Algorithm 1 $ϵ$-Admissible Branch and Bound

Require:  Priority Queue $Q_{open}$, Queue $Q_{closed}$, evaluation function $f(·)$, $ϵ$-admissible heuristic $\tilde{g}(·)$, priority heuristic $P(·,·)$, Start node $N_{start}$, end time $Tmax$, maximum number of iterations $Imax$, heuristic reward $B_0$ 1:$B\leftarrow B_0$ 2:$Q_{open}.insert\left(N_{start}\right)$ 3:$i\leftarrow 0$ 4:while $Q_{open}$ is not empty or $i<Imax$ do 5: $i\leftarrow i+1$ 6: $N\leftarrow Q_{open}.pop\left(\right)$ 7: $Q_{closed}.insert\left(N\right)$ 8: if N is a complete candidate solution and $f\left(N\right)>B$ then 9:  $B\leftarrow f\left(N\right)$                                                //new best solution found. Store it. 10: end if 11: $\mathcal{N}\leftarrow Branch\left(N\right)$ 12: for all $N_i\in \mathcal{N}$ do 13:  if $Bound(N,B,\tilde{g})$ and $(N$ not in $Q_{open}$ and N not in $Q_{closed}$) then 14:   $N_i.priority\leftarrow P(N_i,\tilde{g})$ 15:   $N_i.parent\leftarrow N$ 16:   $N_i.R\leftarrow f\left(N_i\right)$ 17:   $Q_{open}.insert\left(N_i\right)$ 18:  end if 19: end for 20:end while