survey

A Survey of Multiobjective Evolutionary Clustering

Authors:

Anirban Mukhopadhyay,

Sanghamitra BandyopadhyayAuthors Info & Claims

ACM Computing Surveys (CSUR), Volume 47, Issue 4

Article No.: 61, Pages 1 - 46

https://doi.org/10.1145/2742642

Published: 26 May 2015 Publication History

Abstract

Data clustering is a popular unsupervised data mining tool that is used for partitioning a given dataset into homogeneous groups based on some similarity/dissimilarity metric. Traditional clustering algorithms often make prior assumptions about the cluster structure and adopt a corresponding suitable objective function that is optimized either through classical techniques or metaheuristic approaches. These algorithms are known to perform poorly when the cluster assumptions do not hold in the data. Multiobjective clustering, in which multiple objective functions are simultaneously optimized, has emerged as an attractive and robust alternative in such situations. In particular, application of multiobjective evolutionary algorithms for clustering has become popular in the past decade because of their population-based nature. Here, we provide a comprehensive and critical survey of the multitude of multiobjective evolutionary clustering techniques existing in the literature. The techniques are classified according to the encoding strategies adopted, objective functions, evolutionary operators, strategy for maintaining nondominated solutions, and the method of selection of the final solution. The pros and cons of the different approaches are mentioned. Finally, we have discussed some real-life applications of multiobjective clustering in the domains of image segmentation, bioinformatics, web mining, and so forth.

References

[1]

H. A. Abbass and R. A. Sarker. 2002. The Pareto differential evolution algorithm. International Journal on Artificial Intelligence Tools 11, 4, 531--552.

[2]

S. Agrawal, B. K. Panigrahi, and M. K. Tiwari. 2008. Multiobjective particle swarm algorithm with fuzzy clustering for electrical power dispatch. IEEE Transactions on Evolutionary Computation 12, 5, 529--541.

Digital Library

[3]

B. Amiri, L. Hossain, and J. Crowford. 2012. A multiobjective hybrid evolutionary algorithm for clustering in social networks. In Proceedings of the 14th International Conference on Genetic and Evolutionary Computation Conference Companion (GECCO Companion’12). ACM, New York, NY, 1445--1446.

Digital Library

[4]

S. Bandyopadhyay, R. Baragona, and U. Maulik. 2010. Clustering multivariate time series by genetic multiobjective optimization. Metron - International Journal of Statistics LXVIII, 2, 161--183.

[5]

S. Bandyopadhyay, U. Maulik, and A. Mukhopadhyay. 2007a. Multiobjective genetic clustering for pixel classification in remote sensing imagery. IEEE Transactions on Geoscience and Remote Sensing 45, 5, 1506--1511.

[6]

S. Bandyopadhyay, A. Mukhopadhyay, and U. Maulik. 2007b. An improved algorithm for clustering gene expression data. Bioinformatics 23, 21, 2859--2865.

Digital Library

[7]

S. Bandyopadhyay and S. K. Pal. 2007. Classification and Learning Using Genetic Algorithms: Applications in Bioinformatics and Web Intelligence. Springer, New York, NY.

Digital Library

[8]

S. Bandyopadhyay, S. Saha, U. Maulik, and K. Deb. 2008. A simulated annealing-based multiobjective optimization algorithm: AMOSA. IEEE Transactions on Evolutionary Computation 12, 3, 269--283.

Digital Library

[9]

W. Banzhaf, F. D. Francone, R. E. Keller, and P. Nordin. 1998. Genetic Programming: An Introduction: on the Automatic Evolution of Computer Programs and Its Applications. Morgan Kaufmann, San Francisco, CA.

Digital Library

[10]

N. Beume, B. Naujoks, and M. Emmerich. 2007. SMS-EMOA: Multiobjective selection based on dominated hypervolume. European Journal of Operational Research 181, 3, 1653--1669.

[11]

J. C. Bezdek. 1981. Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New York, NY.

Digital Library

[12]

J. C. Bezdek and N. R. Pal. 1998. Some new indexes of cluster validity. IEEE Transactions on Systems, Man and Cybernetics 28, 301--315.

Digital Library

[13]

R. Caballero, M. Laguna, R. Marti, and J. Molina. 2006. Multiobjective clustering with metaheuristic optimization technology. Technical Report. Leeds School of Business in the University of Colorado, Boulder, CO.

[14]

E. Chen and F. Wang. 2005. Dynamic clustering using multi-objective evolutionary algorithm. In Proceedings of the 2005 International Conference on Computational Intelligence and Security - Volume Part I (CIS’05). Springer-Verlag, Berlin, 73--80.

