Neural Networks for Combinatorial Optimization: A Review of More Than a Decade of Research

References

• Aarts E. H. L. , Korst J. Simulated Annealing and Boltzmann Machines (1998) (John Wiley & Sons, Essex, UK) Google Scholar
• Aarts E. H. L. , Laarhoven P. J. M. Statistical cooling: A general approach to combinatorial optimisation problems. Philips J. Res. (1985) 40 193 226 Google Scholar
• Abe S. , Kawakami J. , Hirasawa K. Solving inequality constrained combinatorial optimization problems by the Hopfield neural networks. Neural Networks (1992) 5 663 670 Crossref, Google Scholar
• Ackley D. H. , Hinton G. E. , Sejnowski T. J. A learning algorithm for Boltzmann machines. Cognitive Sci. (1985) 9 147 169 Crossref, Google Scholar
• Adorf H. M. , Johnston M. D. A discrete stochastic neural network algorithm for constraint satisfaction problems. Proc. Internat. Joint Conf. Neural Networks (1990) 3 (San Diego) 917 924 Crossref, Google Scholar
• Aiyer S. V. B. , Niranjan M. , Fallside F. A theoretical investigation into the performance of the Hopfield model. IEEE Trans. Neural Networks (1990) 1 204 215 Crossref, Google Scholar
• Aiyer S. V. B. Solving combinatorial optimization problems using neural networks. (1991) . Technical report CUED/F-INFENG/TR 89 Cambridge University Engineering Department, Cambridge, UK Google Scholar
• Akiyama Y. , Yamashita A. , Kajiura M. , Aiso H. Combinatorial optimization with gaussian machines. Proc. IEEE Internat. Joint Conf. Neural Networks (1989) 1 533 540 Crossref, Google Scholar
• Amartur S. C. , Piraino D. , Takefuji Y. Optimization neural networks for the segmentation of magnetic resonance images. IEEE Trans. Medical Imaging (1992) 11 215 220 Crossref, Google Scholar
• Andresol R. , Gendreau M. , Potvin J.-Y. , Voss S. , et al. A Hopfield-Tank neural network model for the generalized traveling salesman problem. Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization (1997) (Kluwer Academic Publishers, Boston) 393 402 Google Scholar
• Angeniol B. , de la Croix G. , Le Texier J.-Y. Self organising feature maps and the travelling salesman problem. Neural Networks (1988) 1 289 293 Crossref, Google Scholar
• Ansari N. , Zhang Z. Z. , Hou E. S. H. , Wang J. , Takefuji Y. Scheduling computation tasks onto a multiprocessor system by mean field annealing of a Hopfield neural network. Neural Networks in Design and Manufacturing (1993) (World Scientific, Singapore) 163 184 Crossref, Google Scholar
• Aourid S. M. , Do X. D. , Kaminska B. Penalty formulation for 0–1 linear programming problem: A neural network approach. Proc. Internat. Conf. Neural Networks (1995) 4 1690 1693 Crossref, Google Scholar
• Arabas J. A genetic approach to the hopfield neural network in the optimization problems. Bull. Polish Acad. Sci. (1994) 42 59 66 Google Scholar
• Babu G. P. , Murty M. N. Connectionist approach for clustering. Proc. Internat. Conf. Neural Networks (1994) 7 4661 4666 Crossref, Google Scholar
• Bahrami A. , Dagli C. Hybrid intelligent packing system (HIPS) through integration of artificial neural networks, artificial intelligence and mathematical programming. Appl. Intelligence (1994) 4 321 336 Crossref, Google Scholar
• Barr R. S. , Golden B. L. , Kelly J. P. , Resende M. G. C. , Stewart W. R. Designing and reporting on computational experiments with heuristic methods. J. Heuristics (1995) 1 9 32 Crossref, Google Scholar
• Beale R. , Jackson T. Neural Computing: An Introduction (1990) (IOP Publishing Ltd., Bristol, UK) Crossref, Google Scholar
