{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1363386073367356672.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.1002/ecjb.10070"}},{"identifier":{"@type":"URI","@value":"https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2Fecjb.10070"}},{"identifier":{"@type":"URI","@value":"https://onlinelibrary.wiley.com/doi/pdf/10.1002/ecjb.10070"}},{"identifier":{"@type":"NAID","@value":"210000162968"}}],"dc:title":[{"@value":"“Optimal” neural representation of higher order for traveling salesman problems"}],"description":[{"type":"abstract","notation":[{"@value":"<jats:title>Abstract</jats:title><jats:p>The optimal formulation has been shown based on theoretical measure when the combinatorial optimization problem with linear cost function is solved by a symmetrically connected neural network (Hopfield network)<jats:ext-link xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"#bib15\">15</jats:ext-link>; however, in this paper, we will present an optimal formulation of higher order for traveling salesman problems defined by a quadratic cost function. The Hopfield neural network constructed by this formulation becomes higher order, and the asymptotic stability and the optimal solution will coincide so far as the vertex of the hypercube which expresses the network state is concerned. Therefore, an optimal solution can always be obtained if the network converges to the vertex. We will confirm by simulations that a good solution of the optimal solutions can be obtained with higher frequency compared to the conventional formulation. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 85(9): 32–42, 2002; Published online in Wiley InterScience (<jats:ext-link xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"http://www. interscience.wiley.com\">www. interscience.wiley.com</jats:ext-link>). DOI 10.1002/ecjb.10070</jats:p>"}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1583106132851375232","@type":"Researcher","personIdentifier":[{"@type":"NRID","@value":"9000415147302"}],"foaf:name":[{"@value":"Satoshi Matsuda"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"8756663X"},{"@type":"EISSN","@value":"15206432"}],"prism:publicationName":[{"@value":"Electronics and Communications in Japan (Part II: Electronics)"}],"dc:publisher":[{"@value":"Wiley"}],"prism:publicationDate":"2002-08-15","prism:volume":"85","prism:number":"9","prism:startingPage":"32","prism:endingPage":"42"},"reviewed":"false","dc:rights":["http://onlinelibrary.wiley.com/termsAndConditions#vor"],"url":[{"@id":"https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2Fecjb.10070"},{"@id":"https://onlinelibrary.wiley.com/doi/pdf/10.1002/ecjb.10070"}],"createdAt":"2002-09-05","modifiedAt":"2024-12-09","relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1360011143719288704","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"On the stability of the Travelling Salesman Problem algorithm of Hopfield and Tank"}]},{"@id":"https://cir.nii.ac.jp/crid/1360011144420313088","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"“Neural” computation of decisions in optimization problems"}]},{"@id":"https://cir.nii.ac.jp/crid/1360298454805998336","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"A neural network for solving the travelling salesman problem on the basis of city adjacency in the tour"}]},{"@id":"https://cir.nii.ac.jp/crid/1360302868778519808","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Theoretical characterizations of possibilities and impossibilities of Hopfield neural networks in solving combinatorial optimization problems"}]},{"@id":"https://cir.nii.ac.jp/crid/1360574095296172544","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"A theoretical investigation into the performance of the Hopfield model"}]},{"@id":"https://cir.nii.ac.jp/crid/1360865819408750464","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Distribution of asymptotically stable states in Hopfield network for TSP"}]},{"@id":"https://cir.nii.ac.jp/crid/1363107369039766656","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Global convergence and suppression of spurious states of the Hopfield neural networks"}]},{"@id":"https://cir.nii.ac.jp/crid/1363951795821669120","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"On problem solving with Hopfield neural networks"}]},{"@id":"https://cir.nii.ac.jp/crid/1364233268284169216","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"\"Optimal\" Hopfield network for combinatorial optimization with linear cost function"}]},{"@id":"https://cir.nii.ac.jp/crid/1370016974112018690","@type":"Product","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Hopfield neural networks and simulated annealing"}]},{"@id":"https://cir.nii.ac.jp/crid/1370016974112018691","@type":"Product","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Stability of solution in Hopfield neural network"}]},{"@id":"https://cir.nii.ac.jp/crid/1390001205343584384","@type":"Article","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@language":"en","@value":"Activation of Neural Networks and Nonlinear Analyses"},{"@language":"ja","@value":"ニューラルネットワークのアクティブ化と非線形解析"}]},{"@id":"https://cir.nii.ac.jp/crid/1390282680321159936","@type":"Article","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@language":"en","@value":"An application of higher order connection to inverse function delayed network"}]},{"@id":"https://cir.nii.ac.jp/crid/1571980074490018304","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@language":"en","@value":"Set-theoretic comparison of the mappings of combinatorial optimization problems to Hopfield neural networks"},{"@value":"Set‐theoretic comparison of the mapping of combinatorial optimization problems to Hopfield neural networks"}]}],"dataSourceIdentifier":[{"@type":"CROSSREF","@value":"10.1002/ecjb.10070"},{"@type":"CIA","@value":"210000162968"},{"@type":"OPENAIRE","@value":"doi_dedup___::40ab5c002cab22b74fb92efa5df1d0e5"},{"@type":"CROSSREF","@value":"10.1587/nolta.2.180_references_DOI_Zkg1wUtDr8y6DBl2crNJ1Kx9wc3"},{"@type":"CROSSREF","@value":"10.1587/essfr.6.123_references_DOI_Zkg1wUtDr8y6DBl2crNJ1Kx9wc3"}]}