Digital Library

[15]

A. L. V. Coelho, E. Fernandes, and K. Faceli. 2010. Inducing multi-objective clustering ensembles with genetic programming. Neurocomputing 74, 1--3, 494--498.

Digital Library

[16]

C. A. Coello Coello. 2006. Evolutionary multiobjective optimization: A historical view of the field. IEEE Computational Intelligence Magazine 1, 1, 28--36.

Digital Library

[17]

C. A. Coello Coello, G. B. Lamont, and D. A. van Veldhuizen. 2007. Evolutionary Algorithms for Solving Multi-Objective Problems (2nd ed.). Springer, Berlin.

Digital Library

[18]

C. A. Coello Coello. 1999. A comprehensive survey of evolutionary-based multiobjective optimization techniques. Knowledge and Information Systems 1, 3, 129--156.

Digital Library

[19]

D. W. Corne, N. R. Jerram, J. D. Knowles, and M. J. Oates. 2001. PESA-II: Region-based selection in evolutionary multiobjective optimization. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001), L. Spector, E. D. Goodman, A. Wu, W. B. Langdon, H.-M. Voigt, M. Gen, S. Sen, M. Dorigo, S. Pezeshk, M. H. Garzon, and E. Burke (Eds.). Morgan Kaufmann, San Francisco, CA, 283--290.

[20]

D. W. Corne, J. D. Knowles, and M. J. Oates. 2000. The Pareto envelope-based selection algorithm for multiobjective optimization. In Proceedings of the Parallel Problem Solving from Nature VI Conference. Springer, 839--848.

Digital Library

[21]

G. Corral, A. Garcia-Piquer, A. Orriols-Puig, A. Fornells, and E. Golobardes. 2009. Multiobjective evolutionary clustering approach to security vulnerability assesments. In Proceedings of the 4th International Conference on Hybrid Artificial Intelligence Systems (HAIS’09) (Lecture Notes in Computer Science), Emilio Corchado, Xindong Wu, Erkki Oja, lvaro Herrero, and Bruno Baruque (Eds.), Vol. 5572. Springer, 597--604.

Digital Library

[22]

D. L. Davies and D. W. Bouldin. 1979. A cluster separation measure. IEEE Transactions on Pattern Analysis and Machine Intelligence 1, 224--227.

Digital Library

[23]

K. Deb. 2001. Multi-objective Optimization Using Evolutionary Algorithms. John Wiley and Sons, England.

Digital Library

[24]

K. Deb, A. Pratap, S. Agrawal, and T. Meyarivan. 2002. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6, 182--197.

Digital Library

[25]

G. N. Demir, A. S. Uyar, and S. G. Ögüdücü. 2007. Graph-based sequence clustering through multiobjective evolutionary algorithms for web recommender systems. In Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation (GECCO’07). ACM, New York, NY, 1943--1950.

Digital Library

[26]

G. N. Demir, A. S. Uyar, and S. G. Ögüdücü. 2010. Multiobjective evolutionary clustering of Web user sessions: A case study in Web page recommendation. Soft Computing 14, 6, 579--597.

Digital Library

[27]

J. Du, E. E. Korkmaz, R. Alhajj, and K. Barker. 2005. Alternative clustering by utilizing multi-objective genetic algorithm with linked-list based chromosome encoding. In MLDM (Lecture Notes in Computer Science), Vol. 3587. Springer, 346--355.

Digital Library

[28]

J. C. Dunn. 1974. Well separated clusters and optimal fuzzy partitions. J. Cyberns. 4 (1974), 95--104.

[29]

K. Faceli, M. C. P. de Souto, and A. C. P. L. F. de Carvalho. 2008. A strategy for the selection of solutions of the Pareto front approximation in multi-objective clustering approaches. In Proceedings of the 2008 10th Brazilian Symposium on Neural Networks (SBRN’08). IEEE Computer Society, Washington, DC, 27--32.

Digital Library

[30]

A. Fahad, N. Alshatri, Z. Tari, A. Alamri, I. Khalil, A.Y. Zomaya, S. Foufou, and A. Bouras. 2014. A survey of clustering algorithms for big data: Taxonomy and empirical analysis. IEEE Transactions on Emerging Topics in Computing 2, 3, 267--279.

[31]

C. Ferreira. 2001. Gene expression programming: A new adaptive algorithm for solving problems. Complex Systems 13, 2, 87--129.

[32]

F. Folino and C. Pizzuti. 2010. A multiobjective and evolutionary clustering method for dynamic networks. In Proceedings of the International Conference on Advances in Social Networks Analysis and Mining (ASONAM’10). IEEE Computer Society, 256--263.