• Berger M. O. k-Coloring vertices using a neural network with convergence to valid solutions. Proc. Internat. Conf. Neural Networks (1994) 7 4514 4517 Crossref, Google Scholar
• Botros N. , Abdul-Aziz M. Hardware implementation of an artificial neural network using field programmable gate arrays (FPGA's). IEEE Trans. Indust. Electronics (1994) 41 665 667 Crossref, Google Scholar
• Brandt R. D. , Wang Y. , Laub A. J. , Mitra S. K. Alternative networks for solving the travelling salesman problem and the list-matching problem. Proc. Internat. Conf. Neural Networks (1988) 2 333 340 Crossref, Google Scholar
• Bultan T. , Aykanat C. Circuit partitioning using parallel mean field annealing algorithms. Proc. 3rd IEEE Sympos. Parallel Distributed Processing (1991) 534 541 Crossref, Google Scholar
• Burke L. I. Adaptive neural networks for the traveling salesman problem: Insights from operations research. Neural Networks (1994) 7 681 690 Crossref, Google Scholar
• Burke L. I. , Damany P. The guilty net for the travelling salesman problem. Comput. Oper. Res. (1992) 19 255 265 Crossref, Google Scholar
• Burke L. I. , Ignizio J. P. Neural networks and operations research: An overview. Comput. Oper. Res. (1992) 19 179 189 Crossref, Google Scholar
• Carpenter G. , Grossberg S. ART2: Self-organization of stable category recognition codes for analog input patterns. Appl. Optics (1987) 26 4919 4946 Crossref, Google Scholar
• Caviglia D. D. , Bisio G. M. , Curatelli F. , Giovannacci L. , Raffo L. Neural algorithms for cell placement in VLSI design. Proc. IEEE Internat. Joint Conf. Neural Networks (1989) 1 573 580 Crossref, Google Scholar
• Chang S. , Nam B. H. Hopfield-type neural networks for standard form linear programming and jobshop scheduling. Trans. Korean Inst. Electr. Engrg. (1994) 43 1361 1369 Google Scholar
• Chen L. , Aihara K. Chaotic simulated annealing by a neural network model with transient chaos. Neural Networks (1995) 8 915 930 Crossref, Google Scholar
• Chen S. K. , Mangiameli P. , West D. The comparative ability of self-organizing neural networks to define cluster structure. Omega (1995) 23 271 279 Crossref, Google Scholar
• Cho Y. B. , Kurokawa T. , Takefuji Y. , Kim H. S. An O(1) approximate parallel algorithm for the n-task n-person assignment problem. Proc. Internat. Joint Conf. Neural Networks (1993) 2 (Nagoya) 1503 1506 Google Scholar
• Christofides N. Graph Theory: An Algorithmic Approach (1975) (Academic Press, New York) Google Scholar
• Chu P. A neural network for solving optimization problems with linear equality constraints. Proc. IEEE Internat. Joint Conf. Neural Networks (1992) 2 272 277 Crossref, Google Scholar
• Collins J. , Penz P. A. Considerations for neural network hardware implementations. Proc. IEEE Internat. Sympos. Circuits and Systems (1989) Portland 834 847 Crossref, Google Scholar
• Cottrell M. , Fort J. C. A stochastic model of retinotopy: A self-organizing process. Biol. Cybernetics (1986) 53 166 170 Crossref, Google Scholar
• Coy S. , Golden B. , Wasil E. , Runger G. , Dagli et al C. Evaluating the effectiveness of fine-tuned learning enhancement to backpropagation. Intelligent Engineering Systems Through Artificial Neural Networks (1997) (ASME Press, New York) 105 111 Google Scholar
• Craig G. , Krishnamoorthy M. , Palaniswami M. , Osman I. H. , Kelly J. P. Comparison of heuristic algorithms for the degree constrained minimum spanning tree. Meta-Heuristics: Theory and Applications (1996) (Kluwer Academic Press, Boston) 83 96 Crossref, Google Scholar
