## 5 Machine-Learning-Based Transfer Point Optimisation of Journey Profiles (Online)
### Neural-Network Travel-Time Predictions  
In ML-TZSA, feed-forward neural networks are used to rapidly approximate shortest time paths from anywhere in an origin transfer zone to anywhere in a destination transfer zone in any transport network. As such, we train a separate neural network for each pair of origin and destination transfer zones and each transport mode. Regarding the training of each neural network, we firstly generate the neural-network structure according to the specified number of input features, output responses and the numbers of neurons in each layer. In this case, there are 13 input features and two output responses (travel time and distance). The input features for making a prediction include origin and destination longitudes and latitudes (4 features); origin and destination longitudes and latitudes relative to their respective transfer-zone centroids (4 features); the angles and distances of the origin and destination relative to their respective transfer-zone centroids (4 features) and the \"as-the-crow-flies\" distance between the origin and destination (1 feature). These features can be calculated much more rapidly than the exact shortest path between an origin and destination can be, as can a forwards pass of a neural network for making a prediction based on these features. Figure 5 illustrates the structure of the neural networks, which consists of a layer by layer fully-connected feed-forward structure. The hyperbolic tangent activation function is used for all neurons, and the synapse weights were calculated using the back propagation algorithm. The number of neurons in the layers between the input signal and output layer varies smoothly between the input vector size and output vector size (13-[10-6]-2), which is a common heuristic that helps to reduce the risk of overfitting. For each neural network, a sample of training data is generated, consisting of pairs of input features and output responses for randomly selected origins and destinations within the transfer zones of interest. The \(A^{*}\) shortest-path algorithm is used to calculate the desired output responses. The back propagation algorithm is used to train the weights of the neurons of the neural network. The training procedure involves repeatedly selecting random instances from the training data and performing a neural-network forwards pass to make a travel-time prediction based on the feature data, followed by a backward pass for updating the neuron weights to reduce prediction error in the future. This procedure requires a learning rate scheme which determines how aggressively the neuron weights are updated in response to prediction errors. The learning rate starts small and becomes lower in order to prevent over fitting to individual training data instances. Appendix B provides neural-network prediction accuracy and time results. In summary, travel-time prediction errors are around 3% on average and tend to decrease with increasing transfer-zone sample sizes. Prediction response times are always a tiny fraction of the time required to calculate travel times using shortest-path algorithms.