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Journals / Karaelmas Fen ve Mühendislik Dergisi / 2026 / Cilt: 16 Sayı: 1

Clustering with Meta-Heuristic Algorithms: Comparative Analysis of Different Objective Functions with MetaCluster Platform

Meta-Sezgisel Algoritmalarla Kümeleme: MetaCluster Platformu ile Farklı Hedef Fonksiyonların Karşılaştırmalı Analizi

Münevver Bahar(ADNAN MENDERES UNIVERSITY)0009-0009-0489-0884
Murat Karakoyun(NECMETTIN ERBAKAN UNIVERSITY)0000-0002-0677-9313
Pages
57–74
Publication Date
2026-04-21
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The results show that the performances of the algorithms differ significantly depending on the geometry of the datasets and the objective functions.

📌 3 Key Takeaways

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Objective & Hypothesis:Data clustering is a basic analysis method among unsupervised learning methods that aims to discover natural groups within data sets.
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Key Findings & Data:In this study, the clustering performances of a total of 13 different metaheuristic algorithms on three different artificial data sets, circles, moons and blobs, under three different objective functions (BHI, MIS, XBI) were compared using the Python-based MetaCluster platform.
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Conclusion & Impact:The results show that the performances of the algorithms differ significantly depending on the geometry of the datasets and the objective functions.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Meta-sezgisel algoritmalar · metaCluster · veri kümeleme

Abstract

Data clustering is a basic analysis method among unsupervised learning methods that aims to discover natural groups within data sets. Traditional clustering algorithms cannot provide sufficient success especially in complex structured data sets. For this reason, metaheuristic algorithms have come to the forefront as an effective alternative in data clustering problems in recent years. In this study, the clustering performances of a total of 13 different metaheuristic algorithms on three different artificial data sets, circles, moons and blobs, under three different objective functions (BHI, MIS, XBI) were compared using the Python-based MetaCluster platform. The evaluation was made with BRI, DBI, DRI, CHI and KDI metrics. The results show that the performances of the algorithms differ significantly depending on the geometry of the datasets and the objective functions. On the Blobs dataset, 12 algorithms (ALO, AOA, BBO, FBIO, GCO, GWO, HGSO, HHO, ICA, SMA, TLO, WOA) achieved the same optimal DBI value (≈0.2804) under the BHI and MIS objective functions. On the XBI objective function, the entire group, including BMO, produced almost the same clustering quality at ≈0.2612. On the Circles dataset, the FBIO algorithm achieved the lowest DBI value (≈0.6444) under the XBI objective function, followed by the SMA, HHO, and BMO algorithms with similar but higher values. HGSO and ICA exhibited the weakest and most unstable performance on this dataset in terms of both DBI means and variances. On the Moons dataset, the WOA and GCO algorithms performed best with a DBI value of ≈0.8093 under the BHI objective function, while the majority of the other algorithms concentrated around 0.8094; ICA distinguished itself with relatively higher DBI values across all combinations. When examining the overall ranking by DBI, the FBIO, HHO, ALO, and TLO algorithms were among the most successful, while ICA ranked last when considering all datasets and objective functions. This study reveals that metaheuristic algorithms can provide more successful and applicable clustering solutions compared to traditional methods thanks to their flexible structures. The findings are guiding for researchers in the selection of algorithms and target functions.

Özet

Veri kümeleme, denetimsiz öğrenme yöntemleri arasında yer alan ve veri setlerinde doğal grupların keşfedilmesini amaçlayan temel bir analiz yöntemidir. Geleneksel kümeleme algoritmaları, özellikle karmaşık yapılı veri setlerinde yeterli başarıyı sağlayamamaktadır. Bu nedenle, meta-sezgisel algoritmalar son yıllarda veri kümeleme problemlerinde etkili bir alternatif olarak ön plana çıkmıştır. Bu çalışmada, Python tabanlı MetaCluster platformu kullanılarak toplam 13 farklı meta-sezgisel algoritmanın üç ayrı hedef fonksiyon (BHI, MIS, XBI) altında circles, moons ve blobs olmak üzere üç farklı yapay veri seti üzerindeki kümeleme performansları karşılaştırılmıştır. Değerlendirme, BRI, DBI, DRI, CHI ve KDI metrikleri ile yapılmıştır. Sonuçlar, veri setlerinin geometrisine ve hedef fonksiyonlara bağlı olarak algoritmaların performanslarının anlamlı biçimde farklılaştığını göstermektedir. Blobs veri setinde, BHI ve MIS hedef fonksiyonları altında 12 algoritma (ALO, AOA, BBO, FBIO, GCO, GWO, HGSO, HHO, ICA, SMA, TLO, WOA) aynı optimum DBI değerine (≈0.2804) ulaşırken, XBI hedef fonksiyonu altında bu grubun tamamı ile birlikte BMO’nun da yer aldığı 13 algoritma ≈0.2612 düzeyinde, neredeyse aynı kümeleme kalitesini üretmiştir. Circles veri setinde ise XBI hedef fonksiyonu altında FBIO algoritması en düşük DBI değerini (≈0.6444) sağlamış; SMA, HHO ve BMO algoritmaları benzer fakat daha yüksek değerlerle onu takip etmiştir. HGSO ve ICA bu veri setinde hem DBI ortalamaları hem de varyansları açısından en zayıf ve en dengesiz performansı sergilemiştir. Moons veri setinde ise BHI hedef fonksiyonu altında WOA ve GCO algoritmaları ≈0.8093 DBI değeri ile en iyi sonucu vermiş, diğer algoritmaların büyük kısmı yaklaşık 0.8094 civarında yoğunlaşmış; ICA ise tüm kombinasyonlar içinde nispeten daha yüksek DBI değerleri ile ayrışmıştır. DBI’ye göre genel sıralama incelendiğinde, FBIO, HHO, ALO ve TLO algoritmaları en başarılı grubun içinde yer alırken, ICA tüm veri setleri ve hedef fonksiyonlar dikkate alındığında son sırada konumlanmıştır. Bu çalışma, meta-sezgisel algoritmaların esnek yapıları sayesinde geleneksel yöntemlere kıyasla daha başarılı ve uygulanabilir kümeleme çözümleri sunabileceğini ortaya koymaktadır. Elde edilen bulgular, araştırmacılara algoritma ve hedef fonksiyon seçiminde yol gösterici niteliktedir.

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Cite This Article

Bahar, M., Karakoyun, M. (2026). Clustering with Meta-Heuristic Algorithms: Comparative Analysis of Different Objective Functions with MetaCluster Platform. Karaelmas Fen ve Mühendislik Dergisi, Cilt: 16 Sayı: 1, 57–74. https://doi.org/10.7212/karaelmasfen.1789235

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