Dynamic Origin-Destination Matrix Estimation Based on Urban Rail Transit AFC Data: Deep Optimization Framework with Forward Passing and Backpropagation Techniques

Table 2

Algorithm steps.

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Step 1: initialization

Step 2: iterative optimization process

 Step 2.1: perform the forward propagations

 Based on the fixed passenger flow proportion variables in the multilayer passenger flow network, assign a passenger from the origin station layer to the departure time layer, from the departure time layer to the destination station layer, from the destination station layer to the path layer, and from the path layer to the travel time layer

 Step 2.2: calculate the subgradient information

 Calculate the subgradient of the passenger flow in the output layer of the multilayer passenger flow network

 Step 2.3: set the “error”

 Set the “error” of the output layer in the multilayer passenger flow network

 Step 2.4: perform the backward error propagations

 Perform the backward error propagations in the multilayer passenger flow network from the travel time layer to the path layer, from the path layer to the destination station layer, from the destination station layer to the departure time layer, and from the departure time layer to the origin station layer

 Step 2.5: update the auxiliary flow proportion variables

 Update the auxiliary passenger flow proportion variables

Step 3: termination

 Determine if all the iterations are complete; if not, go back to Step 2

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