Comparative study on the performance of four fundamental optimization algorithms applied for transportation mode choice modelling

Abstract

This study aims to improve the understanding of the numerical procedure involved in estimating the parameters of discrete mode choice models using four optimization algorithms that have value pedagogically in transportation mode choice modelling. To implement the numerical experiments, the mathematical formulas of gradient vectors and Hessian matrices are analytically derived from a log-likelihood function that was structured for a given choice data and situation. The parameter estimation mechanism of the four algorithms was interpreted into Visual Basic Application computer codes. The parameters of the mode choice multinomial logit model are empirically estimated based on the four optimization algorithms using a total of 540 revealed mode choice preference data collected from airport passengers. Extensive numerical experiments are performed to compare the performance of the four algorithms in terms of performance measures chosen. The test results indicate that each algorithm behaves differently depending on the plugged-in factors at the initial phase of the estimation. The plugged-in factors controlling the overall performance of algorithms are step size, initial guessing of parameters, and convergence criterion level. The experimental results of this study will benefit modellers who have interests in developing specific computer codes for a given particular choice situation.