Application of Genetic Algorithm on Inclusive Labeling of a Graph

Kiswara Agung Santoso, Bagus Arief Setiawan, Kusbudiono Kusbudiono


As science developed, heuristic methods began to be used in graph coloring. Heuristic methods that have been used for graph coloring include Genetic Algorithm, Tabu Search, and Ant Colony Algorithm. A Genetic Algorithm is a method for solving optimization problems. In this study, the Genetic Algorithm will be used for the issue of labeling irregular vertices of inclusive distances to label any graph inclusively. We restrict an inclusive 1-distance to a simple graph using one-point crossover and mutation. The steps are a generation of random chromosomes, evaluating chromosome fitness values with tournament selection, conducting an evolutionary process consisting of one-point crossover and mutation, repeating the process until the termination criteria are met. The results of implementing the genetic algorithm on inclusive labeling can be determined by the chromatic number based on the adjacency matrix. The results of this labeling can be used as an alternative solution to the problem of inclusive labeling.

Keywords: Genetic Algorithm; graph labeling; inclusive labeling.



Seiring berkembangnya ilmu pengetahuan metode heuristic mulai digunakan dalam pewarnaan graf. Metode heuristic yang telah digunakan untuk pewarnaan graf antara lain Algoritma Genetika, Tabu Search, dan Algoritma Semut (Ant Colony). Algoritma Genetika merupakan metode untuk menyelesaikan masalah optimasi. Pada penelitian ini, Algoritma Genetika digunakan untuk masalah pelabelan titik tak-teratur jarak inclusive agar dapat melabeli sebarang graf secara inclusive. Kami membatasi lingkup penelitian dengan menerapkan jarak inclusive 1 pada graf sederhana, menggunakan crossover satu titik dan mutasi. Metode yang digunakan dalam penelitian ini adalah studi literatur dengan mengkaji penggunaan Algoritma Genetika pada pelabelan titik tak-teratur jarak inclusive suatu graf. Langkah-langkah yang dilakukan adalah: pembangkitan kromosom secara acak, evaluasi nilai fitness kromosom dengan tournament selection, melakukan proses evolusi yang terdiri dari crossover satu titik dan mutasi, perulangan proses sampai kriteria pemerhentian terpenuhi. Hasil implementasi algoritma genetika pada pelabelan inclusive adalah dapat mengetahui bilangan kromatik berdasarkan matriks adjacency. Hasil pelabelan ini dapat dijadikan sebagai salah satu alternatif penyelesaian masalah pelabelan inklusif.

Kata Kunci : Algoritma Genetikapelabelan grafpelabelan inklusif.


Genetic Algorithm; Graph Labeling; Inclusive Labeling.


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DOI: 10.15408/inprime.v4i1.24327


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