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All Journal JURNAL EKONOMI DAN KEBIJAKAN PEMBANGUNAN Jurnal Manajemen dan Agribisnis Jurnal Keuangan dan Perbankan TELKOMNIKA (Telecommunication Computing Electronics and Control) SEMIRATA 2015 BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Jambura Journal of Mathematics International Journal of Industrial Optimization (IJIO) Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Milang Journal of Mathematics and Its Applications Jurnal Matematika Integratif Jurnal Ekonomi dan Pembangunan Indonesia MILANG Journal of Mathematics and Its Applications
Toni Bakhtiar
Departemen Matematika, Fakultas Matematika Dan Ilmu Pengetahuan Alam, Institut Pertanian Bogor
Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Industrial & Manufacturing Engineering Mathematics Mechanical Engineering Physics Transportation

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Enhancing Adaptive Particle Swarm Optimization Based on Human Social Learning with Human Learning Strategies for the Traveling Salesman Problem Qomah, Yusti; Silalahi, Bib Paruhum; Bakhtiar, Toni
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 4 (2025): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i4.31466

Abstract

Particle Swarm Optimization (PSO) is a widely used metaheuristic approach for solving optimization problems. Recent developments in this field involve the adaptation of human learning behaviors to enhance algorithmic performance. One such adaptation is the Adaptive Particle Swarm Optimization based on Human Social Learning (APSO-HSL), a variant of PSO that incorporates human inspired learning strategies. This study aims to enhance the performance of APSO-HSL on the Traveling Salesman Problem (TSP) by incorporating additional human learning strategies. The proposed algorithm, named Modified Adaptive Particle Swarm Optimization–Human Learning Strategies (MAPSO-HLS), integrates learning mechanisms from Human Learning Optimization (HLO), including individual, random, and social learning. This research is classified as applied research and algorithmic experimentation, focusing on the development and modification of a metaheuristic algorithm to solve a well-known combinatorial optimization problem. Benchmark datasets from the Traveling Salesman Problem Library (TSPLIB) are used for evaluation, and all computations and experiments are implemented in Python. The performance of MAPSO-HLS is compared with the exact method in terms of shortest distance and computation time. The results of the study indicate that the MAPSO-HLS algorithm is capable of producing TSP solutions with low total distance deviation, below 10%, compared to exact solutions across all tested datasets. This reflects a high level of solution accuracy. In addition, MAPSO-HLS demonstrates better time efficiency than the exact ILP method, particularly for datasets with a large number of cities. The integration of human learning strategies within the adaptive PSO framework provides significant advantages in terms of both efficiency and effectiveness in solving TSP.
PENJADWALAN TENAGA SUKARELAWAN DI KABUPATEN PURWOREJO MENGGUNAKAN INTEGER PROGRAMMING Amriyah, Amanatul; Bakhtiar, Toni; Hanum, Farida; Supriyo, Prapto Tri; Mayyani, Hidayatul
MILANG Journal of Mathematics and Its Applications Vol. 18 No. 2 (2022): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.18.2.155-167

Abstract

Kabupaten Purworejo termasuk salah satu kabupaten rawan bencana di Jawa Tengah. Daerah rawan bencana membutuhkan banyak tenaga sukarelawan ketika bencana terjadi. Saat ini, sukarelawan di Kabupaten Purworejo memiliki latar belakang profesi yang beragam dan masih terbatas jumlahnya. Keberagaman profesi dan keterbatasan jumlah tersebut membutuhkan pengaturan yang baik sehingga sukarelawan dapat bekerja secara optimal. Penelitian ini membahas penjadwalan tenaga sukarelawan di Kabupaten Purworejo yang dimodelkan menggunakan integer programming. Fungsi objektif masalah ini adalah memaksimumkan preferensi sukarelawan terhadap sektor kerja, shift waktu, dan jarak antara lokasi domisili sukarelawan dengan titik lokasi bencana. Penyelesaian masalah ini menggunakan software LINGO 17.0 menghasilkan jadwal sukarelawan selama satu periode yang memenuhi semua kendala dan memaksimumkan preferensi sukarelawan.
PENENTUAN RUTE DISTRIBUSI RASTRA MENGGUNAKAN ALGORITMA GENETIKA Syakina, Lana; Bakhtiar, Toni; Hanum, Farida; Supriyo, Prapto Tri
MILANG Journal of Mathematics and Its Applications Vol. 19 No. 2 (2023): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.19.2.97-115

