an algorithm for a multicriteria optimization problem and its application to a facility location problem

In this paper, a new algorithm is proposed for solving a multicriteria optimization problem where the feasible set is an $m-$dimensional cube. in fact, the idea of the multicriteria big cube small cube method is employed to develop the new algorithm. it is proved that, for a given epsilon vector, the output of the suggested algorithm involves all epsilon efficient solutions as well as all efficient solutions. furthermore, the algorithm is applied to a multicriteria location problem. the results show that the recommended algorithm can obtain more epsilon efficient solutions in comparison with the main multicriteria big cube small cube method.