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All Journal Kubik Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai-Nilai Islami) Jurnal Matematika: MANTIK Jurnal Tadris Matematika KUBIK: Jurnal Publikasi Ilmiah Matematika Jurnal Riset Mahasiswa Matematika Jurnal Tadris Matematika Journal of Research on Community Engagement
Mohammad Nafie Jauhari
Universitas Islam Negeri Maulana Malik Ibrahim Malang, Indonesia
Arts Humanities Computer Science & IT Economics, Econometrics & Finance Education Mathematics Social Sciences

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Optimasi Algoritma Cheapest Insertion Heuristic dengan Algoritma Tabu Search dalam Pencarian Rute Terpendek Yulianti, Silviyatus; Jauhari, Mohammad Nafie; Nashichuddin, Achmad
Jurnal Riset Mahasiswa Matematika Vol 4, No 6 (2025): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v4i6.33343

Abstract

The shortest route finding problem is a significant topic in graph theory and combinatorial optimization, with wide applications in logistics, transportation, and scheduling. This research aims to improve the quality of the solution and time efficiency in solving the Traveling Salesman Problem (TSP) by optimizing the Cheapest Insertion Heuristic (CIH) algorithm using the application of the Tabu Search algorithm. The CIH algorithm constructs an initial solution by inserting points based on minimum weight. At the same time, the Tabu Search algorithm is applied to enhance the solution by avoiding local optima using a tabu list mechanism. The research data, consisting of the distances between parking retribution collection points by the Malang City Transportation Agency in Sukun Sub-district, were obtained from Google Maps. The algorithm performance evaluation is done by comparing the total mileage before and after optimization, and statistically analyzed using the Wilcoxon signed-rank test because the data does not follow a normal distribution. The results showed that optimizing the CIH algorithm using the Tabu Search algorithm significantly resulted in routes with shorter travel distances than using the CIH algorithm alone. This finding proves that optimizing the CIH algorithm with Tabu Search increases the effectiveness of finding the shortest route.The shortest route finding problem is a significant topic in graph theory and combinato-rial optimization, with wide applications in logistics, transportation, and scheduling. Thisresearch aims to improve the quality of the solution and time efficiency in solving the Trav-eling Salesman Problem (TSP) by optimizing the Cheapest Insertion Heuristic (CIH) algo-rithm using the application of the Tabu Search algorithm. The CIH algorithm constructs aninitial solution by inserting points based on minimum weight. At the same time, the TabuSearch algorithm is applied to enhance the solution by avoiding local optima using a tabulist mechanism. The research data, consisting of the distances between parking retributioncollection points by the Malang City Transportation Agency in Sukun Sub-district, were ob-tained from Google Maps. The algorithm performance evaluation is done by comparing thetotal mileage before and after optimization, and statistically analyzed using the Wilcoxonsigned-rank test because the data does not follow a normal distribution. The results showedthat optimizing the CIH algorithm using the Tabu Search algorithm significantly resulted inroutes with shorter travel distances than using the CIH algorithm alone. This finding provesthat optimizing the CIH algorithm with Tabu Search increases the effectiveness of findingthe shortest route.
On the Forgotten Index and Jacobson Graphs Associated with Integer Rings Modulo n Jauhari, Mohammad Nafie; Jannah, Shahnaz Latifatul; Turmudi, Turmudi; Nisfulaila, Intan
KUBIK Vol 9 No 2 (2024): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v9i2.39585

Abstract

This paper investigates the connections between the Jacobson graph and the algebraic properties of rings through the analysis of the Jacobson graph of the ring \mathbb{Z}_{3p}, where p is a prime number greater than 3. The Jacobson graph of a commutative ring R is constructed by taking the elements of R, excluding its Jacobson Radical, as vertices, and connecting two distinct vertices if 1 minus their product is not a unit in R. The F-Index is utilized to capture and represent the structural properties of the ring through its associated graph. A detailed examination of the Jacobson Radical, maximal ideals, and vertex degrees in \mathbb{Z}_{3p} leads to the calculation of the F-Index, providing insights into the graph’s connectivity and underlying algebraic structure. This study contributes to the intersection of algebra and graph theory, offering a foundation for further research into more complex algebraic structures.
Pembobotan Ulang pada Graf Berbobot Negatif untuk Menerapkan Algoritma Dijkstra dalam Menentukan Lintasan Terpendek Salsabillah, Natasya Thalia; Jauhari, Mohammad Nafie; Nashichuddin, Achmad
Jurnal Riset Mahasiswa Matematika Vol 5, No 1 (2025): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v5i1.34383