Abstract

Proses distribusi produk yang dilakukan oleh produsen untuk memenuhi kebutuhan konsumen sering kali melibatkan penyelesaian masalah perutean kendaraan. Vehicle routing problem (VRP) dapat digunakan untuk menentukan rute dan alokasi kendaraan agar biaya distribusi minimum. Penelitian ini membahas masalah penentuan rute distribusi beras untuk keluarga sejahtera (rastra) dari gudang penyimpanan Perum Bulog di Kabupaten Ponorogo ke beberapa desa/kelurahan. Periode pendistribusian yang diambil dalam penelitian ini hanya satu dari dua belas periode yang tersedia. Terdapat desa/kelurahan dengan permintaan yang melebihi kapasitas kendaraan, sehingga memerlukan distribusi terpisah. VRP dapat diselesaikan menggunakan metode eksak maupun heuristik. Dalam penelitian ini, metode heuristik yang digunakan adalah algoritma genetika dengan solusi awal diperoleh dari metode nearest neighbour untuk distribusi beras di Perum Bulog. Dari hasil implementasi diperoleh rute kendaraan yang meminimumkan biaya distribusi dan memenuhi semua kendala yang ada menggunakan algorima genetika dan diberikan pula hasil perbandingannya dengan solusi dari metode eksak.
PERENCANAAN PRODUKSI MENGGUNAKAN FUZZY GOAL PROGRAMMING: STUDI KASUS PRODUKSI JILBAB PADA KONVEKSI RUMAHAN Suhairi, Rafif; Supriyo, Prapto Tri; Mayyani, Hidayatul; Bakhtiar, Toni; Julianto, Mochamad Tito
MILANG Journal of Mathematics and Its Applications Vol. 20 No. 1 (2024): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.20.1.43-53

Abstract

Perencanaan produksi adalah salah satu strategi untuk menghadapi berbagai permasalahan dalam proses produksi. Tujuan yang ingin dicapai dalam perencanaan produksi cukup bervariasi. Seringkali tujuan-tujuan tersebut bersifat samar sehingga mengandung ketidakpastian atau fuzzy. Penelitian ini bertujuan memodelkan masalah perencanaan produksi sebagai model fuzzy goal programming (FGP). Ketidakpastian pada fungsi tujuan diselesaikan menggunakan fungsi keanggotaan fuzzy. Fungsi keanggotaan fuzzy dibangun dengan refererensi batas optimal dari masing-masing fungsi tujuan dan batas toleransi yang diinginkan oleh pembuat keputusan. Model FGP diformulasikan dengan pendekatan max-min Bellman-Zadeh. Model diimplementasikan menggunakan bantuan software LINGO pada industri rumahan konveksi jilbab di Kebon Jeruk, Jakarta Barat dengan fungsi tujuan meminimumkan waktu produksi dan memaksimumkan keuntungan. Hasil implementasi menghasilkan tingkat produksi jilbab yang mengoptimalkan fungsi tujuan, yaitu meminimumkan waktu produksi dan memaksimumkan keuntungan. Minimum waktu produksi yang diperoleh 2105 menit, sedangkan maksimum keuntungan yang diperoleh yaitu Rp 3.460.295,68.
Optimalitas Rute pada Pengiriman Multiperjalanan dengan Armada Kendaraan Listrik Heterogen Salsabilla, Kamilia; Bakhtiar, Toni; Hanum, Farida
Jambura Journal of Mathematics Vol 6, No 1: February 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v6i1.23993

Abstract

Electric vehicles are emerging as a key trend in sustainable mobility, mitigating emissions, and reducing dependence on fossil fuels. The challenge in optimizing route modeling lies in some limitations, such as battery range, charging time, and the diversity of electric vehicle types. This article explores the optimality of routes in a multiple-trip distribution system using a heterogeneous fleet of electric vehicles. The electric vehicle routing problem is formulated as a mixed-integer linear programming aiming to find the most cost-efficient optimal route. A notable feature of the model allows electric vehicle fleets to undertake additional travel to complete distribution tasks, i.e., multiple trips. The model is implemented in two illustrative examples involving the delivery of goods using homogeneous and heterogeneous electric vehicle fleets characterized by loading and battery capacities. Each case includes one depot, 8 and 10 customers, and 2 battery swapping stations, solved using the branch-and-bound method through Lingo 18.0. Simulation results indicate that battery capacity and the presence of battery swapping stations significantly influence the routes selection.
OPTIMAL STRATEGIES FOR DENGUE CONTROL: WOLBACHIA-INFECTED MOSQUITOES DEPLOYMENT, PUBLIC HEALTH EDUCATION, AND VACCINATION Bakhtiar, Toni; Jaharuddin, Jaharuddin; Hanum, Farida
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1301-1316