Digital Library

[33]

C. M. Fonseca and P. J. Fleming. 1993. Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization. In Proceedings of the 5th International Conference on Genetic Algorithms. Morgan Kaufmann, 416--423.

Digital Library

[34]

A. A. Freitas. 2004. A critical review of multi-objective optimization in data mining: A position paper. SIGKDD Exploration Newsletter 6, 2, 77--86.

Digital Library

[35]

A. P. Gasch and M. B. Eisen. 2002. Exploring the conditional coregulation of yeast gene expression through fuzzy k-means clustering. Genome Biology 3, 11, 0059.1--0059.22.

[36]

D. E. Goldberg. 1989. Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, New York.

Digital Library

[37]

D. E. Goldberg and P. Segrest. 1987. Finite Markov chain analysis of genetic algorithms. In Proceedings of the 2nd International Conference on Genetic Algorithms and Their Application. L. Erlbaum Associates Inc., Hillsdale, NJ, 1--8.

Digital Library

[38]

M. Gong, L. Zhang, L. Jiao, and S. Gou. 2007. Solving multiobjective clustering using an immune-inspired algorithm. In IEEE Congress on Evolutionary Computation. 15--22.

[39]

L. Groll and J. Jakel. 2005. A new convergence proof of fuzzy c-means. IEEE Transactions on Fuzzy Systems 13, 5, 717--720.

Digital Library

[40]

M. Halkidi, Y. Batistakis, and M. Vazirgiannis. 2001. On clustering validation techniques. Journal of Intelligent Information Systems 17, 2/3, 107--145.

Digital Library

[41]

M. Halkidi, M. Vazirgiannis, and Y. Batistakis. 2000. Quality scheme assessment in the clustering process. In Proceedings of the 4th European Conference on Principles of Data Mining and Knowledge Discovery (PKDD’00). Springer-Verlag, London, 265--276.

Digital Library

[42]

J. Handl and J. D. Knowles. 2004. Evolutionary multiobjective clustering. In Proceedings of the 8th International Conference on Parallel Problem Solving in Nature (PPSN’04). 1081--1091.

[43]

J. Handl and J. D. Knowles. 2005a. Exploiting the trade-of—the benefits of multiple objectives in data clustering. In Proceedings of the 3rd International Conference on Evolutionary Multi-Criterion Optimization (EMO’05). Springer-Verlag, Berlin, 547--560.

Digital Library

[44]

J. Handl and J. D. Knowles. 2005b. Improvements to the scalability of multiobjective clustering. In Proceedings of the Congress on Evolutionary Computation (IEEE CEC’05). IEEE, 2372--2379.

[45]

J. Handl and J. D. Knowles. 2005c. Multiobjective clustering around medoids. In Proceedings of the IEEE Congress on Evolutionary Computation, Vol. 1. 632--639.

[46]

J. Handl and J. D. Knowles. 2006. Multiobjective clustering and cluster validation. Computational Intelligence, Vol. 16. Springer, 21--47.

[47]

J. Handl and J. D. Knowles. 2007. An evolutionary approach to multiobjective clustering. IEEE Transactions on Evolutionary Computation 11, 1, 56--76.

Digital Library

[48]

J. Handl and J. D. Knowles. 2012. Clustering criteria in multiobjective data clustering. In Parallel Problem Solving from Nature - PPSN XII, C. A. Coello Coello, V. Cutello, K. Deb, S. Forrest, G. Nicosia, and M. Pavone (Eds.). Lecture Notes in Computer Science, Vol. 7492. Springer, Berlin, 32--41.

Digital Library

[49]

J. Handl, J. D. Knowles, and D. B. Kell. 2005. Computational cluster validation in post-genomic data analysis. Bioinformatics 21, 15, 3201--3212.

Digital Library

[50]

J. Holland. 1975. Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, MI.

Digital Library

[51]

J. Horn and N. Nafpliotis. 1993. Multiobjective Optimization Using Niched Pareto Genetic Algorithm. Technical Report IlliGAL Report 93005. University of Illinois at Urbana-Champaign, Urbana, IL.

[52]

E. R. Hruschka, R. J. G. B. Campello, A. A. Freitas, and A. C. P. L. F. De Carvalho. 2009. A survey of evolutionary algorithms for clustering. IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews 39, 2, 133--155.

Digital Library

[53]

A. W. Iorio and X. Li. 2004. Solving rotated multi-objective optimization problems using differential evolution. In Australian Conference on Artificial Intelligence (Lecture Notes in Computer Science), G. I. Webb and X. Yu (Eds.), Vol. 3339. Springer, 861--872.

