When selecting the best design of a system among a finite set of possible designs, there may be multiple selection criterion. One formulation of such a multi-criteria problem is minimization (or maximization) of one of the criterions while constraining the others. In this paper, we assume the criteria are unobservable mean values of stochastic outputs of simulation. We propose a new heuristic iterative algorithm for finding the best in this situation and use a number of experiments to demonstrate the performance of the algorithm.