• Croall I. F. , Mason J. P. Industrial Applications of Neural Networks (1992) (Springer-Verlag, Luxembourg) 160 218 Crossref, Google Scholar
• Culioli J. C. , Protopopescu V. , Britton C. L. , Ericson M. N. Neural network models for linear programming. Proc. Internat. Joint Conf. Neural Networks (1990) 293 296 Google Scholar
• Dagli C. , Lammers S. Possible applications of neural networks in manufacturing. Proc. IEEE Internat. Joint Conf. Neural Networks (1989) 2 605 . (abstract only) Crossref, Google Scholar
• Dagli C. H. , Sittisathanchai S. Genetic neuro-scheduler for job-shop scheduling. Comput. Indust. Engrg. (1993) 25 267 270 Crossref, Google Scholar
• Dai Z. , Cha J. , Guo W. , Wang F. A heuristic-based neural network for packing problems. Proc. Internat. Conf. Data Knowledge Systems Manufacturing Engrg. (1994) 2 698 703 Google Scholar
• Dantzig G. B. Linear Programming and Extensions (1963) (Princeton University Press, Princeton, NJ) Crossref, Google Scholar
• Date H. , Seki M. , Hayashi T. LSI module placement using neural computation networks. Proc. Internat. Joint Conf. Neural Networks (1990) 3 San Diego 831 836 Crossref, Google Scholar
• Davis G. W. Sensitivity analysis in neural net solutions. IEEE Trans Systems, Man and Cybernetics (1989) 19 1078 1082 Crossref, Google Scholar
• Davis L. Handbook of Genetic Algorithms (1991) (Van Nostrand Reinhold, New York) Google Scholar
• Desieno D. Adding a conscience mechanism to competitive learning. Proc. IEEE Internat. Conf. Neural Networks (1988) 1 117 124 Crossref, Google Scholar
• Dijkstra E. W. A note on two problems in connection with graphs. Numerische Mathematik (1959) 1 269 Crossref, Google Scholar
• Durbin R. , Willshaw D. An analogue approach to the travelling salesman problem using an elastic net method. Nature (1987) 326 689 691 Crossref, Google Scholar
• Fang L. , Li T. Design of competition-based neural networks for combinatorial optimization. Internat. J. Neural Systems (1990) 1 221 235 Crossref, Google Scholar
• Fang L. , Wilson W. H. , Li T. Mean-field annealing neural net for quadratic assignment. Proc. Internat. Conf. Neural Networks (1990) Paris 282 286 Google Scholar
• Favata F. , Walker R. A study of the application of Kohonen-type neural networks to the travelling salesman problem. Biol. Cybernetics (1991) 64 463 468 Crossref, Google Scholar
• Foo Y. P. S. , Takefuji Y. Stochastic neural networks for job-shop scheduling: Parts 1 and 2. Proc. IEEE Internat. Conf. Neural Networks (1988) 2 275 290 Google Scholar
• Foo Y. P. S. , Takefuji Y. Integer linear programming neural networks for job shop scheduling. Proc. IEEE Internat. Conf. Neural Networks (1988) 2 341 348 Google Scholar
• Foo Y. P. S. , Szu H. Solving large-scale optimization problems by divide-and-conquer neural networks. Proc. IEEE Internat. Joint Conf. Neural Networks (1989) 1 507 511 Crossref, Google Scholar
• Fort J. C. Solving a combinatorial problem via self-organizing process: An application of the Kohonen algorithm to the traveling salesman problem. Biol. Cybernetics (1988) 59 33 40 Crossref, Google Scholar
• Fujita T. , Yasuda K. , Yokoyama R. Global optimization method using chaos in dissipative system. Electronics Comm. Japan, Part 3 (1995) 78 881 889 Google Scholar
