{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T11:05:02Z","timestamp":1780052702740,"version":"3.53.1"},"reference-count":24,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,2,17]],"date-time":"2017-02-17T00:00:00Z","timestamp":1487289600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Liaoning Provincial Department of Education Science Foundation","award":["L2013064"],"award-info":[{"award-number":["L2013064"]}]},{"name":"AVIC Technology Innovation Fund (basic research)","award":["2013S60109R"],"award-info":[{"award-number":["2013S60109R"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The Fireworks Algorithm is a recently developed swarm intelligence algorithm to simulate the explosion process of fireworks. Based on the analysis of each operator of Fireworks Algorithm (FWA), this paper improves the FWA and proves that the improved algorithm converges to the global optimal solution with probability 1. The proposed algorithm improves the goal of further boosting performance and achieving global optimization where mainly include the following strategies. Firstly using the opposition-based learning initialization population. Secondly a new explosion amplitude mechanism for the optimal firework is proposed. In addition, the adaptive t-distribution mutation for non-optimal individuals and elite opposition-based learning for the optimal individual are used. Finally, a new selection strategy, namely Disruptive Selection, is proposed to reduce the running time of the algorithm compared with FWA. In our simulation, we apply the CEC2013 standard functions and compare the proposed algorithm (IFWA) with SPSO2011, FWA, EFWA and dynFWA. The results show that the proposed algorithm has better overall performance on the test functions.<\/jats:p>","DOI":"10.3390\/a10010026","type":"journal-article","created":{"date-parts":[[2017,2,17]],"date-time":"2017-02-17T12:10:34Z","timestamp":1487333434000},"page":"26","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Analysis and Improvement of Fireworks Algorithm"],"prefix":"10.3390","volume":"10","author":[{"given":"Xi-Guang","family":"Li","sequence":"first","affiliation":[{"name":"School of Computer, Shenyang Aerospace University, Shenyang 110136, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3583-7735","authenticated-orcid":false,"given":"Shou-Fei","family":"Han","sequence":"additional","affiliation":[{"name":"School of Computer, Shenyang Aerospace University, Shenyang 110136, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chang-Qing","family":"Gong","sequence":"additional","affiliation":[{"name":"School of Computer, Shenyang Aerospace University, Shenyang 110136, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,2,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Tan, Y., and Zhu, Y. (2010). Advances in Swarm Intelligence, Springer.","DOI":"10.1007\/978-3-642-13495-1"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Tan, Y. (2015). Fireworks Algorithm Introduction, Science Press. [1st ed.]. (In Chinese).","DOI":"10.1007\/978-3-662-46353-6_1"},{"key":"ref_3","unstructured":"Andreas, J., and Tan, Y. (2011). Advances in Swarm Intelligence, Springer."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1504\/IJMIC.2011.043157","article-title":"Cultural firework algorithm and its application for digital filters design","volume":"4","author":"Gao","year":"2011","journal-title":"Int. J. Model. Identif. Control"},{"key":"ref_5","unstructured":"Wen, R., Mi, G.Y., and Tan, Y. (2013, January 12\u201315). Parameter optimization of local-concentration model for spam detection by using fireworks algorithm. 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