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The convergence analysis is based on the relation between ABC variants and the general solution of the food source regeneration equation. To show the fitness of the proposed algorithm, a comparison is made between VPS-ABC versus classical ABC, PSO, and GA algorithms in tuning the proportional-integral-derivative (PID) controllers. Simulation results show that VPS-ABC algorithm is highly competitive, often outperforming PSO and GA algorithms.<\/jats:p>","DOI":"10.1142\/s1469026817500183","type":"journal-article","created":{"date-parts":[[2017,9,6]],"date-time":"2017-09-06T07:14:56Z","timestamp":1504682096000},"page":"1750018","source":"Crossref","is-referenced-by-count":8,"title":["A Novel Variable Population Size Artificial Bee Colony Algorithm with Convergence Analysis for Optimal Parameter Tuning"],"prefix":"10.1142","volume":"16","author":[{"given":"Nasr","family":"Elkhateeb","sequence":"first","affiliation":[{"name":"Electrical Communications Department, Modern University for Technology and Information, Cairo, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ragia","family":"Badr","sequence":"additional","affiliation":[{"name":"Electronics and Communications Department, Faculty of Engineering,Cairo University, Giza, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2017,9,25]]},"reference":[{"key":"S1469026817500183BIB001","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780195099713.001.0001","volume-title":"Evolutionary Algorithms in Theory and Practice","author":"Back T.","year":"1996"},{"key":"S1469026817500183BIB002","volume-title":"Introduction to Genetic Algorithms","author":"Sivanandam S. 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