{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T19:45:38Z","timestamp":1760384738589,"version":"3.33.0"},"reference-count":21,"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":5558,"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":[[1992,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>By using competitive learning, which causes just one or a group of a small number of neurons to respond to a given input, self\u2010organization of entire neural networks can be achieved. When this self\u2010organization process is applied to various kinds of travelling salesman problems in a Euclidean space, a good approximation or the true solution is obtained. We use a sequential update which looks at the position vector of each city one at a time as the training method for a neural network arranged as a closed loop. In this case, we use symmetrical connections between neurons. The number of neurons required is approximately linear in the number of cities. In the first experiment, we carried out a quantitative comparison with the simulated annealing method using 500 sets of 30 cities and demonstrated this method's superiority. Next, we obtained a good approximation on a set of 532 U.S. cities and demonstrate its superiority with respect to the increase in the number of cities in actual (realistic) data. Further, for a generalized constrained multiple\u2010salesman problem, we explain this method's compactness and efficiency and give an experimental example. The computation can be adequately performed by a common workstation with a serial processor.<\/jats:p>","DOI":"10.1002\/scj.4690230209","type":"journal-article","created":{"date-parts":[[2007,7,7]],"date-time":"2007-07-07T22:51:09Z","timestamp":1183848669000},"page":"101-112","source":"Crossref","is-referenced-by-count":18,"title":["Self\u2010organizing neural networks and various euclidean traveling salesman problems"],"prefix":"10.1002","volume":"23","author":[{"given":"Yasuo","family":"Matsuyama","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2007,3,21]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.7551\/mitpress\/5236.001.0001","volume-title":"Parallel Distributed Processing: Explorations in the Microstructure of Cognition","author":"Rumelhart D. E.","year":"1986"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1038\/326689a0"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","unstructured":"H.RitterandK.Schulten.Kohonen's self\u2010organizing maps: Exploring their computational capabilities. Proc. of IEEE Int. Conf. on Neural Networks pp.I109\u2013116(1988).","DOI":"10.1109\/ICNN.1988.23838"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0893-6080(88)90002-0"},{"key":"e_1_2_1_6_2","doi-asserted-by":"crossref","unstructured":"D.Van den BoutandT. K.Miller III.TInMANN: The integer Markovian artificial neural network. Proc. of the Int. Joint Conf. on Neural Networks pp.II205\u2013211(1989).","DOI":"10.1109\/IJCNN.1989.118700"},{"key":"e_1_2_1_7_2","first-page":"9","volume-title":"Computers and Intractability","author":"Geary M. R.","year":"1979"},{"volume-title":"The Travelling Salesman Problem\u2014A Guided Tour of Combinatorial Optimization","year":"1985","author":"Lawler E.","key":"e_1_2_1_8_2"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/BF00339943","article-title":"Neural computation of decisions in optimization problems","volume":"52","author":"Hopfield J.","year":"1985","journal-title":"Biological Cybernetics"},{"key":"e_1_2_1_10_2","doi-asserted-by":"crossref","unstructured":"Y.Akiyamaet al.Combinatorial optimization with Gaussian machines. Proc. of the Int. Joint Conf. on Neural Networks pp.I533\u2013540(1989).","DOI":"10.1109\/IJCNN.1989.118630"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.1699114"},{"volume-title":"Numerical Recipes","year":"1988","author":"Press W. H.","key":"e_1_2_1_12_2"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6377(87)90002-2"},{"key":"e_1_2_1_14_2","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1109\/TIT.1982.1056489","article-title":"Least\u2010squares quantization in PCM","volume":"28","author":"Lloyd S. P.","year":"1987","journal-title":"IEEE Trans. Inf. Theory"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1960.1057548"},{"key":"e_1_2_1_16_2","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1109\/TCOM.1980.1094577","article-title":"An algorithm for the vector quantizer design","volume":"28","author":"Linde J.","year":"1989","journal-title":"IEEE Trans. Commun."},{"issue":"12","key":"e_1_2_1_17_2","first-page":"887","article-title":"Universal information source coding and voice compression","volume":"62","author":"Matsuyama Y.","year":"1979","journal-title":"Tsushin Gakkai Ronbunshi (Journal of the Communication Society)"},{"volume-title":"Self\u2010Organization and Associative Memory","year":"1984","author":"Kohonen T.","key":"e_1_2_1_18_2"},{"key":"e_1_2_1_19_2","first-page":"1830","article-title":"Variable region vector quantization","volume":"70","author":"Matsuyama Y.","year":"1987","journal-title":"Tsushin Gakkai Ronbunshi (Journal of the Communication Society)"},{"issue":"1","key":"e_1_2_1_20_2","first-page":"36","article-title":"Vector quantization with optimized grouping and parallel distributed processing","volume":"1","author":"Matsuyama Y.","year":"1988","journal-title":"Neural Networks"},{"key":"e_1_2_1_21_2","unstructured":"Y.Matsuyama.Multiple descent cost algorithms. Proc. of the Int. Joint Conf. on Neural Networks Washington DC pp.436\u2013439(1990)."},{"key":"e_1_2_1_22_2","doi-asserted-by":"crossref","unstructured":"Y.Matsuyama.Multiple descent cost competitive learning. Proc. of the Int. Joint Conference on Neural Networks San Diego pp.II299\u2013306(1990).","DOI":"10.1109\/IJCNN.1990.137730"}],"container-title":["Systems and Computers in Japan"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fscj.4690230209","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/scj.4690230209","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,18]],"date-time":"2025-01-18T18:41:14Z","timestamp":1737225674000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/scj.4690230209"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,1]]},"references-count":21,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1992,1]]}},"alternative-id":["10.1002\/scj.4690230209"],"URL":"https:\/\/doi.org\/10.1002\/scj.4690230209","archive":["Portico"],"relation":{},"ISSN":["0882-1666","1520-684X"],"issn-type":[{"type":"print","value":"0882-1666"},{"type":"electronic","value":"1520-684X"}],"subject":[],"published":{"date-parts":[[1992,1]]}}}