In this study a realistic bi-objective unrelated parallel machine scheduling problem is considered. This problem has been inspired from block erection scheduling problem in a shipyard. Conventional (NSGA-II) and new approach of BicriterionAnt algorithm are proposed to solve this problem. A new approach of Taguchi method is used to calibrate the parameters of the algorithms. The results indicate that the proposed (MOACO) is more reliable against (NSGA-II) in solving the test problems.