Dear Omid,

Mean ideal distance (MID) is the one that measure the convergence rate of the algorithms.For example MID measures the convergence rate of Pareto frontier members to a certain point (0,0). Also, diversity measures the extension of the Pareto frontier. Spacing is the one that measure the diversity rate of the algorithms. It measures the standard deviation of the distances among solutions of the Pareto frontier. The Diversity and the MID metrics, as representatives of the multi-objective goals, are used to define multi-objectivecoefficient of variation (MOCV) in Eq. as follows:

MOCV = MID/Diversity

Here is attached files for example of MID.

Best regards

Dear Mr. Lafifi,

Thank you for your reply.

It seems that I should ask the question in a different way.

Suppose that you are comparing several meta-heuristic algorithms developed for a multi-objective optimization problem. You need some metrics to compare the Pareto solutions of the algorithms. One the most popular metric used in the literature is MID.

How do you calculate MID for each Pareto Solution when the problem is maximization?

Dear Mr Taheri

Salaam

As you said in minimization problem MID is used but in my opinion in maximization problem it is not necessary you changed the ideal point. In these problems you can concluded that the algorithms are better that have greater MID.

Best regards

Dear Mr. Behnamian,

I appreciate your kind reply.

As the definition of MID is MINIMUM ideal distance, I was not sure whether to use this metric as a Positive Critera (the more the better).

However, I would be grateful if you provide some references in which MID is used for a maximization problem.

Kind regards

Dear Omid,

here attached files of MID  used for a maximization problem.

Best regards

Dear Mr. Lafifi,

I appreciate your effort in providing the above references.

Unfortunately, I could not find my answer in the texts. MID is merely used in the first reference which is a minimization problem.

Thanks for your attention.

Best regards

I "trick" we learned in my optimization class was that we can redefine a "maximization" problem as a "minimization" problem by changing the objective functions. Suppose you want to maximize Y = 5X1 + 3X2. You can change this to a minimization problem by minimizing 1/Y. 

I don't know if this will help you in this situation but, it might spur some other thoughts.