##### Title: Maximize Minimum Utility Function of Fractional Cloud Computing System Based on Search Algorithm Utilizing the Mittag-Leffler Sum

##### Pages: 125-136

##### Cite as:

Rabha W. Ibrahim, Maximize Minimum Utility Function of Fractional Cloud Computing System Based on Search Algorithm Utilizing the Mittag-Leffler Sum, Int. J. Anal. Appl., 16 (1) (2018), 125-136.#### Abstract

The maximum min utility function (MMUF) problem is an important representative of a large class of cloud computing systems (CCS). Having numerous applications in practice, especially in economy and industry. This paper introduces an effective solution-based search (SBS) algorithm for solving the problem MMUF. First, we suggest a new formula of the utility function in term of the capacity of the cloud. We formulate the capacity in CCS, by using a fractional diffeo-integral equation. This equation usually describes the flow of CCS. The new formula of the utility function is modified recent active utility functions. The suggested technique first creates a high-quality initial solution by eliminating the less promising components, and then develops the quality of the achieved solution by the summation search solution (SSS). This method is considered by the Mittag-Leffler sum as hash functions to determine the position of the agent. Experimental results commonly utilized in the literature demonstrate that the proposed algorithm competes approvingly with the state-of-the-art algorithms both in terms of solution quality and computational efficiency.

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