# A NOVEL HYBRID META-HEURISTIC ALGORITHM BASED ON BLACK HOLE AND HARMONY SEARCH FOR FUZZY CLUSTERING PROBLEM

### Abstract

Fuzzy clustering problem (FCP) is a process of assigning data elements to clusters associated with membership values showing the level of degrees that the elements belong to the groups. It is an optimization problem whose constraints involve the membership degrees. The conventional approach to solve the FCP problem is using an iterative scheme to calculate the membership degrees and the centers until the stopping conditions hold. This approach, named as Fuzzy C-Means (FCM), was invented by Bezdek et al. (1984). Nonetheless, it was shown to converge to local optimum or the saddle points. This leads to a natural question of how to define an algorithm that is able to escape from local optimal point to improve solution quality. In this paper, a new hybrid meta-heuristic algorithm for FCP called BHHS which combines the power of existing meta-heuristic frameworks such as Black Hole and Harmony Search is proposed. These two algorithms cooperate and support each other. The Black Hole part of the algorithm has the goal to find good candidate solution while the Harmony Search part has the goal to generate new candidate solutions for Black Hole when the event horizon of the Black Hole occurs. In addition, new best solutions of these two components are exchanged with each other to improve the quality of the search. The experiments on the benchmark UCI Machine Learning datasets indicate that the proposed framework outperforms the recent state-of-art algorithms for this problem.

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*UTEHY Journal of Science and Technology*,

*27*, 47-53. Retrieved from http://tapchi.utehy.edu.vn/index.php/jst/article/view/388