Digital Library

[54]

A. K. Jain and R. C. Dubes. 1988. Algorithms for Clustering Data. Prentice-Hall, Englewood Cliffs, NJ.

Digital Library

[55]

A. K. Jain, M. N. Murty, and P. J. Flynn. 1999. Data clustering: A review. Computing Surveys 31.

Digital Library

[56]

K. Kim, R. I. McKay, and B.-R. Moon. 2010. Multiobjective evolutionary algorithms for dynamic social network clustering. In Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation (GECCO’10). ACM, New York, NY, 1179--1186.

Digital Library

[57]

O. Kirkland, V. Rayward-Smith, and B. de la Iglesia. 2011. A novel multi-objective genetic algorithm for clustering. In Intelligent Data Engineering and Automated Learning (IDEAL’11), H. Yin, W. Wang, and V. Rayward-Smith (Eds.). Lecture Notes in Computer Science, Vol. 6936. Springer, Berlin, 317--326.

Digital Library

[58]

J. D. Knowles and D. W. Corne. 1999. The Pareto archived evolution strategy: A new baseline algorithm for Pareto multiobjective optimisation. In Proceedings of the IEEE Congress on Evolutionary Computation. IEEE Press, Piscataway, NJ, 98--105.

[59]

L. I. Kuncheva and J. C. Bezdek. 1997. Selection of cluster prototypes from data by a genetic algorithm. In Proceedings of the 5th European Conference on Intelligent Techniques and Soft Computing. 1683--1688.

[60]

D. Kundu, K. Suresh, S. Ghosh, S. Das, A. Abraham, and Y. Badr. 2009. Automatic clustering using a synergy of genetic algorithm and multi-objective differential evolution. In Proceedings of the 4th International Conference on Hybrid Artificial Intelligence Systems (HAIS’09). Springer-Verlag, Berlin, 177--186.

Digital Library

[61]

R. Liu, W. Zhang, L. Jiao, and F. Liu. 2010. A multiobjective immune clustering ensemble technique applied to unsupervised SAR image segmentation. In CIVR. 158--165.

Digital Library

[62]

Y. Liu, T. Özyer, R. Alhajj, and K. Barker. 2005. Integrating multi-objective genetic algorithm and validity analysis for locating and ranking alternative clustering. Informatica 29, 33--40.

[63]

N. Matake, T. Hiroyasu, M. Miki, and T. Senda. 2007. Multiobjective clustering with automatic k-determination for large-scale data. In Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation (GECCO’07). ACM, New York, NY, 861--868.

Digital Library

[64]

U. Maulik and S. Bandyopadhyay. 2000. Genetic algorithm based clustering technique. Pattern Recognition 33, 1455--1465.

[65]

U. Maulik and S. Bandyopadhyay. 2002. Performance evaluation of some clustering algorithms and validity indices. IEEE Transactions on Pattern Analysis and Machine Intelligence 24, 12, 1650--1654.

Digital Library

[66]

U. Maulik, S. Bandyopadhyay, and A. Mukhopadhyay. 2011. Multiobjective Genetic Algorithms for Clustering - Applications in Data Mining and Bioinformatics. Springer.

Digital Library

[67]

U. Maulik, A. Mukhopadhyay, and S. Bandyopadhyay. 2009. Combining Pareto-optimal clusters using supervised learning for identifying co-expressed genes. BMC Bioinformatics 10, 27.

[68]

U. Maulik, A. Mukhopadhyay, S. Bandyopadhyay, M. Q. Zhang, and X. Zhang. 2008. Multiobjective fuzzy biclustering in microarray data: Method and a new performance measure. In Proceedings of the IEEE World Congress on Computational Intelligence (WCCI’08)/IEEE Congress on Evolutionary Computation (CEC’08). 383--388.

[69]

K. C. Mondal, A. Mukhopadhyay, U. Maulik, S. Bandyopadhyay, and N. Pasquier. 2010. MOSCFRA: A multi-objective genetic approach for simultaneous clustering and gene ranking. In CIBB. 174--187.

Digital Library

[70]

A. Mukhopadhyay, S. Bandyopadhyay, and U. Maulik. 2006. Clustering using multi-objective genetic algorithm and its application to image segmentation. Proceedings of the IEEE International Conference on Systems, Man and Cybernetics (SMC’06) 3, 2678--2683.

