Evaluation of Transportation Network Reliability under Emergency Based on Reserve Capacity

Algorithm 2

Dynamic penalty function algorithm.

Step 1: Initialization.

  (1.1) Set , initialize parameters including penalty function parameters , penalty function coefficients and

convergence criteria and ;

  (1.2) Set valid paths of each O-D pair .

Step 2: Calculate initial solution

  (2.1) Calculate the generalized travel time according to the initial link flow , and find the shortest path

between each OD pair;

  (2.2) Apply all-or-nothing assignment to get the initial path flow .

Step 3: For each OD pair :

  (3.1) Update the set of valid paths and calculate the generalized travel time , obtain the shortest path and its travel

time between each OD pair . If the convergence criterion Eq. () is not satisfied, then ;

()

  (3.2) Linearize the NCP problem composed of effective paths at and solve it by improved Lemke algorithm

[22] to get new ;

  (3.3) If the convergence criterion Eq. () is not satisfied, return to (3.2).

()

Step 4: Update the link flow and penalty function parameter .

Step 5: Termination criterion.

 If the convergence criterion Eq. () is satisfied, is the answer. Otherwise, let and turn to Step 3.

()