• Funabiki N. , Takefuji Y. A neural network parallel algorithm for channel assignment problems in cellular radio networks. IEEE Trans. Vehicular Tech. (1992) 41 430 437 Crossref, Google Scholar
• Gaspin C. Automatic translation of constraints for solving optimization problems by neural networks. Proc. Internat. Joint Conf. Neural Networks (1990) 857 861 Crossref, Google Scholar
• Garey M. R. , Johnson D. S. Computers and Intractability (1979) (W. H. Freeman, New York) Google Scholar
• Gassen D. W. , Carothers J. D. Graph color minimization using neural networks. Proc. Internat. Joint Conf. Neural Networks (1993) 2 Nagoya 1541 1544 Crossref, Google Scholar
• Gee A. H. Problem solving with optimization networks. (1993) (Queen's College, Cambridge University, Cambridge, UK) . Ph.D. thesis Google Scholar
• Gee A. H. , Prager R. W. Limitations of neural networks for solving traveling salesman problems. IEEE Trans. Neural Networks (1995) 6 280 282 Crossref, Google Scholar
• Ghaziri H. , Osman I. H. , Kelly J. P. Supervision in the self-organizing feature map: Application to the vehicle routing problem. Metaheuristics: Theory and Applications (1996) (Kluwer, Boston) 651 660 Crossref, Google Scholar
• Gislen L. , Peterson C. , Soderberg B. Teachers and classes with neural networks. Internat. J. Neural Systems (1989) 1 167 176 Crossref, Google Scholar
• Glover F. Future paths for integer programming and links to artificial intelligence. Comput. Oper. Res. (1986) 5 533 549 Crossref, Google Scholar
• Glover F. A user's guide to tabu search. Ann. Oper. Res. (1993) 41 3 28 Crossref, Google Scholar
• Goldberg D. E. Genetic Algorithms in Search Optimization, and Machine Learning (1989) (Addison-Wesley, Reading, MA) Google Scholar
• Goldstein M. Self-organizing feature maps for the multiple traveling salesman problem (MTSP). Proc. IEEE Internat. Conf. Neural Networks (1990) Paris 258 261 Google Scholar
• Gong D. , Gen M. , Yamazaki G. , Xu W. Neural network approach for general assignment problem. Proc. Internat. Conf. Neural Networks (1995) 4 Perth 1861 1866 Google Scholar
• Gomory R. E. Outline for an algorithm for integer solution to linear programs. Bull. Amer. Math. Soc. (1958) 64 5 Crossref, Google Scholar
• Grossberg S. Nonlinear neural networks: Principles mechanisms and architectures. Neural Networks (1988) 1 17 61 Crossref, Google Scholar
• Guerrero F. , Lozano S. , Canca D. , Smith K. , Bulsari et al A. B. Machine grouping in cellular manufacturing: A self-organising neural network. Engineering Benefits from Neural Networks (1998) (Systems Engineering Association, Turku, Finland) 374 377 Google Scholar
• Hameenanttila T. , Carothers J. D. A Hopfield neural network solution to the TCM partitioning problem. Proc. IEEE Internat. Conf. Neural Networks (1994) 7 4676 4680 Crossref, Google Scholar
• Hammerstrom D. A VLSI architecture for high performance, low cost, on-chip learning. Proc. IEEE Internat. Joint Conf. Neural Networks (1990) 2 537 543 Crossref, Google Scholar
• Hayakawa Y. , Marumotot A. , Sawada Y. Effects of the chaotic noise on the performance of a neural network model for optimization problems. Phys. Rev. E (1995) 51 2693 2700 Crossref, Google Scholar
• Hecht-Nielsen R. Applications of counterpropagation networks. Neural Networks (1988) 1 131 139 Crossref, Google Scholar
• Hedge S. , Sweet J. , Levy W. Determination of parameters in a Hopfield/Tank computational network. Proc. IEEE Internat. Conference Neural Networks (1988) 2 291 298 Crossref, Google Scholar