[71]

A. Mukhopadhyay, S. Bandyopadhyay, and U. Maulik. 2008. Combining multiobjective fuzzy clustering and probabilistic ANN classifier for unsupervised pattern classification: Application to satellite image segmentation. In Proceedings of the IEEE World Congress on Computational Intelligence (WCCI 2008)/IEEE Congress on Evolutionary Computation (CEC’08). 877--883.

[72]

A. Mukhopadhyay, S. Bandyopadhyay, and U. Maulik. 2009. Analysis of microarray data using multiobjective variable string length genetic fuzzy clustering. In Proceedings of the 11th Conference on Congress on Evolutionary Computation (CEC’09). IEEE Press, Piscataway, NJ, 1313--1319.

Digital Library

[73]

A. Mukhopadhyay, S. Bandyopadhyay, and U. Maulik. 2010. Multi-class clustering of cancer subtypes through SVM based ensemble of Pareto-optimal solutions for gene marker identification. PloS One 5, 11, e13803.

[74]

A. Mukhopadhyay and U. Maulik. 2007. Multiobjective approach to categorical data clustering. Proc. IEEE Congress on Evolutionary Computation (CEC 2007) (September 2007), 1296--1303.

[75]

A. Mukhopadhyay and U. Maulik. 2009. Unsupervised pixel classification in satellite imagery using multiobjective fuzzy clustering combined with SVM classifier. IEEE Transactions on Geoscience and Remote Sensing 47, 4, 1132--1138.

[76]

A. Mukhopadhyay and U. Maulik. 2011. A multiobjective approach to MR brain image segmentation. Applied Soft Computing 11, 872--880.

Digital Library

[77]

A. Mukhopadhyay, U. Maulik, and S. Bandyopadhyay. 2009a. Multi-objective genetic algorithm based fuzzy clustering of categorical attributes. IEEE Transactions on Evolutionary Computation 13, 5 (2009), 991--1005.

Digital Library

[78]

A. Mukhopadhyay, U. Maulik, and S. Bandyopadhyay. 2009b. Multiobjective genetic clustering with ensemble among Pareto front solutions: Application to MRI brain image segmentation. In Proceedings of the International Conference on Advances in Pattern Recognition (ICAPR’09). 236--239.

Digital Library

[79]

A. Mukhopadhyay, U. Maulik, and S. Bandyopadhyay. 2010. Simultaneous informative gene selection and clustering through multiobjective optimization. In IEEE Congress on Evolutionary Computation. 1--8.

[80]

A. Mukhopadhyay, U. Maulik, and S. Bandyopadhyay. 2011. Gene expression data analysis using multiobjective clustering improved with SVM based ensemble. In Silico Biology 11, 1--2, 19--27.

[81]

A. Mukhopadhyay, U. Maulik, and S. Bandyopadhyay. 2013. An interactive approach to multiobjective clustering of gene expression patterns. IEEE Transactions on Biomedical Engineering 60, 1, 35--41.

[82]

A. Mukhopadhyay, U. Maulik, S. Bandyopadhyay, and C. A. Coello Coello. 2014a. A survey of multiobjective evolutionary algorithms for data mining: Part I. IEEE Transactions on Evolutionary Computation 18, 1, 4--19.

[83]

A. Mukhopadhyay, U. Maulik, S. Bandyopadhyay, and C. A. Coello Coello. 2014b. Survey of multiobjective evolutionary algorithms for data mining: Part II. IEEE Transactions on Evolutionary Computation 18, 1, 20--35.

[84]

A. Mukhopadhyay, S. Ray, and M. De. 2012. Detecting protein complexes in a PPI network: a gene ontology based multi-objective evolutionary approach. Molecular Biosystems 8, 11, 3036--3048.

[85]

T. Özyer, Y. Liu, R. Alhajj, and K. Barker. 2004. Multi-objective genetic algorithm based clustering approach and its application to gene expression data. In Proceedings of the 3rd International Conference on Advances in Information Systems (ADVIS’04). Springer-Verlag, Berlin, 451--461.

Digital Library

[86]

T. Özyer, Y. Liu, R. Alhajj, and K. Barker. 2005. Multi-objective genetic algorithm based clustering approach and its application to gene expression data. In Advances in Information Systems, Tatyana Yakhno (Ed.). Lecture Notes in Computer Science, Vol. 3261. Springer, Berlin, 451--461.

Digital Library

[87]

T. Özyer, M. Zhang, and R. Alhajj. 2011. Integrating multi-objective genetic algorithm based clustering and data partitioning for skyline computation. Applied Intelligence 35, 1, 110--122.

Digital Library

[88]

M. K. Pakhira, S. Bandyopadhyay, and U. Maulik. 2004. Validity index for crisp and fuzzy clusters. Pattern Recognition 37, 487--501.

