Algorithm 2. Modified ant colony algorithm.

Input: the number of sensor nodes $N$, the power expended to run the transmitter or receiver circuitry of sensor node $E_{elec}$, energy consumption of multi-path fading amplifier $E_{amp}$, energy consumption of free-space amplifier $E_{fs}$, distance threshold $d_0$, impact factors of pheromone information $\varsigma$, impact factors of heuristic information $\xi$, $\mu$ is a small positive constant $\in (0,1]$, pheromone information on edge $(i,j)$$\tau$, heuristic information on edge $(i,j)$ $\rho$, $\beta$ and $\sigma$ are $\in [0,1]$ constants.

Output: optimal routing $Routing$.

1 Initialization routing $R(Path,iter,\vartheta )$, energy for each node and tabu

2 calculate distance $d_{ij}$ of different nodes, ${\rho }_{ij}=1/d_{ij}$

3 while maximum iterations has not be reached

4  for $\vartheta$=1: ${\mathsf{\Theta }}^{\prime }$

5   compute $allowe{d}_{\vartheta }$ according to the node communication radius.

6   generate transition probability $p_{ij}^{\vartheta }$ based on Equations (15) and (16)

7   choose the next hop node, relying on $p_{ij}^{\vartheta }$, modify routing and tabu

8   the destination node or not? If not, go back to step 2, or proceed to step 9

9   update the node residual energy based on Equations (5) and (6), routing depending on Equation (17)

10  end for

11 end while

12 return the optimal routing $Routing$.