Abstract

Wolbachia-infected mosquitoes present a promising method for dengue control by inhibiting viral replication, reducing mosquito reproductive capacity, and shortening the lifespan of Aedes aegypti mosquitoes. This study introduces a novel optimal control model that uniquely integrates two distinct release strategies for Wolbachia-infected mosquitoes—constant and proportional rates. While prior research has explored Wolbachia deployment, our model is the first to directly compare and contrast these two rate types within the same framework to assess their differential impact on dengue transmission dynamics. This provides a more comprehensive understanding of effective release protocols, addressing a critical gap in the literature regarding optimal and adaptive Wolbachia deployment. Based on model simulations for North Kembangan Village, Jakarta, we find that a single-control strategy using Wolbachia mosquito release alone can reduce dengue cases by up to 15%. However, a multiple-control strategy that combines Wolbachia releases with public health education and vaccination is the most effective approach, achieving a substantial reduction of up to 58%. In a cost-effectiveness analysis, the study reveals that the Wolbachia-only strategy (proportional release) is the most cost-effective in terms of cost per infection averted. In terms of release dynamics, the study reveals that a constant release rate provides long-term benefits by establishing a stable Wolbachia-infected mosquito population, whereas a proportional release rate is more effective for achieving a rapid, short-term reduction in dengue cases.
PENGEMBANGAN MODEL OPTIMASI DISTRIBUSI LIMBAH DENGAN LINEAR PROGRAMMING: CONTOH KASUS STATELINE SHIPPING & TRANSPORT COMPANY Angelica, E. C.; Widiyanto, M. A. N.; Khodijah, S; Sonia, A. N.; Napitupulu, B. N.; Putera, M. L. H.; Mayyani, Hidayatul; Bakhtiar, Toni
MILANG Journal of Mathematics and Its Applications Vol. 21 No. 2 (2025): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.21.2.129-143

Abstract

Pengelolaan distribusi limbah industri memerlukan sistem transportasi yang efisien, karena perbedaan jarak, kapasitas pembuangan, dan biaya di setiap lokasi yang meningkatkan biaya operasional secara signifikan. Oleh sebab itu, diperlukan pendekatan optimasi untuk menentukan pola pengiriman yang paling ekonomis. Penelitian ini mengembangkan model optimasi distribusi limbah berbasis Linear Programming pada contoh kasus Stateline Shipping & Transport Company dengan mempertimbangkan berbagai struktur jaringan distribusi. Kebaruan penelitian ini terletak pada pemodelan pembatasan proporsi aliran transit sebagai representasi kebijakan operasional dan risiko lingkungan, serta analisis dampak penambahan node transit baru terhadap struktur aliran dan biaya distribusi dalam suatu kerangka optimasi. Empat skenario dianalisis, yaitu pengiriman langsung, transhipment, pembatasan volume transit, dan penambahan node transit. Hasil penelitian menunjukkan bahwa mekanisme transhipment mampu menurunkan biaya distribusi dibandingkan pengiriman langsung, sementara pembatasan proporsi transit tetap mempertahankan solusi optimal pada batas tertentu. Penambahan node transit menghasilkan penurunan biaya paling signifikan dengan membuka jalur alternatif berbiaya lebih rendah tanpa melanggar kendala operasional. Penelitian ini menunjukkan bahwa pengaturan struktur jaringan dan kebijakan transit berperan penting dalam optimasi distribusi limbah. Kata kunci: distribusi limbah, linear programming, optimasi jaringan, transhipment, transit
Co-Authors Amalia, Imas Saumi Amanatul Amriyah Amril Aman Amriyah, Amanatul Angelica, E. C. Annisa, Winda Nur Bambang Juanda Bib Paruhum Silalahi Bustanul Arifin Cahyona, Dwizani Vinoma Dedi Budiman Hakim Endy Jeri Suswono Erliza Noor Farhana Zahrotunnisa Farida Hanum Farida Hanum Farida Hanum Ferry Syarifuddin JAENAL EFFENDI Jaharuddin Jaharuddin, Jaharuddin Khodijah, S Kinanti, Yoanda Astri Ayu Kurniawan, Benny Robby Lana Syakina Luciana, Shelen Maya Widyastiti Mayyani, Hidayatul Mochamad Tito Julianto Napitupulu, B. N. Nunung Nuryartono Nur Azizah Paian Sianturi Permana, Rendy Candra Prapto Tri Supriyo Putera, M. L. H. Qomah, Yusti Rachman, Muhammad Ibrahim Rafif Suhairi Rahma Nurlailawati Salsabilla, Kamilia Sonia, A. N. Sugema, Iman Suhairi, Rafif Syakina, Lana Tan, Elfina Widiyanto, M. A. N.