Input: The graph \(G\), the parameter \(K\), a starting solution \(s\), and the probability of agent taxis \(p_{rl}\).

Output: A solution for the current time step

1: while time is available do

2:       First iteration: Fix the agent taxis \(T\) using \(p_{rl}\);

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

4:       Add solution s to \(BG;\)

5:       while \(BG\) has less than \(E_{\max} \times \left( 1 - p_{rl} \right)\) arcs do

6:             For each taxi \(t\) not in \(T\), generate a random walk on \(KG\) from \(t\);

7:             Add those arcs to \(BG;\)

8:       end while

9:       All agents choose their actions (paths) using Q-learning to complete \(E_{\max}\) arcs in \(BG;\)

10:     Solve MIPmaxflow on \(BG;\)

11:     Update the solution \(s;\)

\(12:\) end while