You could be looking at maximizing the distances between the different clusters (high inter-cluster distances) while having each cluster as compact as possible (low intra-cluster distances).

Check the wikipedia page about cluster analysis: https://en.wikipedia.org/wiki/Cluster_analysis

Hello dear friends

Thanks a lot for your answers.

Mr. Amir Ehsan Ranginkaman, The role of clustering  is the task of grouping population, in such a way the members of each group are similar finally. what are fitness functions  in multi objective algorithms when they combine with clustering method? Are they related to objectives of optimization problem or they are related to minimizing the distance between clusters members and center of clusters?!

As a follow up to your comment, it could be related to just clustering as in Brain Storm Optimization (BSO) where similar individuals (representing ideas) are grouped in clusters in every iteration.

Hello

Partitioning of Objects can be done using Multiple Criteria like rand index, intra_cluster, inter_clusters,DBindex  

see te work 

Multiobjective data clustering: Law, M.H.C.  Topchy, A.P. ; Jain, A.K.

Thank you all...

Mr. Amir Ehsan Ranginkaman I just want to use clustering method to form several sub swarms with the MOPSO algorithm in order to thoroughly sample the search space. You are right. I agree with you and think fitness functions in MOPSO algorithm depend on optimization problem.

Anyway thank you so much dear friends.

Best regards

Hello

I suggest you this paper about VEPSO

Multiobjective Optimization Using Parallel Vector Evaluated Particle Swarm Optimization (2004)

by K. E. Parsopoulos , D. K. Tasoulis , M. N. Vrahatis , 

Hello dear Souadfel Salima

Of course I will read it .Thank you.

Best Regards...

A Novel Authentication Scheme with Secure Compressed Sensing in Cloud

https://www.researchgate.net/publication/280244004_A_comparative_study_of_metaheuristic_optimization_approaches_for_directional_overcurrent_relays_coordination

Article A comparative study of metaheuristic optimization approaches...

https://www.researchgate.net/publication/297245624_Particle_Swarm_Optimization_Algorithm_and_its_Codes_in_MATLAB

Research Particle Swarm Optimization: Algorithm and its Codes in MATLAB

https://www.researchgate.net/publication/296636431_Codes_in_MATLAB_for_Particle_Swarm_Optimization

Code Codes in MATLAB for Particle Swarm Optimization

Hello,

Can anyone suggest me, How to evaluate the accuracy of clustering algorithms by using different datasets