{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T13:51:11Z","timestamp":1725889871539},"publisher-location":"Boston, MA","reference-count":84,"publisher":"Springer US","isbn-type":[{"type":"print","value":"9781441948137"},{"type":"electronic","value":"9781475730234"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1999]]},"DOI":"10.1007\/978-1-4757-3023-4_5","type":"book-chapter","created":{"date-parts":[[2013,2,21]],"date-time":"2013-02-21T08:28:50Z","timestamp":1361435330000},"page":"259-293","source":"Crossref","is-referenced-by-count":0,"title":["Neural Networks Approaches for Combinatorial Optimization Problems"],"prefix":"10.1007","author":[{"given":"Theodore B.","family":"Trafalis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Suat","family":"Kasap","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"5_CR1","doi-asserted-by":"publisher","first-page":"663","DOI":"10.1016\/S0893-6080(05)80043-7","volume":"5","author":"S Abe","year":"1992","unstructured":"S. Abe, J. Kawakami, and K. Hirasawa, Solving inequality constrained combinatorial optimization problems by the Hopfield neural networks, Neural Networks Vol. 5 (1992) pp. 663\u2013670.","journal-title":"Neural Networks"},{"key":"5_CR2","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1207\/s15516709cog0901_7","volume":"9","author":"DH Ackley","year":"1985","unstructured":"D.H. Ackley, G.E.. Hinton, and T.J. Sejnowski, A learning algorithm for Boltzman machines, Cognitive Science Vol. 9 (1985) pp. 147\u2013169.","journal-title":"Cognitive Science"},{"issue":"2","key":"5_CR3","doi-asserted-by":"publisher","first-page":"470","DOI":"10.1109\/72.363481","volume":"6","author":"N Ansari","year":"1995","unstructured":"N. Ansari, E.S.H. Hou, and Y. Yu, A new method to optimize the satellite broadcasting schedules using the mean field annealing of a Hopfield neural network, IEEE Transactions on Neural Networks Vol. 6 No. 2 (1995) pp. 470\u2013482.","journal-title":"Ieee Transactions on Neural Networks"},{"issue":"2","key":"5_CR4","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1142\/S012906579500010X","volume":"6","author":"M Bengtsson","year":"1995","unstructured":"M. Bengtsson and P. Roivainen, Using the Potts glass for solving the clustering problem, International Journal of Neural Systems Vol. 6 No. 2 (1995) pp. 119\u2013132.","journal-title":"International Journal of Neural Systems"},{"key":"5_CR5","unstructured":"G. Bilbro, R. Mann, T.K. Miller, W.E. Snyder, D.E. Van Den Bout, and M. White, Optimization by mean field annealing, in D.S. Touretzky (ed.) Proceedings of the Annual Conferences on Advances in Neural Information Processing Systems, Volume 1, (Morgan Kaufmann Publishers, 1988 ) pp. 91\u201398."},{"key":"5_CR6","doi-asserted-by":"crossref","unstructured":"A. Bovier and P. Picco, Mathematical Aspects of Spin Glasses and Neural Networks, (Birkh\u00e4user, 1998 ).","DOI":"10.1007\/978-1-4612-4102-7"},{"key":"5_CR7","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1006\/jmre.1997.1106","volume":"125","author":"NE Buchler","year":"1997","unstructured":"N.E.G. Buchler, E.R.P. Zuiderweg, H. Wang, and R.A. Goldstein, Protein heteronuclear NMR assignments using mean-field simulated annealing, Journal of Magnetic Resonance Vol. 125 (1997) pp. 34\u201342.","journal-title":"Journal of Magnetic Resonance"},{"key":"5_CR8","volume-title":"12th European Conference on Artificial Intelligence","author":"B Cabon","year":"1996","unstructured":"B. Cabon, G. Verfaillie, D. Martinez, and P. Bourret, Using mean field methods for boosting backtrack search in constraint satisfaction problems, in W. Wahlster (ed.) 12th European Conference on Artificial Intelligence, ( John Wiley and Sons, Ltd., 1996 )."