Dear Friends, We have 3 objective function (f1,f2,f3). I would like to compare the two following approaches by some appropriate measures: 1) considering f1 f2 f3 in multiobjective optimization. 2) considering f1, f2 as the objective functions and f3 as a constraint in the objective function. How can I compare them? Best,Reza asked 30 Nov '12, 12:47 Reza Salehiz... fbahr ♦ 
Your second modeling method is similar to \(\epsilon\)constraint, which is known to give Pareto optimal solutions for different \(\epsilon\) values. Considering that your solution method is capable of finding Pareto optimal sets for each modeling method (e.g., using an evolutionary algorithm such as NSGAII), you might compare these modeling methods based on multiple criteria including:
You might see the following papers for more discussion of the above metrics:
Some other criteria are discussed by Deb in his book on multiobjective evolutionary algorithms. answered 30 Nov '12, 15:02 Ehsan ♦ Thank you. but if we would like to solve both models via epsilonconstraint, what kind of measures should we use?
(30 Nov '12, 15:14)
Reza Salehiz...
\(\epsilon\)constraint is designed to work with one objective function as the main one and the other objective functions as constraints. Hence if you want to use \(\epsilon\)constraint method, you have to change your current models that would result in three models each with one of objective functions \(f_1\), \(f_2\), and \(f_3\) and the other objective functions as constraints. Therefore, I don't think your models could be compared with each other anymore if you use \(\epsilon\)constraint method.
(30 Nov '12, 15:21)
Ehsan ♦

How are you planning to balance three objectives in the first case (archimedean weights, weighted norm, distance from a utopia point, preemptive priorities, ...)? I think the answer to that might have implications for how to do the comparison.
Thank you Paul. We find pareto optimal front for both approaches so the method of normalization is not matter of importance I think.