[89]

N. R. Pal and J. C. Bezdek. 1995. On cluster validity for the fuzzy C-means model. IEEE Transactions on Fuzzy Systems 3, 370--379.

Digital Library

[90]

K. Praditwong, M. Harman, and X. Yao. 2011. Software module clustering as a multi-objective search problem. IEEE Transactions on Software Engineering 37, 2, 264--282.

Digital Library

[91]

K. V. Price, R. M. Storn, and J. A. Lampinen. 2005. Differential Evolution: A Practical Approach to Global Optimization. Springer-Verlag, Berlin.

Digital Library

[92]

X. Qian, X. Zhang, L. Jiao, and W. Ma. 2008. Unsupervised texture image segmentation using multiobjective evolutionary clustering ensemble algorithm. In Proceedings of the IEEE Congress on Evolutionary Computation (CEC’08). 3561--3567.

[93]

K. S. N. Ripon and M. N. H. Siddique. 2009. Evolutionary multi-objective clustering for overlapping clusters detection. In Proceedings of the 11th Conference on Congress on Evolutionary Computation (CEC’09). IEEE Press, Piscataway, NJ, 976--982.

Digital Library

[94]

K. S. N. Ripon, C.-H. Tsang, and S. Kwong. 2006a. Multi-objective data clustering using variable-length real jumping genes genetic algorithm and local search method. In Proceedings of the International Joint Conference on Neural Networks. 3609--3616.

[95]

K. S. N. Ripon, C.-H. Tsang, S. Kwong, and M.-K. Ip. 2006b. Multi-objective evolutionary clustering using variable-length real jumping genes genetic algorithm. In Proceedings of the International Conference on Pattern Recognition (ICPR’06). 1200--1203.

Digital Library

[96]

T. Robic and B. Filipic. 2005. DEMO: Differential evolution for multiobjective optimization. Lecture Notes in Computer Science, C. A. Coello Coello, A. Hernandez Aguirre, and E. Zitzler (Eds.), Vol. 3410. Springer, 520--533.

Digital Library

[97]

P. J. Rousseeuw. 1987. Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Journal of Computational Applied Mathematics 20, 53--65.

Digital Library

[98]

I. Saha and U. Maulik. 2014. Multiobjective differential evolution-based fuzzy clustering for MR brain image segmentation. In Advanced Computational Approaches to Biomedical Engineering, P. K. Saha, U. Maulik, and S. Basu (Eds.). Springer, Berlin, 71--86.

[99]

I. Saha, U. Maulik, and D. Plewczynski. 2011a. Multiobjective differential crisp clustering for evaluation of clusters dynamically. In Man-Machine Interactions 2, T. Czachorski, S. Kozielski, and U. Stanczyk (Eds.). Advances in Intelligent and Soft Computing, Vol. 103. Springer, Berlin, 307--313.

[100]

I. Saha, U. Maulik, and D. Plewczynski. 2011b. A new multi-objective technique for differential fuzzy clustering. Applied Soft Computing 11, 2, 2765--2776.

Digital Library

[101]

S. Saha and S. Bandyopadhyay. 2009. A new multiobjective simulated annealing based clustering technique using symmetry. Pattern Recognition Letters 30, 15, 1392--1403.

Digital Library

[102]

S. Saha and S. Bandyopadhyay. 2013. A generalized automatic clustering algorithm in a multiobjective framework. Applied Soft Computing 13, 1, 89--108.

Digital Library

[103]

D. K. Saxena, J. A. Duro, A. Tiwari, K. Deb, and Q. Zhang. 2013. Objective reduction in many-objective optimization: Linear and nonlinear algorithms. IEEE Transactions on Evolutionary Computation 17, 1, 77--99.

Digital Library

[104]

H.-P. Schwefel. 1993. Evolution and Optimum Seeking: The Sixth Generation. John Wiley & Sons, New York, NY.

Digital Library

[105]

S. Z. Selim and M. A. Ismail. 1984. K-means type algorithms: A generalized convergence theorem and characterization of local optimality. IEEE Transactions on Pattern Analysis and Machine Intelligence 6, 81--87.

Digital Library

[106]

W. Shannon, R. Culverhouse, and J. Duncan. 2003. Analyzing microarray data using cluster analysis. Pharmacogenomics 4, 1, 41--51.

[107]

S. Shirakawa and T. Nagao. 2009. Evolutionary image segmentation based on multiobjective clustering. In Proceedings of the 11th Conference on Congress on Evolutionary Computation (CEC’09). IEEE Press, Piscataway, NJ, 2466--2473.