},{"key":"5_CR9","doi-asserted-by":"crossref","unstructured":"D. Chowdhury, Spin Glasses and Other Frustrated Systems, (Princeton University Press, 1986 ).","DOI":"10.1142\/0223"},{"key":"5_CR10","doi-asserted-by":"crossref","unstructured":"D. Chowdhury, Spin Glasses and Other Frustrated Systems, (Princeton University Press, 1986 ).","DOI":"10.1142\/0223"},{"key":"5_CR11","unstructured":"A. Cichocki and R. Unbehauen, Neural Networks for Optimization and Signal Processing, (John Wiley and Sons, 1993 )."},{"key":"5_CR12","unstructured":"R. Courant and D. Hilbert, Methods of Mathematical Physics, (Inter-science Publishers Inc., 1953 )."},{"key":"5_CR13","first-page":"20","volume-title":"Modern Heuristic Techniques for Combinatorial Problems, (John Wiley and Sons","author":"KA Dowsland","year":"1993","unstructured":"K.A. Dowsland, Simulated annealing, in C.R. Reeves (ed.) Modern Heuristic Techniques for Combinatorial Problems, (John Wiley and Sons, 1993 ) pp. 20\u201369."},{"key":"5_CR14","unstructured":"R. Durbin, R. Szeliski, and A.L. Yuille, An analysis of the elastic net approach to the travelling salesman problem, Neural Computation Vold (1989) pp. 348\u2013358."},{"key":"5_CR15","doi-asserted-by":"publisher","first-page":"1079","DOI":"10.1162\/neco.1995.7.5.1079","volume":"7","author":"IM Elfadel","year":"1995","unstructured":"I.M. Elfadel, Convex potential and their conjugates in analog mean-field optimization, Neural Computation Vol. 7 (1995) pp. 1079\u20131104.","journal-title":"Neural Computation"},{"key":"5_CR16","unstructured":"S. Elmohamed, P. Coddington, and G. Fox, A comparison of annealing techniques for academic course scheduling, Northeast Parallel Architectures Center (NPAC) technical report SCCS-777, January 25, 1997."},{"key":"5_CR17","first-page":"221","volume":"3","author":"L Fang","year":"1990","unstructured":"L. Fang and T. Li, Design of competition-based neural networks for combinatorial optimization, International Journal of Neural Systems Vold No. 3 (1990) pp. 221\u2013235.","journal-title":"Design of competition-based neural networks for combinatorial optimization, International Journal of Neural Systems Vold"},{"key":"5_CR18","unstructured":"L. Fang, W.H. Wilson, and T. Li, Mean field annealing neural net for quadratic assignment, in International Neural Network Conference, July 9\u201313, Paris, France,(Kluwer Academic Publishers, 1990) pp. 282286."},{"key":"5_CR19","unstructured":"L. Fausett, Fundamentals of Neural Networks: Architectures, Algorithms, and Applications, (Prentice-Hall, 1994 )."},{"key":"5_CR20","unstructured":"L. Faybusovich, Interior point methods and entropy, IEEE Conference on Decision and Control, (1991) pp. 2094\u20132095."},{"key":"5_CR21","doi-asserted-by":"crossref","unstructured":"K.H. Fischer and J.A. Hertz, Spin Glasses, (Cambridge University Press, 1991 ).","DOI":"10.1017\/CBO9780511628771"},{"key":"5_CR22","unstructured":"C.A. Floudas and P.M. Pardalos, Recent Advances in Global Optimization, (Princeton University Press, 1994 )."},{"key":"5_CR23","first-page":"660","volume-title":"Proceedings of the Annual Conferences on Advances in Neural Information Processing Systems, Volume 2, (Morgan Kaufmann Publishers","author":"D Geiger","year":"1989","unstructured":"D. Geiger and F. Girosi, Coupled Markov random fields and mean field theory, in D.S. Touretzky (ed.) Proceedings of the Annual Conferences on Advances in Neural Information Processing Systems, Volume 2, (Morgan Kaufmann Publishers, 1989 ) pp. 660\u2013667."