Since you provide little detail, you can perform a web search on "epsilon constrained method multi objective" - which provides quite many hits on Google scholar - and see what others have done in the near past. It is a quite popular tool.

I do not believe that multiobjective problems have optimal solutions. You have no choice but to intervene and reformulate the multiobjective problem into a single-objective counterpart: whether you use goal programming, the epsilon constraints method, preemptive optimisation, or some combination. So, the single-objective-counterpart may have an optimal solution... but that is already an adapted version of the original, truly multiobjective problem.

What is important, is that you need to ensure an efficient solution. What is optimal for one objective may not be optimal for another. Not all interventions yield efficient solutions, however.

See the following book

Ehrgott, M.: Multicriteria Optimization. Springer, Berlin 2005.

Hi my dear friend

Good day!

I think the below book will help you a lot to provide relevant codes.

Messac, A. (2015). Optimization in practice with MATLAB®: for engineering students and professionals. Cambridge University Press.

best regards.

Saeed Rezaeian-Marjani

[email protected]

Hi dear friend,

In MOO problems we can use different types of methods such as Weighted-sum or eps-constraint which allows us to find the optimal solutions for the problem.

eps-constraint method is a simple way to find the optimal solutions which you should consider your problem as a single objective optimization with additional constraints. These additional constraints are other objective functions which should be smaller than epsilon value (we can say smaller than the worst value that the objective functions could take).

Good Luck