Digital Library

[108]

N. Srinivas and K. Deb. 1994. Multiobjective optimization using nondominated sorting in genetic algorithms. Evolutionary Computation 2, 3, 221--248.

Digital Library

[109]

A. Strehl and J. Ghosh. 2002. Cluster ensembles - a knowledge reuse framework for combining multiple partitions. In Machine Learning Research, Vol. 3. 583--617.

Digital Library

[110]

J. Sun, W. Sverdlik, and S. Tout. 2006. Parallel hybrid clustering using genetic programming and multi-objective fitness with density (PYRAMID). In DMIN, S. F. Crone, S. Lessmann, and R. Stahlbock (Eds.). CSREA Press, 197--203.

[111]

K. Suresh, D. Kundu, S. Ghosh, S. Das, and A. Abraham. 2009b. Data clustering using multi-objective differential evolution algorithms. Fundamenta Informatica 97, 4, 381--403.

Digital Library

[112]

K. Suresh, D. Kundu, S. Ghosh, S. Das, A. Abraham, and S. Y. Han. 2009a. Multi-objective differential evolution for automatic clustering with application to micro-array data analysis. Sensors 9, 5, 3981--4004.

[113]

R. Tibshirani, G. Walther, and T. Hastie. 2001. Estimating the number of clusters in a dataset via the Gap statistic. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 63, 2, 411--423.

[114]

W. Wanga and Y. Zhanga. 2007. On fuzzy cluster validity indices. Fuzzy Sets and Systems 158, 19, 2095--2117.

Digital Library

[115]

J.-M. Won, S. Ullah, and F. Karray. 2008. Data clustering using multi-objective hybrid evolutionary algorithm. In Proceedings of the International Conference on Control, Automation and Systems. 2298--2303.

[116]

X. L. Xie and G. Beni. 1991. A validity measure for fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence 13, 841--847.

Digital Library

[117]

F. Xue, A. C. Sanderson, and R. J. Graves. 2005. Multi-objective differential evolution - algorithm, convergence analysis, and applications. Proceedings of the IEEE Congress on Evolutionary Computation (CEC’05) 1, 743--750.

[118]

Y. Zheng, L. Jia, and H. Cao. 2012. Multi-objective gene expression programming for clustering. Information Technology and Control 41, 3, 283--294.

[119]

L. Zhu, L. Cao, and J. Yang. 2012. Multiobjective evolutionary algorithm-based soft subspace clustering. In IEEE Congress on Evolutionary Computation. 1--8.

[120]

E. Zitzler. 1999. Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications. Ph.D. Dissertation. Swiss Federal Institute of Technology (ETH), Zurich, Switzerland.

[121]

E. Zitzler and S. Künzli. 2004. Indicator-based selection in multiobjective search. In Parallel Problem Solving from Nature - PPSN VIII, X. Yao et al. (Ed.). Springer-Verlag. Lecture Notes in Computer Science Vol. 3242, Birmingham, UK, 832--842.

[122]

E. Zitzler, M. Laumanns, and L. Thiele. 2001. SPEA2: Improving the Strength Pareto Evolutionary Algorithm. Technical Report 103. Universität Zürich, Zürich, Switzerland.

[123]

E. Zitzler and L. Thiele. 1998. An Evolutionary Algorithm for Multiobjective Optimization: The Strength Pareto Approach. Technical Report 43. Universität Zürich, Zürich, Switzerland.

Cited By

Naderi MAmiri M(2025)Text clustering with a hybrid multi-objective optimization approach: The multi-objective firefly differential Jaya AlgorithmSwarm and Evolutionary Computation10.1016/j.swevo.2025.10184793(101847)Online publication date: Mar-2025
https://doi.org/10.1016/j.swevo.2025.101847
Qiu MZhang YLei SGu M(2024)An Improved Evolutionary Multi-Objective Clustering Algorithm Based on AutoencoderApplied Sciences10.3390/app1406245414:6(2454)Online publication date: 14-Mar-2024
https://doi.org/10.3390/app14062454
Wang RLi WShen KZhang TLiao X(2024)Evolutionary Multi-Tasking Optimization for High-Efficiency Time Series Data ClusteringTsinghua Science and Technology10.26599/TST.2023.901003629:2(343-355)Online publication date: Apr-2024
https://doi.org/10.26599/TST.2023.9010036
Show More Cited By