},{"key":"5_CR24","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1142\/S0129065789000074","volume":"1","author":"L Gislen","year":"1989","unstructured":"L. Gislen, C. Peterson, and B. Soderberg, Teachers and classes with neural networks, International Journal of Neural Systems Vol.1 No. 1 (1989) pp. 167\u2013183.","journal-title":"International Journal of Neural Systems Vol.1"},{"key":"5_CR25","doi-asserted-by":"publisher","first-page":"805","DOI":"10.1162\/neco.1992.4.6.805","volume":"4","author":"L Gislen","year":"1992","unstructured":"L. Gislen, C. Peterson, and B. Soderberg, Complex scheduling with Potts neural networks, Neural Computation Vol. 4 (1992) pp. 805\u2013831.","journal-title":"Neural Computation"},{"issue":"2","key":"5_CR26","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1063\/1.1703954","volume":"4","author":"RJ Glauber","year":"1963","unstructured":"R.J. Glauber, Time-dependent statistics of the Ising model, Journal of Mathematical Physics Vol. 4 No. 2 (1963) pp. 294\u2013307.","journal-title":"Journal of Mathematical Physics"},{"key":"5_CR27","unstructured":"S. Haykin, Neural Networks: A Comprehensive Foundation, (Macmillan College Publishing Company, 1994 )."},{"key":"5_CR28","first-page":"165","volume-title":"Neural Networks: Advances and Applications","author":"L Herault","year":"1991","unstructured":"L. Herault and J.-J. Niez, Neural networks and combinatorial optimization: a study of NP-complete graph problems, in E. Gelenbe (ed.) Neural Networks: Advances and Applications, ( Elsevier Science Publishers B. V., 1991 ) pp. 165\u2013213."},{"issue":"1","key":"5_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/34.566806","volume":"19","author":"T Hofmann","year":"1997","unstructured":"T. Hofmann and J.M. Buhmann, Pairwise data clustering by deterministic annealing, IEEE Transactions on Pattern Analysis and Machine Intelligence Vol. 19 No. 1 (1997) pp. 1\u201314.","journal-title":"Ieee Transactions on Pattern Analysis and Machine Intelligence"},{"key":"5_CR30","unstructured":"J.J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, in Proceedings of the National Academy of Sciences of the U.S.A., Biophysics, (1982) pp. 2554\u20132558."},{"key":"5_CR31","unstructured":"J.J. Hopfield, Neurons with graded response have collective computational properties like those of two-state neurons, in Proceedings of the National Academy of Sciences of the U.S.A., Biophysics, (1984) pp. 3088\u20133092."},{"key":"5_CR32","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/BF00339943","volume":"52","author":"J.J. Hopfield","year":"1985","unstructured":"J.J. Hopfield and D.W. Tank, \u201cNeural\u201d computation of decisions in optimization problems, Biological Cybernetics Vol.52 (1985) pp. 141\u2013152.","journal-title":"Biological Cybernetics"},{"key":"5_CR33","doi-asserted-by":"crossref","unstructured":"R. Horst, P.M. Pardalos, and N.V. Thoai, Introduction to Global Optimization, (Kluwer Academic Publishers, 1995 ).","DOI":"10.1007\/978-1-4615-2025-2"},{"key":"5_CR34","unstructured":"H. Igarashi, A solution to combinatorial optimization problems using a two-layer random field model: Mean-field approximation, in World Congress on Neural Networks, July 11\u201315, Portland, Oregon, Volume 1, ( Lawrance Erlbaum Associates Inc. Publishers, 1993 ) pp. 283\u2013286."},{"issue":"8","key":"5_CR35","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1002\/scj.4690250806","volume":"25","author":"H Igarashi","year":"1994","unstructured":"H. Igarashi, A solution for combinatorial optimization problems using a two-layer random field model: Mean-field approximation, Systems and Computers in Japan Vol. 25 No. 8 (1994) pp. 61\u201371.","journal-title":"Systems and Computers in Japan"},{"key":"5_CR36","unstructured":"S. Ishii and M.-A. Sato, Chaotic Potts spin model for combinatorial optimization problems, Neural Networks Vol.10 No. 5 (1997) pp. 941963."