Forecasting origin-destination matrices by using neural network approach: A comparison of testing performance between back propagation, variable learning rate and levenberg-marquardt algorithms

Abstract

The previous studies suggest that the Neural Network (NN) approach is able to model the commodity, migration and work trip flows. However, its generalization performance is poor, compared to the well known doubly constrained gravity model. This paper is intended to fix the testing performance of NN by training the models with the Levenberg-Marquardt (LM) algorithm, while the previous studies used standard Back propagation (BP), Quickprop and Variable Learning Rate (VLR) algorithms. The main difference between those algorithms is the technique used in defining the optimum connection weights. Then, the trained and validated model is used to forecast trip numbers from different Trip production and Trip Attraction dataset. The testing results suggest that the Root Mean Square Error (RMSE) are 168, 152 and 125 for model trained with BP, VLR and LM respectively, while the R 2 values are 0.194 0.315, 0.505. The models trained by using BP and VLR have underestimate of forecasted total trip numbers, while the LM algorithm has slightly higher numbers. The same data set is then calibrated by using Hyman's technique for the doubly constrained gravity model. The testing RMSE and R 2 for gravity model is 127 and 0.507 respectively. It means the NN model has about the same level of error and goodness of fit as the gravity model, for testing level. Based on these results from this study, it can be concluded that the testing performance of NN approach can be refined to the same level as doubly constrained gravity model when the model is trained by LM algorithm.

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