Perbandingan Estimasi Parameter pada Data Lengkap dan Sparse Menggunakan Regresi Linier, Levenberg-Marquardt, dan Algoritma Genetika

Pratiwi, Prasasti Intan (2026) Perbandingan Estimasi Parameter pada Data Lengkap dan Sparse Menggunakan Regresi Linier, Levenberg-Marquardt, dan Algoritma Genetika. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Estimasi parameter merupakan aspek fundamental dalam pemodelan matematika agar model dapat menggambarkan perilaku sistem yang sebenarnya. Perbandingan performa metode non-iteratif dan iteratif dalam estimasi parameter pada kondisi data tidak lengkap masih belum banyak dikaji secara sistematis. Penelitian ini membandingkan tiga metode estimasi parameter, yaitu regresi linier, algoritma Levenberg-Marquardt, dan algoritma genetika, yang diterapkan pada model SIR, model SIRD, dan sistem Lorenz. Pengujian dilakukan pada data lengkap dan data sparse, dengan dua skenario pada data sparse berupa estimasi secara langsung dan estimasi yang diawali interpolasi cubic spline. Data sintetik untuk model SIR dan sistem Lorenz dibangkitkan menggunakan metode Runge-Kutta orde 4, sedangkan model SIRD menggunakan data aktual COVID-19 di Indonesia periode Maret-Agustus 2020. Ketiga metode mengestimasi parameter melalui pendekatan yang berbeda, yaitu regresi linier secara langsung melalui perhitungan analitik, sedangkan Levenberg-Marquardt dan algoritma genetika secara bertahap melalui proses pencarian berulang. Performa dievaluasi berdasarkan galat relatif dan waktu komputasi. Hasil penelitian menunjukkan bahwa pada data lengkap, ketiga metode umumnya menghasilkan estimasi dengan galat relatif kecil, kecuali LM yang gagal konvergen pada sistem Lorenz akibat sifat chaotic. Pada data sparse, akurasi menurun, terutama pada sistem Lorenz akibat sifatnya yang chaotic. Interpolasi cubic spline terbukti efektif meningkatkan akurasi estimasi pada sebagian besar skenario data sparse, khususnya model SIR dan SIRD. Algoritma genetika menunjukkan kestabilan estimasi terbaik pada data sparse, meskipun waktu komputasinya lebih lama dibanding dua metode lain.
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Parameter estimation is a fundamental aspect of mathematical modeling, allowing a model to accurately represent the actual behavior of a system. The performance comparison between non-iterative and iterative parameter estimation methods under incomplete data conditions has not been widely studied in a systematic manner. This study compares three parameter estimation methods, namely linear regression, the Levenberg-Marquardt algorithm, and the genetic algorithm, applied to the SIR model, the SIRD model, and the Lorenz system. Testing was conducted on both complete and sparse data conditions, with two scenarios applied to the sparse data: direct estimation and estimation preceded by cubic spline interpolation. Synthetic data for the SIR model and the Lorenz system were generated using the fourth-order Runge-Kutta method, while the SIRD model used actual COVID-19 spread data in Indonesia for the period of March–August 2020. The three methods estimate parameters through different approaches, with linear regression performing direct estimation through analytical calculation, while the Levenberg-Marquardt algorithm and the genetic algorithm perform estimation gradually through an iterative search process. Performance was evaluated based on the relative error and computation time of each method. The results show that under complete data conditions, all three methods produced estimates with small relative errors. Under sparse data conditions, accuracy declined, particularly for the Lorenz system due to its chaotic nature, which caused the Levenberg-Marquardt algorithm to consistently fail to converge. Cubic spline interpolation proved effective in improving estimation accuracy in most sparse data scenarios, especially for the SIR and SIRD models. The genetic algorithm exhibited the best estimation stability under sparse data conditions, although with a relatively longer computation time compared to the other two methods.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Data Sparse, Estimasi Parameter, Interpolasi Cubic Spline, Metode Iteratif, Metode Non-iteratif, Cubic Spline Interpolation, Iterative Method, Non-iterative Method, Parameter Estimation, Sparse Data
Subjects:	Q Science Q Science > QA Mathematics Q Science > QA Mathematics > QA402.5 Genetic algorithms. Interior-point methods.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Prasasti Intan Pratiwi
Date Deposited:	28 Jul 2026 02:12
Last Modified:	28 Jul 2026 02:12
URI:	http://repository.its.ac.id/id/eprint/138302

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