},{"key":"5_CR37","doi-asserted-by":"publisher","first-page":"L673","DOI":"10.1088\/0305-4470\/20\/11\/001","volume":"20","author":"I Kanter","year":"1987","unstructured":"I. Kanter and H. Sompolinsky, Graph optimisation problems and the Potts glass, Journal of Physics A: Math. Gen. Vol. 20 (1987) pp. L673 - L679.","journal-title":"Journal of Physics A: Math. Gen"},{"issue":"4598","key":"5_CR38","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1126\/science.220.4598.671","volume":"220","author":"S Kirkpatrick","year":"1983","unstructured":"S. Kirkpatrick, C.D. Gelatt, and M.P. Vecchi, Optimization by simulated annealing, Science Vol. 220 No. 4598 (1983) pp. 671\u2013680.","journal-title":"Science"},{"issue":"3","key":"5_CR39","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1016\/0893-6080(94)90081-7","volume":"7","author":"JJ Kosowsky","year":"1994","unstructured":"J.J. Kosowsky and A.L. Yuille, The invisible hand algorithm: Solving the assignment problem with statistical physics, Neural Networks Vol. 7 No. 3 (1994) pp. 477\u2013490.","journal-title":"Neural Networks"},{"issue":"9","key":"5_CR40","doi-asserted-by":"publisher","first-page":"1531","DOI":"10.1016\/0893-6080(95)00129-8","volume":"9","author":"N Kurita","year":"1996","unstructured":"N. Kurita and K.-I. Funahashi, On the Hopfield neural networks and mean field theory, Neural Networks Vol. 9 No. 9 (1996) pp. 1531\u20131540.","journal-title":"Neural Networks"},{"key":"5_CR41","unstructured":"T. Kurokawa and S. Kozuka, Use of neural networks for the optimum frequency assignment problem, Electronics and Communications in Japan, Part 1 Vol. 77 No. 11 (1994) pp. 106\u2013116."},{"key":"5_CR42","doi-asserted-by":"publisher","first-page":"1589","DOI":"10.1162\/neco.1997.9.7.1589","volume":"9","author":"M Lagerholm","year":"1997","unstructured":"M. Lagerholm, C. Peterson, and B. Soderberg, Airline crew scheduling with Potts neurons, Neural Computation Vol. 9 (1997) pp. 1589\u20131599.","journal-title":"Neural Computation"},{"key":"5_CR43","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1142\/9789812832122_0003","volume-title":"Neural Computing for Optimization and Combinatorics, (World Scientific","author":"KC Lee","year":"1996","unstructured":"K.-C. Lee and Y. Takefuji, Maximum clique problems: Part 1, in Y. Takefuji and J. Wang (eds.) Neural Computing for Optimization and Combinatorics, (World Scientific, 1996 ) pp. 31\u201361."},{"key":"5_CR44","first-page":"63","volume-title":"Neural Computing for Optimization and Combinatorics, (World Scientific","author":"KC Lee","year":"1996","unstructured":"K.-C. Lee and Y. Takefuji, Maximum clique problems: Part 2, in Y. Takefuji and J. Wang (eds.) Neural Computing for Optimization and Combinatorics, (World Scientific, 1996 ) pp. 63\u201377."},{"key":"5_CR45","unstructured":"B.C. Levy and M.B. Adams, Global optimization with stochastic neural networks, in Neural Networks for Optimization and Signal Processing, Proceedings of the First International Conference on Neural Networks, San Diego,(1987) pp. 681\u2013690."},{"key":"5_CR46","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1016\/0025-5564(74)90031-5","volume":"19","author":"WA Little","year":"1974","unstructured":"W.A. Little, The existence of persistent states in the brain, Mathematical Biosciences Vol. 19 (1974) pp. 101\u2013120.","journal-title":"Mathematical Biosciences"},{"key":"5_CR47","unstructured":"C.-K. Looi, Neural network methods in combinatorial optimization, Computers in Operations Research Vol.19 No. 3 \/4 (1992) pp. 191\u2013208."},{"issue":"6","key":"5_CR48","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1002\/scj.4690270605","volume":"27","author":"S Matsuda","year":"1996","unstructured":"S. Matsuda, Set-theoretic comparison of mapping of combinatorial optimization problems to Hopfield neural networks, Systems and Computers in Japan Vol. 27 No. 6 (1996) pp. 45\u201359.","journal-title":"Systems and Computers in Japan"},{"key":"5_CR49","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1007\/BF02478259","volume":"5","author":"WS Mccullough","year":"1943","unstructured":"W.S. McCullough and W. Pitts, A logical calculus of the ideas immanent in nervous activity, Bulletin of Mathematical Biophysics Vol. 5 (1943) pp. 115\u2013133.","journal-title":"Bulletin