| Input: The initial temperature |
| Output: Pareto-solution and for all and |
| Step 1. Randomly generate a feasible solution according to the fuzzy simulation for possibilistic |
| constraints and take it as the initial parameter for the lower level; |
| Step 2. Solve all the multiobjective optimization problems on the lower level by SMOSA based on |
| the fuzzy simulation and we obtain the Pareto optimal solution for all . Put , |
| into a Pareto set of solutions and compute all objective values of the upper and lower |
| levels; |
| Step 3. Generate a new solution in the neighborhood of by the |
| random perturbation; |
| Step 4. Check the feasibility by fuzzy simulation according to all the constraints on both levels. |
| If not, return to Step 3; |
| Step 5. Compute the objective values on both level, respectively. Compare the generated solution |
| with all solutions in the Pareto set and update the Pareto set if necessary; |
| Step 6. Replace the current solution with the generated solution if is archived and go to |
| Step 7; |
| Step 7. Accept the generated solution as the input solution for the lower level if it is not |
| archived with the probability: , where |
| . If the generated solution is accepted, |
| take it into the lower level and solve them. Then we get a new solution |
| and put it into the Pareto set. If not, go to Step 9; |
| Step 8. Compare and according to the evaluation function based on the compromise |
| approach proposed by Xu and Li [15]. If is more optimal than , let . If not |
| Step 9. Periodically, restart with a randomly selected solution from the Pareto set. |
| While periodically restarting with the archived solutions, Suppapitnarm et al. [16] |
| have recommended biasing towards the extreme ends of the trade-off surface; |
| Step 10. Periodically reduce the temperature by using a problem-dependent annealing schedule |
| Step 11. Repeat steps 2–10, until a predefined number of iterations is carried out. |
