{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,9]],"date-time":"2024-07-09T13:58:46Z","timestamp":1720533526201},"reference-count":11,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>Much of the previous work in D-optimal design for regression models with correlated errors focused on polynomial models with a single predictor variable, in large part because of the intractability of an analytic solution. In this paper, we present a modified, improved simulated annealing algorithm, providing practical approaches to specifications of the annealing cooling parameters, thresholds, and search neighborhoods for the perturbation scheme, which finds approximate D-optimal designs for 2-way and 3-way polynomial regression for a variety of specific correlation structures with a given correlation coefficient. Results in each correlated-errors case are compared with traditional simulated annealing algorithm, that is, the SA algorithm without our improvement. Our improved simulated annealing results had generally higher D-efficiency than traditional simulated annealing algorithm, especially when the correlation parameter was well away from 0.<\/jats:p>","DOI":"10.1155\/2014\/746914","type":"journal-article","created":{"date-parts":[[2014,3,26]],"date-time":"2014-03-26T17:07:01Z","timestamp":1395853621000},"page":"1-6","source":"Crossref","is-referenced-by-count":5,"title":["A Simulated Annealing Algorithm for D-Optimal Design for 2-Way and 3-Way Polynomial Regression with Correlated Observations"],"prefix":"10.1155","volume":"2014","author":[{"given":"Chang","family":"Li","sequence":"first","affiliation":[{"name":"Business School, Shandong University of Political Science and Law, 63 East Jiefang Road, Jinan, Shandong 250014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel C.","family":"Coster","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Utah State University, Logan, UT 84341, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"key":"14","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1002\/nla.312","volume":"10","year":"2003","journal-title":"Electronic Journal of Linear Algebra"},{"issue":"1","key":"6","first-page":"135","volume":"18","year":"2008","journal-title":"Statistica Sinica"},{"key":"10","first-page":"xii+196","year":"2001"},{"issue":"4","key":"8","first-page":"439","volume":"29","year":"1987","journal-title":"Technometrics"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(02)00292-8"},{"key":"7","year":"2009"},{"issue":"8","key":"1","first-page":"2083","volume":"6","year":"2011","journal-title":"International Journal of Physical Sciences"},{"issue":"2","key":"5","first-page":"485","volume":"5","year":"1995","journal-title":"Statistica Sinica"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719109"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1080\/02664760902803263"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-3758(98)00189-X"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/746914.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/746914.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/746914.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T06:24:35Z","timestamp":1498112675000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/746914\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":11,"alternative-id":["746914","746914"],"URL":"https:\/\/doi.org\/10.1155\/2014\/746914","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}