of Mathematical Biophysics"},{"issue":"11","key":"5_CR50","first-page":"1553","volume":"55","author":"II Melamed","year":"1994","unstructured":"I.I. Melamed, Neural networks and combinatorial optimization, Automation and Remote Control Vol. 55 No. 11 (1994) pp. 1553\u20131584.","journal-title":"Automation and Remote Control"},{"key":"5_CR51","doi-asserted-by":"crossref","unstructured":"M. Mezard, G. Parisi, and M.A. Virasoro, Spin Glass Theory and Beyond, (World Scientific, 1987 ).","DOI":"10.1142\/0271"},{"key":"5_CR52","doi-asserted-by":"crossref","unstructured":"B. Muller and J. Reinhardt, Neural Networks: An Introduction, (Springer-Verlag, 1990 ).","DOI":"10.1007\/978-3-642-97239-3"},{"key":"5_CR53","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1162\/neco.1993.5.2.331","volume":"5","author":"M Ohlsson","year":"1993","unstructured":"M. Ohlsson, C. Peterson, and B. Soderberg, Neural networks for optimization problems with inequality constraints: The knapsack problem, Neural Computation Vol. 5 (1993) pp. 331\u2013339.","journal-title":"Neural Computation"},{"issue":"2","key":"5_CR54","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1016\/S0893-6080(97)89067-3","volume":"10","author":"M Ohlsson","year":"1997","unstructured":"M. Ohlsson and H. Pi, A study of the mean field approach to knapsack problems, Neural Networks Vol. 10 No. 2 (1997) pp. 263\u2013271.","journal-title":"Neural Networks"},{"key":"5_CR55","unstructured":"C.H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, (Prentice-Hall, 1982 )."},{"key":"5_CR56","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1162\/neco.1990.2.3.261","volume":"2","author":"C Peterson","year":"1990","unstructured":"C. Peterson, Parallel distributed approaches to combinatorial optimization: Benchmark studies on traveling salesman problem, Neural Computation Vol. 2 (1990) pp. 261\u2013269.","journal-title":"Neural Computation"},{"issue":"1","key":"5_CR57","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1080\/09540099108946571","volume":"3","author":"C Peterson","year":"1991","unstructured":"C. Peterson, Mean field theory neural networks for feature recognition, content addressable memory and optimization, Connection Science Vol. 3 No. 1 (1991) pp. 3\u201333.","journal-title":"Connection Science"},{"key":"5_CR58","doi-asserted-by":"publisher","first-page":"570","DOI":"10.1016\/0378-4371(93)90562-I","volume":"200","author":"C Peterson","year":"1993","unstructured":"C. Peterson, Solving optimization problems with mean field methods, Physica A Vol. 200 (1993) pp. 570\u2013580.","journal-title":"Physica A"},{"key":"5_CR59","unstructured":"C. Peterson and J.R. Anderson, A mean field theory learning algorithm for neural networks, Complex Systems Vol.1 (1987) pp. 995\u20131019."},{"key":"5_CR60","first-page":"59","volume":"2","author":"C Peterson","year":"1988","unstructured":"C. Peterson and J.R. Anderson, Neural networks and NP-complete optimization problems; a performance study on the graph bisection problem, Complex Systems Vol. 2 (1988) pp. 59\u201389.","journal-title":"Complex Systems"},{"issue":"1","key":"5_CR61","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1142\/S0129065789000414","volume":"1","author":"C Peterson","year":"1989","unstructured":"C. Peterson and B. Soderberg, A new method for mapping optimization problems onto neural networks, International Journal of Neural systems Vol. 1 No. 1 (1989) pp. 3\u201322.","journal-title":"International Journal of Neural systems"},{"key":"5_CR62","first-page":"197","volume-title":"Modern Heuristic Techniques for Combinatorial Problems, (John Wiley and Sons","author":"C Peterson","year":"1993","unstructured":"C. Peterson and B. Soderberg, Artificial neural networks, in C.R. Reeves (ed.) Modern Heuristic Techniques for Combinatorial Problems, (John Wiley and Sons, 1993 ) pp. 197\u2013242."