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In recent years, scholars have proposed various metaheuristic algorithms, such as the genetic algorithm (GA), artificial bee colony, particle swarm optimization (PSO), crow search algorithm, and whale optimization algorithm (WOA), to solve optimization problems. Among these, PSO is the most commonly used. However, different algorithms have different limitations. For example, PSO is prone to premature convergence and falls into a local optimum, whereas GA coding is difficult and uncertain. Therefore, an algorithm that can increase the computing power and particle diversity can address the limitations of existing algorithms. Therefore, this paper proposes a hybrid algorithm, called whale particle optimization (WPO), that combines the advantages of the WOA and PSO to increase particle diversity and can jump out of the local optimum. The performance of the WPO algorithm was evaluated using four optimization problems: function evaluation, image clustering, permutation flow shop scheduling, and data clustering. The test data were selected from real-life situations. The results demonstrate that the proposed algorithm competes well against existing algorithms.\n<\/jats:p>","DOI":"10.1007\/s44196-023-00295-6","type":"journal-article","created":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T17:02:25Z","timestamp":1689613345000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["WPO: A Whale Particle Optimization Algorithm"],"prefix":"10.1007","volume":"16","author":[{"given":"Ko-Wei","family":"Huang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ze-Xue","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chang-Long","family":"Jiang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zih-Hao","family":"Huang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7395-556X","authenticated-orcid":false,"given":"Shih-Hsiung","family":"Lee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,7,17]]},"reference":[{"key":"295_CR1","volume-title":"Introduction to algorithms","author":"TH Cormen","year":"2009","unstructured":"Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to algorithms. 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