Determining the Maximum Value of Goods through Railway Transportation on the Islands of Sumatra and Java by Using the Golden Section Search Method
Alya Dwi Shabila, Azizah, Dena Lutfia Hairunnisa, Fitri Maya Puspita, Sisca Octarina

Sriwijaya University

Abstract

In calculus, the problem of finding extreme values at minimum and maximum can be solved by analytical methods. However, in problems with complex nonlinear function forms, the search for extreme values must be solved by numerical methods. In this case, the search for the value of x for the minimum and maximum of f(x) is carried out. This research uses the idea of the golden ratio value and bisection algorithm to find f(x) = 0 using the Golden Section Search (GSS) method to find the maximum extreme value. This type of research is applied research. The implementation of the Golden Section Search (GSS) algorithm on the number of goods transported from Java Island to Sumatra via rail transportation obtained from the Central Bureau of Statistics (BPS) is analyzed computationally. First, the curve fitting process will be carried out so that the resulting polynomial function using the GSS algorithm will achieve the maximum value. The results of the calculation indicate that the Golden Section Search (GSS) algorithm is a reliable method for predicting the maximum value of polynomial functions but requires multiple iterations until the percentage of error is small.

Keywords: Curve Fitting, Golden Section Search, Polynomial Function, Maximum Value

Topic: Mathematics and Its Applications