Optimasi Algoritma Genetika dalam Inisialisasi Pusat Gerombol K-Prototypes (Studi Kasus: Mata Kuliah S1 IPB University)

Abstract

Sensitivitas algoritme K-Prototypes terhadap pemilihan centroid awal sering menghambat penggerombolan data bertipe campuran. Inisialisasi secara acak cenderung menghasilkan solusi optimum lokal sehingga hasil penggerombolan menjadi kurang stabil pada setiap pengulangan. Penelitian ini bertujuan mengoptimalkan pemilihan centroid awal pada algoritme K-Prototypes menggunakan algoritme genetika. Metode tersebut diterapkan pada data mata kuliah program S1 IPB University sebanyak 1.364 mata kuliah yang terdiri atas tujuh peubah kategorik dan sepuluh peubah numerik. Kebaikan gerombol yang dihasilkan dinilai berdasarkan nilai within-cluster sum of squares (WCSS), dengan nilai yang semakin rendah menunjukkan gerombol yang semakin kompak. Dua belas skenario algoritma genetika dievaluasi berdasarkan variasi ukuran populasi, jenis crossover, dan jumlah generasi maksimum, dengan kinerja diukur menggunakan WCSS dan waktu komputasi. Skenario dengan ukuran populasi 100, one-point crossover, dan 100 generasi dipilih sebagai konfigurasi terbaik karena secara konsisten menghasilkan nilai WCSS terendah dengan waktu komputasi paling efisien. Kombinasi ini menghasilkan WCSS sebesar 24.021,26 pada lima gerombol. Nilai WCSS ini lebih rendah 5,18% dibandingkan inisialisasi acak. Kelima gerombol tersebut terpisah berdasarkan tipe mata kuliah, jumlah kelas paralel, keberadaan praktikum, keberadaan responsi, kapasitas peserta, dan durasi pertemuan. Algoritme genetika terbukti memperbaiki stabilitas proses penggerombolan K-Prototypes. Kualitas hasil gerombol turut meningkat dibandingkan dengan pendekatan inisialisasi acak.

The sensitivity of the K-Prototypes algorithm to initial centroid selection often hinders clustering of mixed-type data. Random initialization tends to produce local optima, resulting in less stable clustering outcomes across repetitions. This study aims to optimize the selection of initial centroids in the K-Prototypes algorithm using a genetic algorithm. The method was applied to course data from undergraduate programs at IPB University, comprising 1,364 courses with seven categorical and ten numerical variables. The quality of the resulting clusters was evaluated based on the within-cluster sum of squares (WCSS), where lower values indicate more compact clusters. Twelve genetic algorithm scenarios were evaluated based on population size, crossover type, and maximum number of generations, with performance measured using WCSS and computational time. The scenario with a population size of 100, one-point crossover, and 100 generations was selected as the best configuration because it consistently produced the lowest WCSS with the most efficient computational time. This combination yielded a WCSS of 24,021.26 for five clusters, which was 5.18% lower than that obtained using random initialization. The five clusters were distinguished by course type, number of parallel classes, availability of practical sessions, availability of tutorials, participant capacity, and meeting duration. The genetic algorithm improved the stability and cluster quality of K-Prototypes compared with random initialization.