Hybrid Dynamic (GA) and Fuzzy C-Means (FCM)CM and HyDyGA can collaborate to improve segmentation process. Typically,FCM cluster the image while HyDyGA finds the best arrangement of cluster centersthat helps in minimizing the objective function of FCM (Equation 8) in order to obtainglobal optimal solution. Given a set of n data patterns, x = xi, . . . , xn, the FCMalgorithm minimizes the weights within the group sum of the squared error objectivefunction J(U, V ) where xk is the kth p-dimensional data vector, vi is the sampleof the cluster center i, uik is the degree of membership of xk in the ith cluster , m isa weighting exponent on each fuzzy membership. The function dik(xk, vi) is a distancemeasure between the data vector xk and the cluster center vi, n is the numberof data vectors and c is the number of clusters . A solution of the objective functionJ(U, V) can be obtained via an iterative process where the degree of membershipuik and the cluster center vi are updated via (Equations 9 and 10), respectively. Thetime is managed and allocated by HyDyGA while locating and then updating clustercenters. Another benefit gained for joining FCM and HyDyGA is the possibility toconverge to a local optimal solution (which is a rare case) if the process fails. ThenHyDyGA, FCM continues with the best cluster centers (local optimal) provided bythe Hybrid Dynamic metaheuristic algorithm. The alternative solution due to HyDyGA failure is to repeat the process with differentindividual chromosomes structure and with different reproduction operators’style and probabilities. The results are expected to be of different value, but Hy-DyGA can keep the process running with different parameters and structure untilit locates a global optimal solution. For a better understanding of this new method,the pseudo code provides detailed and clear explanation of the steps involved in thewhole process. The cooperative method work in series. First HyDyGA finds an optimal solutionby running all the tasks required (initial population , selection reproduction ,mutation ). The results are then fed to FCM which in turn evaluate them and sendresponse to HyDyGA. Normally, it is expected that the solution is the final one andthere the result is unchangeable, then HyDyGA terminates and FCM creates the newsegmented image. The method can be improved in the future by implementing thecooperative method as parallel tasks where the communication between HyDyGAand FCM is done through sending signs as messages between different cooperatingunits or processors. In case no termination sign is sent by FCM, then HyDyGA keepsrunning, and the solutions are saved in a dynamic list. There are many advantagesfor this enhancements which includes improvement of the efficiency of HyDyGA,and increasing clustering speed.

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