In this paper the multi objective optimization problem is studied further with respect to quality indices. In particular, the maximum Pareto front error, accuracy of Pareto frontier, spacing, overall spread, objective spread, maximum spread, and number of distinct choices, cluster, hyper area, dominant area, non-dominated evaluation, and crowding distances are employed to assess the Pareto Front of real case studies. Two algorithms are employed to solve the multi objective problem, namely: the NSGA II and SPEA2 algorithms. These performance indices are analyzed in relation to a set of benchmark problems and conclusions are drawn. Five out of twelve indices can be eliminated. In addition, a new approach to handle both constrained and un-constrained multi objective problems using a modification to the fast elitist multi objective Genetic Algorithm, NSGA II (Non-dominated Sorting Genetic Algorithm II). The approach overcomes shortcomings from previous approaches in handling constrained multi objective problems like Penalty Function Approach, Jimenez-Verdegay-Gomez-Skarmeta's approach, and Ray-Tai-Seow's Method. Comparative studies are conducted using a group of quality indices [2,19] to compare the new approach (M-NSGA II) to two other different algorithms:  regular NSGA, NSGA-II with penalty function. Results show that the new approach is the best among the three approaches.