Input: Distance matrix D, Initial temperature $T_0$ , Cooling rate $\gamma$ , Maximum iteration Maxit

Output: Best Solution

1: Generate n feasible routes randomly, $X=\left\{x_1,x_2,\cdots ,x_n\right\}$ , compute the Euclidean distance/fitness value of each route, $f\left(X\right)=\left\{f\left(x_1\right),f\left(x_2\right),\cdots ,f\left(x_n\right)\right\}$ , assign the value of Maxit and the initial value of $T_0$ and $\gamma$

2: For each iteration, it = 1 to maximum iteration

3: For each route $x_i$ , $i=1$ to n

4: Generate a new route ${x^{\prime }}_i$ by adopting neighborhood structure (described in Section 3.2.1)

5: Compute Euclidean distance/fitness value of the new route $f\left({x^{\prime }}_i\right)$

6: Calculate $\Delta f$ on the basis of Equation (11)

7: If $\Delta f\le 0$ , then update the current route $x_i$ by assigning $x_i\leftarrow {x^{\prime }}_i$

8: If $\Delta f\succ 0$ , then compute the acceptance probability p by using Equation (10). If $p\ge u$ , then update the current route $x_i$ by assigning $x_i\leftarrow {x^{\prime }}_i$ , where u is the random number between 0 and 1

9: End for

10: Decrease the temperature based on Equation (12)

11: Update the best solution ever found

12: End for