, a 3D spatial task data preprocessing technique and a hybrid initialization strategy based on the golden spiral distribution are designed. This ensures the diversity and environmental adaptability of the initial solutions. Second, a dual-modal prototype optimization framework incorporating row prototypes (local refinement) and column prototypes (global combination) was constructed using meta-heuristics and clustering algorithms. The prototype-driven replacement update mechanism simultaneously performs global and local search, balancing the algorithm’s exploration and exploitation capabilities while expanding the solution space. This effectively addresses premature convergence issues in complex search spaces. Simultaneously, a collaborative multi-constraint, dynamically weighted optimization model was constructed, incorporating task requirements and flight distance constraints to ensure that the grouping scheme approximates the global optimum. Simulation results demonstrate that compared to traditional K-means and mainstream meta-heuristic optimization algorithms, DPM-Kmeans achieves an overall improvement of 2–10% in Sum of Squared Errors (SSE), Silhouette Coefficient (SC), and Davies–Bouldin Index (DB) metrics. It exhibits superior convergence speed and solution quality, proving the method’s excellent scalability and robustness in multi-constraint, large-scale 3D scenarios.