{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:58:25Z","timestamp":1753883905861,"version":"3.41.2"},"reference-count":16,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,10,23]],"date-time":"2012-10-23T00:00:00Z","timestamp":1350950400000},"content-version":"vor","delay-in-days":296,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>Ordinary differential equations usefully describe the behavior of a wide range of dynamic physical systems. The particle swarm optimization (PSO) method has been considered an effective tool for solving the engineering optimization problems for ordinary differential equations. This paper proposes a modified hybrid Nelder\u2010Mead simplex search and particle swarm optimization (M\u2010NM\u2010PSO) method for solving parameter estimation problems. The M\u2010NM\u2010PSO method improves the efficiency of the PSO method and the conventional NM\u2010PSO method by rapid convergence and better objective function value. Studies are made for three well\u2010known cases, and the solutions of the M\u2010NM\u2010PSO method are compared with those by other methods published in the literature. The results demonstrate that the proposed M\u2010NM\u2010PSO method yields better estimation results than those obtained by the genetic algorithm, the modified genetic algorithm (real\u2010coded GA (RCGA)), the conventional particle swarm optimization (PSO) method, and the conventional NM\u2010PSO method.<\/jats:p>","DOI":"10.1155\/2012\/530139","type":"journal-article","created":{"date-parts":[[2012,10,23]],"date-time":"2012-10-23T21:01:19Z","timestamp":1351026079000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A Modified NM\u2010PSO Method for Parameter Estimation Problems of Models"],"prefix":"10.1155","volume":"2012","author":[{"given":"An","family":"Liu","sequence":"first","affiliation":[]},{"given":"Erwie","family":"Zahara","sequence":"additional","affiliation":[]},{"given":"Ming-Ta","family":"Yang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,10,23]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1137\/0801027"},{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/7.4.308"},{"key":"e_1_2_6_3_2","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/S0096-3003(02)00190-X","article-title":"Parameter estimation of nonlinear models in biochemistry: a comparative study on optimization methods","volume":"140","author":"Yildirim N.","year":"2003","journal-title":"Applied Mathematics and Computation"},{"key":"e_1_2_6_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0096-3003(95)00098-4"},{"key":"e_1_2_6_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(03)00661-1"},{"key":"e_1_2_6_6_2","unstructured":"ZaharaE.andLiuA. 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