Penerapan Flower Pollination Algorithm dengan Teknik Clustering dalam Penyelesaian Masalah Diophantine

Authors

  • Rahmat Karim Universitas Sembilanbelas November Kolaka
  • - Salim Universitas Sembilanbelas November Kolaka

DOI:

https://doi.org/10.33633/tc.v22i2.7174

Keywords:

Flower Pollination Algorithm, Clustering technique, The Diophantine Problem

Abstract

Permasalahan Diophantine adalah suatu permasalahan yang diwakili persamaan atau sistem persamaan yang memerlukan bilangan bulat non-negatif sebagai solusi. Permasalahan ini banyak dijumpai di berbagai bidang termasuk Computer engineering seperti pengelolaan jaringan dan sinyal. Akan tetapi belum ada metode umum yang secara efektif dapat menyelesaikan permasalahan Diophantine.  Tujuan utama dalam penelitian ini adalah untuk melakukan penyesuaian metode FPAC agar FPAC tidak hanya dapat digunakan pada permasalahan Multimodal tetapi juga dapat dijadikan sebagai alternatif pada permasalahaan Diophantine. Transformasi persamaan ataupun sistem persamaan ke dalam bentuk fungsi optimasi dan transformasi output bilangan real ke bilangan bulat pada setiap tahapan algoritma merupakan kunci utama FPAC dalam menyelesaikan permasalahan Diophantine. Hasil penelitian ini menunjukan bahwa FPAC dapat menemukan seluruh solusi dari persamaan Diophantine baik persamaan yang memiliki jumlah variabel dan pangkat yang berbeda maupun persamaan dalam bentuk eksponensial.  FPAC juga dapat menemukan seluruh solusi yang tersedia pada sistem persamaan Diophantine baik yang berdimensi rendah (kasus 1) maupun dimensi tinggi (kasus 2 dan 3). Secara umum, FPAC terbukti efektif dalam menyelesaikan permasalahan Diophantine baik dalam bentuk persamaan maupun sistem persamaan yang memiliki solusi tunggal maupun jamak dalam sekali running.

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Published

2023-05-26

Issue

Vol. 22 No. 2 (2023): Mei 2023

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