• Hellstrom B. J. , Kanal L. N. Asymmetric mean-field neural networks for multi-processor scheduling. Neural Networks (1992) 5 671 686 Crossref, Google Scholar
• Hérault L. , Niez J. J. , Gelenbe E. Neural network and combinatorial optimization. A study of NP-complete graph problems. Neural Networks: Advances and Applications (1991) (North-Holland, Amsterdam) 165 213 Google Scholar
• Hinton G. E. , Sejnowski T. J. , Ackley D. H. (1984) . Boltzmann machines: Constraint satisfaction networks that learn, Carnegie Mellon University, Technical report CMU-CS-84-119 Google Scholar
• Hong S. G. , Kim S. W. , lee J. J. The minimum cost path finding algorithm using a Hopfield type neural network. Proc. IEEE Internat. Conf. Fuzzy Systems (1995) 4 1719 1726 Google Scholar
• Hooker J. N. Testing heuristics: We have it all wrong. J. Heuristics (1995) 1 33 42 Crossref, Google Scholar
• Hopfield J. J. Neural networks and physical systems with emergent collective computational abilities. Proc. National Acad. Sci. (1982) 79 2554 2558 Crossref, Google Scholar
• Hopfield J. J. Neurons with graded response have collective computational properties like those of two-state neurons. Proc. National Acad. Sci. (1984) 81 3088 3092 Crossref, Google Scholar
• Hopfield J. J. , Tank D. W. “Neural” computation of decisions in optimization problems. Biol. Cybernetics (1985) 52 141 152 Crossref, Google Scholar
• Inoue M. , Nagayoshi A. Solving an optimization problem with a chaos neural network. Proc. Theoret. Phys. (1992) 88 769 773 Crossref, Google Scholar
• Jagota A. Approximating maximum clique with a Hopfield network. IEEE Trans. Neural Networks (1995) 6 724 735 Crossref, Google Scholar
• Jeong H. , Park J. H. Lower bounds of annealing schedule for boltzmann and cauchy machines. Proc. IEEE Internat. Joint Conf. Neural Networks (1989) 1 581 586 Crossref, Google Scholar
• Jain A. K. , Dubes R. C. Algorithms for Clustering (1988) (Prentice Hall, Englewood, NJ) Google Scholar
• Joppe A. , Cardon H. R. A. , Bioch J. C. A neural network for solving the traveling salesman problem. Proc. IEEE Internat. Joint Conf. Neural Networks (1990) 3 961 964 Google Scholar
• Kajiura M. , Akiyama Y. , Anzai Y. Solving large scale puzzles with neural networks. (1990) Proc. Tools for AI Conf. Fairfax 562 569 Google Scholar
• Kamgar-Parsi B. , Gualtieri J. A. , Devaney J. E. , Kamgar-Parsi B. Clustering with neural networks. Biol. Cybernetics (1990) 63 201 208 Crossref, Google Scholar
• Kamgar-Parsi B. , Kamgar-Parsi B. An efficient model of neural networks for optimization. Proc. IEEE Internat. Conf. Neural Networks (1987) 3 785 790 Google Scholar
• Kamgar-Parsi B. , Kamgar-Parsi B. Dynamical stability and parameter selection in neural optimization. Proc. Internat. Joint Conf. Neural Networks (1992) 4 566 571 Crossref, Google Scholar
• Kennedy M. , Chua L. Neural networks for linear and nonlinear programming. IEEE Trans. Circuits Systems (1988) 35 554 562 Crossref, Google Scholar
• Kernighan B. , Lin S. An efficient heuristic procedure for partitioning graphs. Bell System Tech. J. (1970) 49 291 307 Crossref, Google Scholar
• Kim S. Y. , Lee Y. H. , Agnihotri D. A hybrid approach to sequencing jobs using heuristic rules and neural networks. Production Planning and Control (1995) 6 445 454 Crossref, Google Scholar
• Kirkpatrick S. , Gelatt C. , Vecchi M. Optimisation by simulated annealing. Science (1983) 220 671 680 Crossref, Google Scholar
