In decision making when multiple criteria are determined, the best choice depends on having complete information and proper decision-making technique. The permutation method is one of the popular techniques used in the context of multiple criteria decision making (MCDM). In this paper, a method is presented where there is more than one vector of weights for the criteria and there are uncertainties associated with criteria weights or there are multiple decision makers. We first take different weight vectors to create a multi-objective problem and then we solve them simultaneously to achieve appropriate Pareto solutions of the permutation method. Therefore, MOPSO and NSGA-II algorithms are utilized to find non-dominated solutions. Some examples in different sizes are considered to compare the efficiency of the proposed methods. Results show that by increasing the number of options and considering the computational time, the proposed methods perform better compared with the exact method. Moreover, NSGA-II is more efficient than MOPSO for the considered problem.