},{"key":"5_CR63","first-page":"177","volume-title":"Local Search in Combinatorial Optimization, (John Wiley and Sons","author":"C Peterson","year":"1997","unstructured":"C. Peterson and B. Soderberg, Artificial neural networks, in E. Aarts and J.K. Lenstra (eds.) Local Search in Combinatorial Optimization, (John Wiley and Sons, 1997 ) pp. 177\u2013213."},{"issue":"12","key":"5_CR64","first-page":"86","volume":"25","author":"F Qian","year":"1994","unstructured":"F. Qian and H. Hirata, A parallel computation based on mean field theory for combinatorial optimization and Boltzman machines, Systems and Computers in Japan Vol. 25 No. 12 (1994) pp. 86\u201397.","journal-title":"Systems and Computers in Japan"},{"key":"5_CR65","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1016\/0020-0255(94)00052-D","volume":"82","author":"J Ramanujam","year":"1995","unstructured":"J. Ramanujam and P. Sadayappan, Mapping combinatorial optimization problems onto neural networks, Information Sciences Vol. 82 (1995) pp. 239\u2013255.","journal-title":"Information Sciences"},{"key":"5_CR66","unstructured":"C.R. Reeves, Modern Heuristic Techniques for Combinatorial Problems, (John Wiley and Sons, 1993 )."},{"key":"5_CR67","unstructured":"L.E. Reichl, A Modern Course in Statistical Physics, (University of Texas Press, 1980 )."},{"key":"5_CR68","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1038\/323533a0","volume":"323","author":"DE Rumelhart","year":"1986","unstructured":"D.E. Rumelhart, G.E. Hinton, and R.J. Williams, Learning representations by back-propagating errors, Nature (London) Vol. 323 (1986) pp. 533\u2013536.","journal-title":"Nature (London)"},{"issue":"5","key":"5_CR69","doi-asserted-by":"publisher","first-page":"5153","DOI":"10.1103\/PhysRevE.53.5153","volume":"53","author":"MA Sato","year":"1996","unstructured":"M.-A. Sato and S. Ishii, Bifurcations in mean field theory, Physical Review E Vol. 53 No. 5 (1996) pp. 5153\u20135168.","journal-title":"Physical Review E"},{"issue":"2","key":"5_CR70","doi-asserted-by":"publisher","first-page":"1238","DOI":"10.1103\/PhysRevA.45.1238","volume":"45","author":"GM Shim","year":"1992","unstructured":"G.M. Shim, D. Kim, and M.Y. Choi, Potts-glass model of layered feed-forward neural networks, Physical Review A Vol. 45 No. 2 (1992) pp. 1238\u20131248.","journal-title":"Physical Review A"},{"key":"5_CR71","unstructured":"P. Stolorz, Merging constrained optimisation with deterministic annealing to \u201csolve\u201d combinatorially hard problems, in J.E. Moody, S.J. Hanson, and R.P. Lippmann (eds.) Advances in Neural Information Processing Systems, ( Chapman and Hall, 1991 ) pp. 1025\u20131032."},{"issue":"1","key":"5_CR72","first-page":"1","volume":"8","author":"Y Uesaka","year":"1993","unstructured":"Y. Uesaka, Mathematical basis of neural networks for combinatorial optirnization problems, Optoelectronics\u2013Devices and Technologies Vol. 8 No. 1 (1993) pp. 1\u20139.","journal-title":"Optoelectronics - Devices and Technologies"},{"issue":"9","key":"5_CR73","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1002\/ecjc.4430780907","volume":"78","author":"K Urahama","year":"1995","unstructured":"K. Urahama, Mathematical programming formulation for neural combinatorial optimization algorithms, Electronics and Communications in Japan Vol. 78 No. 9 (1995) pp. 67\u201375.","journal-title":"Electronics and Communications in Japan"},{"issue":"1","key":"5_CR74","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1142\/S0129065793000043","volume":"4","author":"K Urahama","year":"1993","unstructured":"K. Urahama and S.