Input: The graph \(G\), the parameter \(K\), the limit number \(E_{\text{max~}}\), and a starting solution \(s\) (could be empty)

Output: A solution for the current time step

1: Compute \(KG\);

2: while time is available do

3:       Initialize the backbone graph \(BG\) by removing all arcs of \(KG;\)

4:       while \(BG\) has less than \(E_{\max}\) arcs do

5:             For each customer \(c\), generate uniformly a pick-up time \(t_{c}\) from \(I_{c}\) or from \(I_{c}^{s}\) (is the time window where the solution \(s\) is propagated in \(I_{c}\) );

6:             Solve maxFlow on \(KG\) with the \(t_{c}\) pick-up times of the customers;

7:             Add the optimal arcs of the solution to the graph \(BG;\)

8:       end while

9:       Solve MIPmaxflow on \(BG;\)

10:     Update the solution \(s;\)

11: end while