Index Terms

A Survey of Multiobjective Evolutionary Clustering

Recommendations

Evolutionary multiobjective optimization in noisy problem environments

This paper presents a multiobjective evolutionary algorithm (MOEA) capable of handling stochastic objective functions. We extend a previously developed approach to solve multiple objective optimization problems in deterministic environments by ...
A fast Pareto genetic algorithm approach for solving expensive multiobjective optimization problems

We present a new multiobjective evolutionary algorithm (MOEA), called fast Pareto genetic algorithm (FastPGA), for the simultaneous optimization of multiple objectives where each solution evaluation is computationally- and/or financially-expensive. This ...
Increasing selective pressure towards the best compromise in evolutionary multiobjective optimization: The extended NOSGA method

Most current approaches in the evolutionary multiobjective optimization literature concentrate on adapting an evolutionary algorithm to generate an approximation of the Pareto frontier. However, finding this set does not solve the problem. The decision-...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image ACM Computing Surveys

ACM Computing Surveys Volume 47, Issue 4

July 2015

573 pages

ISSN:0360-0300

EISSN:1557-7341

DOI:10.1145/2775083

Editor:
Sartaj Sahni
Department of Computer and Information Science and Engineering/University of Florida/Gainesville, FL

Issue’s Table of Contents

Copyright © 2015 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 26 May 2015

Accepted: 01 March 2015

Revised: 01 October 2014

Received: 01 November 2012

Published in CSUR Volume 47, Issue 4

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Survey
Research
Refereed

Funding Sources

DST-INRIA-CNRS
DST, India

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

140
Total Citations
View Citations
1,850
Total Downloads

Downloads (Last 12 months)54
Downloads (Last 6 weeks)6

Reflects downloads up to 14 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

Naderi MAmiri M(2025)Text clustering with a hybrid multi-objective optimization approach: The multi-objective firefly differential Jaya AlgorithmSwarm and Evolutionary Computation10.1016/j.swevo.2025.10184793(101847)Online publication date: Mar-2025
https://doi.org/10.1016/j.swevo.2025.101847
Qiu MZhang YLei SGu M(2024)An Improved Evolutionary Multi-Objective Clustering Algorithm Based on AutoencoderApplied Sciences10.3390/app1406245414:6(2454)Online publication date: 14-Mar-2024
https://doi.org/10.3390/app14062454
Wang RLi WShen KZhang TLiao X(2024)Evolutionary Multi-Tasking Optimization for High-Efficiency Time Series Data ClusteringTsinghua Science and Technology10.26599/TST.2023.901003629:2(343-355)Online publication date: Apr-2024
https://doi.org/10.26599/TST.2023.9010036
Yazdani DBranke JKhorshidi MOmidvar MLi XGandomi AYao XLi XHandl J(2024)Clustering in Dynamic Environments: A Framework for Benchmark Dataset Generation With Heterogeneous ChangesProceedings of the Genetic and Evolutionary Computation Conference10.1145/3638529.3654188(50-58)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638529.3654188
Hadikhani PLai DOng W(2024)Human Activity Discovery With Automatic Multi-Objective Particle Swarm Optimization Clustering With Gaussian Mutation and Game TheoryIEEE Transactions on Multimedia10.1109/TMM.2023.326660326(420-435)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1109/TMM.2023.3266603
Larrañaga PBielza C(2024)Estimation of Distribution Algorithms in Machine Learning: A SurveyIEEE Transactions on Evolutionary Computation10.1109/TEVC.2023.331410528:5(1301-1321)Online publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1109/TEVC.2023.3314105
Qian C(2024)Can Evolutionary Clustering Have Theoretical Guarantees?IEEE Transactions on Evolutionary Computation10.1109/TEVC.2023.329664528:5(1220-1234)Online publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1109/TEVC.2023.3296645
Robles-Berumen HZafra AVentura S(2024)A survey of genetic algorithms for clustering: Taxonomy and empirical analysisSwarm and Evolutionary Computation10.1016/j.swevo.2024.10172091(101720)Online publication date: Dec-2024
https://doi.org/10.1016/j.swevo.2024.101720
Thakral PKumar Y(2024)An Improved Water Flow Optimizer for Data ClusteringSN Computer Science10.1007/s42979-024-03048-05:6Online publication date: 17-Jul-2024
https://doi.org/10.1007/s42979-024-03048-0
Sahoo RKumar TTanwar PPruthi JSingh S(2024)An efficient meta-heuristic algorithm based on water flow optimizer for data clusteringThe Journal of Supercomputing10.1007/s11227-023-05822-y80:8(10301-10326)Online publication date: 1-May-2024
https://dl.acm.org/doi/10.1007/s11227-023-05822-y
Show More Cited By

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Figures

Tables

Media

View Issue’s Table of Contents