{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,28]],"date-time":"2023-10-28T05:40:27Z","timestamp":1698471627311},"reference-count":7,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2007,3,21]],"date-time":"2007-03-21T00:00:00Z","timestamp":1174435200000},"content-version":"vor","delay-in-days":4462,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems &amp; Computers in Japan"],"published-print":{"date-parts":[[1995,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>When solving optimization problems on Hopfield neural networks, good solutions are not obtained due to convergence to local minima of the energy function. The Boltzmann machine can escape from local minima because of its stochastic behavior, but the computation time is very long to reach the (semi\u2010) global minimum.<\/jats:p><jats:p>To avoid these problems, this paper proposes an efficient algorithm for solving optimization problems by the use of binary Hopfield neural networks. This algorithm selects a neuron which reduces the energy function value the most to reduce the energy of the network efficiently. Those algorithms are applied to the traveling salesman problem (TSP) with 10 cities. Near\u2010optimal solutions were obtained more efficiently than an ordinary TSP algorithm because the energy level of the network can reach lower energy states. The computation time was reduced by one order of magnitude because the energy level of the network reached lower energy states much faster than an ordinary TSP algorithm.<\/jats:p>","DOI":"10.1002\/scj.4690260208","type":"journal-article","created":{"date-parts":[[2007,7,8]],"date-time":"2007-07-08T06:16:44Z","timestamp":1183875404000},"page":"73-84","source":"Crossref","is-referenced-by-count":1,"title":["An efficient algorithm for solving optimization problems on Hopfield\u2010type neural networks"],"prefix":"10.1002","volume":"26","author":[{"given":"Toshio","family":"Tanaka","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tetsuya","family":"Higuchi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tatsumi","family":"Furuya","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2007,3,21]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/BF00339943","article-title":"Neural computation decisions in optimization problems","volume":"52","author":"Hopfield J. J.","year":"1985","journal-title":"Biol. Cybern."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1207\/s15516709cog0901_7"},{"key":"e_1_2_1_4_2","unstructured":"Y.Akiyama.Gaussian Machines Neuron Model and Its Analog and Digital Architecture. Technical Papers of the Communication Society I.E.I.C.E. CPYS88\u201316 (1988)."},{"issue":"12","key":"e_1_2_1_5_2","first-page":"2012","article-title":"Search for the minimum value by means of multitransition neural networks","volume":"73","author":"Murashima T.","year":"1990","journal-title":"Trans. (D\u2010II), I.E.I.C.E."},{"key":"e_1_2_1_6_2","first-page":"337","article-title":"An efficient algorithm for solving Hopfield\u2010type neural networks","volume":"4","author":"Tanaka T.","year":"1993","journal-title":"WCNN'93"},{"key":"e_1_2_1_7_2","unstructured":"Y.Akiyama.Three techniques for energy minimization on Hopfield type neural networks. Technical Papers of the Communication Society I.E.I.C.E. NC90\u201340 (1990)."},{"key":"e_1_2_1_8_2","first-page":"1528","article-title":"Cost efficient control method for solving optimization problems on Hopfield\u2010type neural networks","volume":"2","author":"Tanaka T.","year":"1993","journal-title":"IJCNN'93"}],"container-title":["Systems and Computers in Japan"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fscj.4690260208","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/scj.4690260208","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,27]],"date-time":"2023-10-27T04:39:52Z","timestamp":1698381592000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/scj.4690260208"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,1]]},"references-count":7,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1995,1]]}},"alternative-id":["10.1002\/scj.4690260208"],"URL":"https:\/\/doi.org\/10.1002\/scj.4690260208","archive":["Portico"],"relation":{},"ISSN":["0882-1666","1520-684X"],"issn-type":[{"value":"0882-1666","type":"print"},{"value":"1520-684X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,1]]}}}