| Initialization: |
| Set , determine the initial link cost and destination cost by setting and , respectively. |
| For each origin do |
| (i) Find the tree of minimum cost routes rooting from . Let be the minimum route tree. Denote |
| the minimum route cost to destination by , and choose a minimum cost route from p to q. |
| (ii) Compute the initial variable O-D demands by |
| |
| (iii) For , assign the entire O-D demand and to the minimum cost route from to , and obtain initial |
| link flow . |
| (iv) Update the link costs using the initial link flows. |
| (v) Initialize the origin-based approach proportions . |
| Main Loop: |
| Given the current variable O-D demand obtained in ()th-iteration: |
| For to number of main iterations () |
| for each in do |
| Update restricting network |
| Update origin-based approach proportions |
| end for |
| Inner Loop: |
| for to number of inner iterations () |
| for each in do |
| Update origin-based approach proportions |
| end for |
| end for |
| Update O-D flows, retain origin-based approach proportions: |
| Given the origin-based approach proportions , link flows and link costs obtained in the steps |
| above: |
| (i) For each , compute the destination cost by O-D demand and . |
| (ii) Find the set of auxiliary trip demands by solving the following logit distribution model: |
| |
| (iii) Calculate the auxiliary traffic flow on each link a with the approach proportions |
| (iv) Let and solve the one-dimensional search problem defined |
| as follows to obtain the step size |
| |
| (v) Set and check for convergence. Terminate if the convergence |
| criterion is satisfied; otherwise, update total link flows and link costs, set and start |
| a new iteration of the main loop. |
| End for |
