**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. |