An Exhaustive Review of Bio-Inspired Algorithms and its Applications for Optimization in Fuzzy Clustering

1 Abstract: In recent years, new metaheuristic algorithms have been developed taking as reference 2 the inspiration on biological and natural phenomena. This nature-inspired approach for algorithm 3 development has been widely used by many researchers in solving optimization problem. These 4 algorithms have been compared with the traditional ones algorithms and have demonstrated to 5 be superior in complex problems. This paper attempts to describe the algorithms based on nature, 6 that are used in fuzzy clustering. We briefly describe the optimization methods, the most cited 7 nature-inspired algorithms published in recent years, authors, networks and relationship of the 8 works, etc. We believe the paper can serve as a basis for analysis of the new are of nature and 9 bio-inspired optimization of fuzzy clustering.


Introduction
Optimization is a discipline for finding the best solutions to specific problems. Every day we developed many actions, which we have tried to improve to obtain the best solution; for example, the route at work can be optimized depending on several factors, as traffic, distance, etc. On other hand, the design of the new cars implies an optimization process with many objectives as wind resistance, reduce the use of fuel, maximize the potency of motor, etc. These best solutions are found by adapting the parameters of the algorithm to give either a maximum or a minimum value for the 40 Simulated Annealing, the Gravitational Search algorithm and the Big Bang Big Crunch 41 algorithm. 42 43 In this section, we made a general review about the methods using optimization 44 fuzzy clustering with different bio-inspired optimization methods. However, in the 45 following sections a deep study is developed doing specific queries of Web of Science, 46 and the tool VoSviewer to calculate the clusters of the analyzed works. InTable 1, is 47 presented a list with the most popular bio-inspired optimization algorithms based on 48 swarms, physics, populations, chemistry and evolution. This table shows many methods 49 in chronological orders that have been used since 1975 to date. However, only are 50 some methods but can be useful to expand the knowledge about these methods and to 51 observe the inspiration type. We made the query in Web of Science: 'Optimization fuzzy 52 clustering', we found a total of 2208 papers with this topic. However, in this paper only 53 is presented a description of the most recent works, but with the query above mentioned 54 can be seen the updated works. Figure 1, shows the countries with major number of 55 publications. 56 Recently, multi-view clustering research has attracted considerable attention be- 57 cause of duo the rapidly increasing demand for unsupervised analysis of multi-view data 58 in practical applications. In [21], was presented a novel Two-level Weighted Collabora-59 tive Multi-view Fuzzy Clustering (TW-Co-MFC) approach to address the aforementioned 60 issues. In this method, TW-Co-MFC, a two-level weighting strategy is devised to mea- 61 sure the importance of views and features, and a collaborative working mechanism is 62 introduced to balance the within-view clustering quality and the cross-view clustering 63 consistency. 64 Also, in [22], authors proposed the image segmentation using Bat Algorithm with 65 Fuzzy C Means clustering. The proposed segmentation technique was evaluated with 66 existing segmentation techniques. On the other hand, in [23], the authors presented 67 a hybridization of SKH and RKFCM clustering optimization algorithm for efficient 68 moving object exploration. 69 Another recent study on this area is shown in [24], where the authors presented 70 a hybrid interval type-2 semi-supervised possibilistic fuzzy c-means clustering and 71 particle swarm optimization for satellite image analysis.

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Also, in [25] a fuzzy based unequal clustering and context aware routing proce-73 dure with glow-worm swarm optimization was developed in random way point based 74 dynamic wireless sensor networks. Based on fuzzy systems the unequal clustering 75 is formed and the optimal cluster head is nominated to convey the information from 76 cluster member to base station to increase the system lifespan and to decrease the energy 77 consumption.    has no evolution operators such as crossover and mutation. In PSO, the potential 120 solutions, called particles, fly through the problem space by following the current best 121 particles [1,11,66].

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Another reason that PSO is attractive is that there are few parameters to adjust. One        186 Also, with this information was possible to observe, the record by authors, where 187 in Figure 5, it can be appreciated that two authors are the leaders in this area with the 188 topic 'optimization fuzzy clustering with genetic algorithms'. Also, with this information was possible to observe, the records by authors, where 210 in Figure 9, it can be appreciated that two authors are the leaders in this area with the 211 topic 'optimization fuzzy clustering with particle swarm optimization'. we can appreciate the number of clusters is 2 as can be seen in Figure 10 with only 1 link. 226 With these results, it can be seen that this method has not been widely used or combined 227 with fuzzy clustering.
228 Figure 11, shows the total of papers collected from Web of Science and that were 229 used to make the calculus above described in Figure 10. It can be seen how the number 230 of citations and papers are less than the other analyzed methods.
231 Also, with this information was possible to observe, the records by authors, where 232 in Figure 9, it can be appreciated that two authors are the leaders in this area with the 233 topic 'optimization fuzzy clustering with cuckoo search algorithm'.    . Total cluster obtained with the search 'optimization fuzzy clustering with particle swarm optimization' from VOS viewer 248 With these results, it can be seen that this method has not been widely used or combined 249 with fuzzy clustering.
250 Figure 14, shows the total of papers collected from Web of Science and that were 251 used to make the calculus above described in Figure 13. It can be seen how the number 252 of citations and papers are less than the other analyzed methods.
253 Also, with this information was possible to observe, the record by authors, where 254 in Figure 15, it can be appreciated that two authors are the leaders in this area with the 255 topic 'optimization fuzzy clustering with bat algorithm'. In this section is presented an analysis by authors, considering the total cites from 258 web of science, we can appreciate that the author with more works in this area with 259 the analyzed algorithms in this paper is Witold Pedrycz from the University of Alberta,

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Canada. According with the information collected of Web of Science, Figure 16 shows 261 the total of the publications of this author.

Conclusions
After reviewing the state of the art about area optimization fuzzy clustering with optimization methods. We decided to make an analysis, considering four optimization methods, which we have used in the last year. With all collected information of Web of Science, Vos Viewer tool, we can observe that Genetic Algorithms and Particle Swarm Optimization are two very popular methods that the authors have been using in the last years. On the other hand, Cuckoo Search and Bat Algorithm, are two methods newer than the other two. However, not many authors have attempted to make fuzzy clustering using these two methods. Also, we were able to review the author with more works in this area. As a future work, this review can be extended analyzing other optimization methods with fuzzy clustering. The type of queries can be made by authors, keywords, occurrences, etc. However, with the paper can be reviewed the software and tools used and can be extracted all the information here presented.
Funding: This paper did not receive funding.