The Tractor and Semitrailer Routing Considering Carbon Dioxide Emissions

Pseudocode 1

Pseudocode of the proposed SA heuristics for finding the number of tractors.

Simulated Annealing for finding the number of tractors 𝑁_best (𝑇₀,𝑇_𝐹,𝜏,𝑀_𝑒)

Step  1. Let  𝑁=(∑_𝑖∑_𝑗𝑟_𝑖𝑗)/4

Step  2. Generate the initial solution 𝑋 randomly;

Step  3. Let  𝑇=𝑇_𝑜;   𝑤=0;  𝑞=0;  𝑅_best=𝑅(𝑋);

Step  4. 𝑤=𝑤+1;  𝑞=𝑞+1;

Step  5. Generate a solution 𝑌 based on 𝑋 by the three types of operators in Section 4.1;

Step  6. If  Δ=𝑅(𝑌)−𝑅(𝑋)≥0  {Let 𝑋=𝑌;}

Else {

  Generate 𝛾=𝑟𝑎𝑛𝑑𝑜𝑚(0,1);

  If exp(Δ⋅𝑤²/𝑇)>𝛾  {Let 𝑋=𝑌;}

     }

Step  7. 𝑋_best=𝑋;𝑅_best=𝑅(𝑋);

Step  8. If  𝑞=𝑀_𝑒𝑇=𝜏⋅𝑇;𝑞=0;

   Else {Go to Step  3;}

Step  9. If  𝑇−𝑇_𝐹>0  {Go to Step  3;}

   Else  {Terminate the SA heuristics;}

Step  10. If  𝑅_best<100%  {𝑁=𝑁+1; Go to Step  2;}

   If  𝑅_best=100%  {𝑁=𝑁−1; Go to Step  2;}

   Else  𝑁_best=𝑁.