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

Output: Best Solution

1: Assign the value of Maxit and the initial value of $T_0$ and $\gamma$

2: For each city $c_i;i=1,2,\cdots ,n$ , generate a set of n sub-routes consist of one city $c_i$

3: Add a closest city in the right end of each sub-route that is not yet in the route

4: Repeat the process of step 3 until all the cities are added in each sub-route

5: Add starting city in the right side of the last position of each sub-route to generate n feasible routes, $X=\left\{x_1,x_2,\cdots ,x_n\right\}$

6: Compute the Euclidean distance/fitness value of each route, $f\left(X\right)=\left\{f\left(x_1\right),f\left(x_2\right),\cdots ,f\left(x_n\right)\right\}$

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

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

9: Generate a new route $x_i^{\text{'}}$ by adopting neighborhood structure (described in Section 3.2.1)

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

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

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

13: 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

14: End for

15: Decrease the temperature based on Equation (12)

16: Update the best solution ever found

17: End for