-I. Ueno, A gradient system solution to Potts mean field equations and its electronic implementation, International Journal of Neural Systems Vol. 4 No. 1 (1993) pp. 27\u201334.","journal-title":"International Journal of Neural Systems"},{"issue":"3","key":"5_CR75","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1142\/S0129065794000244","volume":"5","author":"K Urahama","year":"1994","unstructured":"K. Urahama and T. Yamada, Constrained Potts mean field systems and their electronic implementation, International Journal of Neural Systems Vol. 5 No. 3 (1994) pp. 229\u2013239.","journal-title":"International Journal of Neural Systems"},{"key":"5_CR76","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1109\/72.80231","volume":"2","author":"DE Bout Den","year":"1990","unstructured":"D.E. Van Den Bout and T.K. Miller, Graph partitioning using annealed networks, IEEE Transactions on Neural Networks Vol.]. No. 2 (1990) pp. 192\u2013203.","journal-title":"Graph partitioning using annealed networks, Ieee Transactions on Neural Networks Vol.]"},{"key":"5_CR77","unstructured":"P.J.M. Van Laarhoven, Theoretical and Computational Aspects of Simulated Annealing, (Stichting Mathematisch Centrum, 1988 )."},{"key":"5_CR78","first-page":"319","volume-title":"Progress in Neural Networks, (Ablex","author":"J Wang","year":"1994","unstructured":"J. Wang, Deterministic neural networks for combinatorial optimization, in O.M. Omidvar (ed.) Progress in Neural Networks, (Ablex, 1994 ) pp. 319\u2013340."},{"issue":"1","key":"5_CR79","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1103\/RevModPhys.54.235","volume":"54","author":"FY Wu","year":"1982","unstructured":"F.Y. Wu, The Potts model, Reviews of Modern Physics Vol. 54 No. 1 (1982) pp. 235\u2013268.","journal-title":"Reviews of Modern Physics"},{"issue":"1","key":"5_CR80","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1109\/72.363442","volume":"6","author":"L Xu","year":"1995","unstructured":"L. Xu and A.L. Yuille, Robust principal component analysis by self-organizing rules based on statistical physics approach, IEEE Transactions on Neural Networks Vol. 6 No. 1 (1995) pp. 131\u2013143.","journal-title":"Ieee Transactions on Neural Networks"},{"key":"5_CR81","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1162\/neco.1990.2.1.1","volume":"2","author":"AL Yuille","year":"1990","unstructured":"A.L. Yuille, Generalized Deformable models, statistical physics, and matching problems, Neural Computation Vol. 2 (1990) pp. 1\u201324.","journal-title":"Neural Computation"},{"key":"5_CR82","first-page":"19","volume-title":"Artificial Neural Networksfor Speech and Vision,(Chapman and Hall","author":"AL Yuille","year":"1993","unstructured":"A.L. Yuille and J.J. Kosowsky, Statistical physics algorithms that converge, in R.J. Mammone (ed.) Artificial Neural Networksfor Speech and Vision,(Chapman and Hall, 1993 ) pp. 19\u201336."},{"key":"5_CR83","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1162\/neco.1994.6.3.341","volume":"6","author":"AL Yuille","year":"1994","unstructured":"A.L. Yuille and J.J. Kosowsky, Statistical physics algorithms that converge, Neural Computation Vol. 6 (1994) pp. 341\u2013356.","journal-title":"Neural Computation"},{"key":"5_CR84","doi-asserted-by":"publisher","first-page":"334","DOI":"10.1162\/neco.1994.6.2.334","volume":"6","author":"AL Yuille","year":"1994","unstructured":"A.L. Yuille, P. Stolorz, and J. Utans, Statistical physics, mixtures of distributions, and the EM algorithm, Neural Computation Vol. 6 (1994) pp. 334\u2013340.","journal-title":"Neural Computation"}],"container-title":["Handbook of Combinatorial Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-1-4757-3023-4_5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,29]],"date-time":"2023-06-29T17:58:51Z","timestamp":1688061531000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-1-4757-3023-4_5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999]]},"ISBN":["9781441948137","9781475730234"],"references-count":84,"URL":"https:\/\/doi.org\/10.1007\/978-1-4757-3023-4_5","relation":{},"subject":[],"published":{"date-parts":[[1999]]}}}