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Journal : Integra: Journal of Integrated Mathematics and Computer Science

The Relation of Noncrossing Partitioning of Odd and Even Numbers with Catalan Numbers Amansyah, Wahyu Dwi; Wamiliana; Hamzah, Nur
Integra: Journal of Integrated Mathematics and Computer Science Vol. 1 No. 1 (2024): March
Publisher : Magister Program of Mathematics, Universitas Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/integrajimcs.2024114

Abstract

Catalan numbers, denoted by Cn, are generally defined by the equation Cn = 1/(n+1) (2nn) with n ≥ 0 and n ∈ ℤ. Catalan numbers have forms that can be determined through generaland recursive forms. Catalan numbers have several applications to various combinatorialproblems, such as in recursive analysis and the application of combinatorial theory topartitions that can form Catalan numbers. The odd numbers are defined as integers that arenot divisible by two, expressed in the form {2k + 1; k ∈ ℤ} . Meanwhile, even numbers aredefined as integers that are divisible by two, expressed in the form {2k; k ∈ ℤ} . In this studywe discuss the noncrossing partitions of positive odd numbers and positive even numbers.The results show those the noncrossing partitions have relationship with Catalan numbers.
Comparison of Support Vector Regression and Random Forest Regression Performance in Vehicle Fuel Consumption Prediction Nurdin, Muhaymi; Wamiliana; Junaidi, Akmal; Lumbanraja, Favorisen Rossyking
Integra: Journal of Integrated Mathematics and Computer Science Vol. 1 No. 2 (2024): July
Publisher : Magister Program of Mathematics, Universitas Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/integrajimcs.20241221

Abstract

Predicting vehicle fuel consumption is an important aspect in improving energy efficiency and supporting sustainable transportation. This study aims to compare the performance of Support Vector Regression (SVR) and Random Forest Regression (RFR) algorithms in predicting combined vehicle fuel consumption (COMBINED, a combination of 55% urban and 45% highway). The Canadian government's Fuel Consumption Ratings dataset was used, with 2015-2023 data (9,185 entries) for training and testing, and 2024 data (764 entries) for further testing. Pre-processing involved StandardScaler for numerical features and OneHotEncoder for categorical features, followed by hyperparameter optimization using Grid Search, resulting in optimal parameters: SVR (C=100, epsilon=0.5, gamma=1) and RFR (n_estimators=200, max_depth=None, min_samples_split=2). Results show RFR is superior with R2 0.8845, RMSE 0.9671, and MAE 0.6566, compared to SVR with R2 0.8648, RMSE 1.0462, and MAE 0.7150. Evaluation on 2024 data and visualization of error distribution corroborate the superiority of RFR. This study concludes RFR is more effective for COMBINED prediction, although SVR is competitive post-optimization, and contributes to the selection of machine learning models for green vehicle technology.
Comparative Analysis of CIH and Christofides Algorithms for Optimal Tourist Route Planning in West Java Hadi, Nur Wafiqoh; Nurfabella, Rehsya; Wamiliana; Mustika, Mira
Integra: Journal of Integrated Mathematics and Computer Science Vol. 2 No. 2 (2025): July
Publisher : Magister Program of Mathematics, Universitas Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/integrajimcs.20252231

Abstract

Efficient route planning plays a crucial role in supporting tourism development, particularly in regions with numerous scattered attractions such as West Java, Indonesia. This study addresses the Traveling Salesman Problem (TSP) by comparing two algorithmic approaches: the Cheapest Insertion Heuristic (CIH) and the Christofides algorithm, to determine the shortest tour among 20 selected tourist sites. Using travel time data obtained from Google Maps, both algorithms were implemented manually and using Python language programming. The manual application of the CIH algorithm resulted in a total travel time of 813 minutes, which was later optimized to 764 minutes after adjustments to eliminate intersecting paths. Meanwhile, the CIH algorithm implemented in Python provided a final route of 717 minutes. In contrast, the Christofides algorithm yielded consistent results for both manual and Python-based calculations, producing a tour with a total travel time of 746 minutes. The findings suggest that the CIH algorithm using Python language offers the most efficient route in this case study. This research contributes to the development of intelligent tour planning systems and can be a valuable reference for optimizing regional tourism logistics.