Abstract

Algoritma Dijkstra merupakan algoritma untuk mencari lintasan terpendek yang bekerja secara optimal pada graf berbobot non-negatif. Namun, dalam berbagai permasalahan nyata seperti sistem transportasi dan jaringan keuangan, sering ditemukan sisi dengan bobot negatif yang menyebabkan Algoritma Dijkstra tidak dapat diterapkan secara langsung. Penelitian ini bertujuan untuk mengatasi keterbatasan tersebut dengan menerapkan metode pembobotan ulang menggunakan Algoritma Johnson. Metode ini mengombinasikan Algoritma Bellman-Ford dan Dijkstra untuk mengubah bobot negatif menjadi non-negatif tanpa mengubah struktur solusi optimal. Data yang digunakan berupa dua graf acak berarah yang masing-masing terdiri dari 31 simpul, yang dibuat menggunakan algoritma Erdos-Renyi. Hasil penelitian menunjukkan bahwa pembobotan ulang berhasil membuat bobot graf menjadi non-negatif sehingga Algoritma Dijkstra dapat diterapkan, dan hasil lintasan terpendek yang diperoleh sama dengan hasil dari Algoritma Bellman-Ford. Dengan demikian, metode pembobotan ulang menggunakan Algoritma Johnson terbukti efektif dalam menangani bobot negatif dan tetap menjaga keakuratan hasil pencarian lintasan terpendek menggunakan Algoritma Dijkstra.
On the Forgotten Index and Jacobson Graphs Associated with Integer Rings Modulo n Jauhari, Mohammad Nafie; Jannah, Shahnaz Latifatul; Turmudi, Turmudi; Nisfulaila, Intan
KUBIK Vol 9 No 2 (2024): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v9i2.39585

Abstract

This paper investigates the connections between the Jacobson graph and the algebraic properties of rings through the analysis of the Jacobson graph of the ring \mathbb{Z}_{3p}, where p is a prime number greater than 3. The Jacobson graph of a commutative ring R is constructed by taking the elements of R, excluding its Jacobson Radical, as vertices, and connecting two distinct vertices if 1 minus their product is not a unit in R. The F-Index is utilized to capture and represent the structural properties of the ring through its associated graph. A detailed examination of the Jacobson Radical, maximal ideals, and vertex degrees in \mathbb{Z}_{3p} leads to the calculation of the F-Index, providing insights into the graph’s connectivity and underlying algebraic structure. This study contributes to the intersection of algebra and graph theory, offering a foundation for further research into more complex algebraic structures.
Aplikasi Diagonalisasi Matriks dalam Penyelesaian Sistem Persamaan Diferensial Biasa Orde Satu Ulfa, Anis Maria; Nisfulaila, Intan; Jauhari, Mohammad Nafie
Jurnal Riset Mahasiswa Matematika Vol 5, No 2 (2025): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v5i2.34798

Abstract

Persamaan diferensial adalah sebarang persamaan dengan nilai tak-diketahui (unknown) berupa suatu fungsi dan yang melibatkan turunan (atau diferensial) dari fungsi yang tidak diketahui ini. Berorde satu karena hanya mengandung turunan pertama, tidak ada turunan yang lebih tinggi. Sebuah sistem persamaan diferensial adalah sekumpulan dua atau lebih persamaan diferensial yang saling berkaitan. Sistem persamaan diferensial membutuhkan metode-metode atau pendekatan dalam penyelesaiannya yang sering kali sulit untuk diselesaikan secara langsung. Salah satu pendekatan efektif yang dapat digunakan dalam penyelesaian sistem persamaan diferensial adalah dengan diagonalisasi matriks. Diagonalisasi matriks adalah proses mengubah suatu matriks menjadi bentuk diagonal. Tujuan penelitian ini adalah untuk membahas dan mengeksplorasi penerapan diagonalisasi matriks dalam penyelesaian sistem persamaan diferensial. Hasil dari penelitian ini adalah sistem persamaan diferensial biasa orde satu yang dapat dinotasikan menjadi matriks dan diselesaikan dengan diagonalisasi matriks jika matriks memiliki nilai eigen berbeda, memiliki vektor eigen bebas linear, dan terdapat sebuah matriks invertibel sehingga adalah sebuah matriks diagonal. 
Co-Authors Ach. Nashichuddin Anisatur Rizqiyah Annisa Hardiningsih HR Anwar, Nurul Hafidhoh Armeyntan, Tata Sutrafia Bella Nafa Savitri Dayanti, Vivi Dewi Ismiarti Elly Susanti Erna Herawati, Erna Evawati Alisah Fika Wahyuni Hairur Rahman Hairur Rahman Harini, Sri Hisyam Fahmi Hisyam Fahmi Iftitahur Rohmah Ismiarti, Dewi Jannah, Shahnaz Latifatul Juhari Juhari, Juhari Lestari, Qhonita Guruh Dwi Lubab, Ahmad Mohammad Jamhuri Mufinnun, Nur Fatin Muhammad Khudzaifah Muhammad Khudzaifah Muhammad Khudzaifah Muhammad Khudzaifah Nasichuddin, Achmad Nisful Laila Novianti, Chofifah Alfin Nur Fatin Mufinnun Nurul Hafidhoh Anwar Reta, Tre Hayu Ria Risma Amelia, Risma Riyan Fahmi Syihabuddin Rizqiyah, Anisatur Safitri, Sukmawati Indah Salsabila, Wardatun Naura Salsabillah, Natasya Thalia Savitri, Bella Nafa Sri Harini Susanti, Elly Syihabuddin, Riyan Fahmi Tre Hayu Ria Reta Turmudi Turmudi, Turmudi Ulfa, Anis Maria Wahyuni, Fika Wike, Wike Nur Yulianti, Silviyatus