• Kohonen T. Self-organized formation of topologically correct feature maps. Biol. Cybernetics (1982) 43 59 69 Crossref, Google Scholar
• Kohonen T. Self-Organisation and Associative Memory (1984) (Springer-Verlag, Berlin) Google Scholar
• Kohonen T. The self-organizing map. Proc. IEEE (1990) 78 1464 1480 Crossref, Google Scholar
• Kovacic M. Timetable construction with Markovian neural network. Eur. J. Oper. Res. (1993) 69 92 96 Crossref, Google Scholar
• Kruskal J. On the shortest spanning subtree of a graph and the travelling salesman problem. Proc. Amer. Math. Soc. (1956) 7 48 Crossref, Google Scholar
• Kunz D. Channel assignment for cellular radio using neural networks. IEEE Trans. Vehicular Tech. (1991) 40 188 193 Crossref, Google Scholar
• Kurokawa T. , Kozuka S. Use of neural networks for the optimum frequency assignment problem. Electronics Comm. Japan, Part 1 (1994) 77 106 116 Crossref, Google Scholar
• Lai J. S. , Kuo S. Y. , Chen I. Y. Neural networks for optimization problems in graph theory. Proc. IEEE Internat. Sympos. Circuits and Systems (1994) 6 269 272 Google Scholar
• Lai W. K. , Coghill G. G. Genetic breeding of control parameters for the Hopfield/Tank neural net. Proc. Internat. Joint Conf. Neural Networks (1992) 4 618 623 Crossref, Google Scholar
• Lai W. K. , Coghill G. G. Initialising the continuous Hopfield net. Proc. Internat. Conf. Neural Networks (1994) 7 4640 4644 Crossref, Google Scholar
• Land A. H. , Doig A. G. An automatic method of solving discrete programming problems. Econometrica (1960) 28 497 520 Crossref, Google Scholar
• Lee B. W. , Sheu B. J. Design of a neural-based A/D converter using modified Hopfield network. IEEE J. Solid-State Circuits (1989) 24 1129 1135 Crossref, Google Scholar
• Lee H.-M. , Hsu C.-C. Neural network processing through energy minimization with learning ability to the multiconstraint zero-one knapsack problem. (1990) Proc. Tools for AI Conf. Fairfax, Virginia 548 555 Google Scholar
• Lee S. , Park J. Dual-mode dynamics neural network (D2NN) for knapsack packing problem. Proc. Internat. Joint Conf. Neural Networks (1993) 3 Nagoya 2425 2428 Google Scholar
• Lin S. , Kernighan B. W. An effective heuristic algorithm for the travelling salesman problem. Oper. Res. (1973) 21 498 516 Link, Google Scholar
• Lin W. , Delgado-Frias J. G. , Pechanek G. G. , Vassiliadis S. Impact of energy function on a neural network model for optimization problems. Proc. IEEE Internat. Conf. Neural Networks (1994) 7 4518 4523 Google Scholar
• Lin Y. , Austin L. M. , Burns J. R. An intelligent algorithm for mixed-integer programming models. Comput. Oper. Res. (1992) 19 461 468 Crossref, Google Scholar
• Lister R. Annealing networks and fractal landscapes. Proc. IEEE Internat. Conf. Neural Networks (1993) 1 257 262 Crossref, Google Scholar
• Lo J. T.-H. A new approach to global optimization and its applications to neural networks. Proc. IEEE Internat. Joint Conf. Neural Networks (1992) 4 600 605 Crossref, Google Scholar
• Looi C.-K. Neural network methods in combinatorial optimization. Comput. Oper. Res. (1992) 19 191 208 Crossref, Google Scholar
• Mansour N. Parallel physical optimization algorithms for allocating data to multicomputer nodes. J. Supercomputing (1994) 8 53 80 Crossref, Google Scholar
• Matsuyama Y. Self-organization via competition, cooperation and categorization applied to extended vehicle routing problems. Proc. Internat. Joint Conf. Neural Networks (1991) 1 385 390 Crossref, Google Scholar
