Estimasi Parameter pada Model Matematis Perubahan Suhu Dinding Rumah menggunakan Algoritma Genetika (Jurnal EurekaMatika, 2024)
A B S T R A C TIn this research, we built a regression model to analyze the factors influencing the percentage of poor people in Cianjur Regency. The method used to model the problem of the percentage of poor people is Durbin spatial regression analysis by considering location aspects of both the dependent variable and the independent variable. Of the six independent variables taken, only four independent variables can be modeled using Durbin spatial regression. This is caused by the results of the Moran Index Test which states that there is spatial autocorrelation in these four variables. Based on Durbin's spatial regression analysis, the results showed that the variables that significantly influenced the percentage of poor people in Cianjur Regency in 2021 were the average length of schooling and life expectancy at birth. A high average number of years of schooling and life expectancy at birth can reduce the percentage of poor people in Cianjur Regency.  In this research, we built a regression model to analyze the factors influencing the percentage of poor people in Cianjur Regency. The method used to model the problem of the percentage of poor people is Durbin spatial regression analysis by considering location aspects of both the dependent variable and the independent variable. Of the six independent variables taken, only four independent variables can be modeled using Durbin spatial regression. This is caused by the results of the Moran Index Test which states that there is spatial autocorrelation in these four variables. Based on Durbin's spatial regression analysis, the results showed that the variables that significantly influenced the percentage of poor people in Cianjur Regency in 2021 were the average length of schooling and life expectancy at birth. A high average number of years of schooling and life expectancy at birth can reduce the percentage of poor people in Cianjur Regency.ABSTRAKPada penelitian ini dibangun model regresi untuk menganalisa faktor-faktor mempengaruhi persentase penduduk miskin di Kabupaten Cianjur. Metode yang digunakan untuk memodelkan masalah persentase penduduk miskin tersebut adalah analisis regresi spasial Durbin dengan mempertimbangkan aspek lokasi baik dari variabel dependen dan variabel independen. Dari enam variabel independen yang diambil hanya empat variabel independen yang dapat dimodelkan menggunakan regresi spasial Durbin. Hal tersebut disebabkan oleh hasil Uji Indeks Moran yang menyatakan terdapat autokorelasi spasial pada empat variabel tersebut. Berdasarkan analisis regresi spasial Durbin didapatkan hasil bahwa variabel yang berpengaruh secara signifikan terhadap persentase penduduk miskin di Kabupaten Cianjur Tahun 2021 adalah rata-rata lama sekolah dan usia harapan hidup saat lahir. Nilai rata-rata lama sekolah dan usia harapan hidup saat lahir yang tinggi dapat menurunkan persentase penduduk miskin di Kabupaten Cianjur.  This research focuses on the problem of temperature variation over 24 hours on house walls, modeled as a differential equation through Newton's law of cooling/heating. To describe this phenomenon accurately, a Genetic Algorithm is employed to estimate the parameters in the model.  This algorithm is valid to be used to model synthetic data (data generated from analytical formulas) because it produces a fairly small error, namely 0.1168. Subsequently, the Genetic Algorithm is used to estimate parameters in vector form, which are then compared with observed data. The Newton's cooling/heating model is solved using finite difference methods. The results indicate that the parameters vary over specific time intervals, showing both negative and positive changes, demonstrating that the walls undergo cooling and heating processes during certain periods. Furthermore, the model results show that this algorithm performs well, with a Root Mean Squared Error (RMSE) of 0.13105.ABSTRAKPada penelitian ini dikaji masalah variasi suhu selama 24 jam pada dinding rumah yang dimodelkan sebagai persamaan diferensial melalui hukum pendinginan/pemanasan Newton. Untuk dapat menggambarkan fenomena tersebut, yakni dalam hal menentukan estimasi parameter pada model tersebut diperlukan Algoritma Genetika. Algoritma ini cukup valid digunakan untuk memodelkan data sintesis (data yang dibangkitkan dari formula analitik) karena menghasilkan error yang cukup kecil yakni sebesar 0.1168. Kemudian algoritma genetika digunakan untuk mengestimasi parameter dalam bentuk vektor yang dibandingkan dengan data hasil pengamatan. Dalam hal ini model pendinginan/pemanasan Newton diselesaaikan dengan metode beda hingga. Hasil penelitian menunjukkan bahwa parameternya bervariasi pada rentang-rentang waktu tertentu, khususnya adanya perubahan nilai negatif dan positif. Hal ini menunjukkan bahwa dinding mengalami proses pendinginan dan pemanasan pada rentang waktu tertentu. Lebih lanjut, hasil modelnya menunjukkan bahwa algoritma ini cukup baik yakni dengan Root Mean Squared Error (RMSE) sebesar 0.13105.
Keywords: Algoritma Genetika; Hukum Pendinginan/Pemanasan Newton; Metode Beda Hingga; Pemanasan Dinding Rumah