• Mausser H. , Magazine M. J. , Moore J. B. Application of an annealed neural network to a timetabling problem. (1993) . Working paper, School of Business Administration, University of Colorado at Boulder Google Scholar
• Mehrez A. , Yuan Y. , Gafni A. Stable solution vs. multiplicative utility solutions for the assignment problem. Oper. Res. lett. (1988) 7 131 139 Crossref, Google Scholar
• Nemhauser G. L. , Wolsey L. A. Integer and Combinatorial Optimization (1988) (John Wiley & Sons, New York) Crossref, Google Scholar
• Nonaka H. , Kobayashi Y. Sub-optimal solution screening in optimization by neural networks. Proc. Internat. Joint Conf. Neural Networks (1992) 4 606 611 Crossref, Google Scholar
• Nozawa H. , Yamaguti M. Solution of the optimization problem using the neural network model as a globally coupled map. Towards the Harnessing of Chaos (1994) (Elsevier Science B. V., Amsterdam) 99 114 Crossref, Google Scholar
• Nygard K. E. , Jueli P. , Kadaba N. Neural networks for selecting vehicle routing heuristics. ORSA J. Comput. (1990) 2 353 364 Link, Google Scholar
• Ohlsson M. , Peterson C. , Soderberg B. Neural networks for optimization problems with inequality constraints: The knapsack problem. Neural Comput. (1993) 5 331 339 Crossref, Google Scholar
• Osman I. H. , Laporte G. Metaheuristics: A bibliography. Ann. Oper. Res. (1996) 63 513 623 Crossref, Google Scholar
• Padman R. Choosing solvers in decision support systems. Recent Developments in Decision Support Systems 101 (1991) (Springer-Verlag, Berlin) 539 574 A neural network application in resource-constrained project scheduling Google Scholar
• Peterson C. , Anderson J. Neural networks and NP-complete optimization problems: A performance study on the graph bisection problem. Complex Systems (1988) 2 59 89 Google Scholar
• Peterson C. , Söderberg B. A new method for mapping optimization problems onto neural networks. Internat. J. Neural Systems (1989) 1 3 22 Crossref, Google Scholar
• Peterson C. , Söderberg B. , Reeves C. R. Artificial neural networks. Modern Heuristic Techniques for Combinatorial Problems (1993) (Blackwell Scientific Publications, Oxford) 197 242 Google Scholar
• Philipoom P. R. , Rees L. P. , Wiegmann L. Using neural networks to determine internally set due-date assignments for shop scheduling. Decision Sci. (1994) 26 825 851 Crossref, Google Scholar
• Platzman L. K. , Bartholdi J. J. Spacefilling curves and the planar travelling salesman problem. J. ACM (1989) 36 719 737 Crossref, Google Scholar
• Poliac M. O. , Lee E. B. , Slagle J. R. , Wick M. R. A crew scheduling problem. Proc. IEEE Internat. Conf. Neural Networks (1987) 2 779 786 Google Scholar
• Pornavalai C. , Chakraborty G. , Shiratori N. Neural networks for solving constrained steiner tree problem. Proc. IEEE Internat. Conf. Neural Networks (1995) 4 1867 1870 Crossref, Google Scholar
• Potvin J.-Y. The traveling salesman problem: A neural network perspective. ORSA J. Comput. (1993) 5 328 348 Link, Google Scholar
• Potvin J.-Y. , Robillard C. Clustering for vehicle routing with a competitive neural network. Neurocomputing (1995) 8 125 139 Crossref, Google Scholar
• Protzel P. W. , Palumbo D. L. , Arras M. K. Performance and fault tolerance of neural networks for optimization. IEEE Trans. Neural Networks (1993) 4 600 614 Crossref, Google Scholar
• Ramanujam J. , Sadayappan P. Mapping combinatorial optimization problems onto neural networks. Inform. Sci. (1995) 82 239 255 Crossref, Google Scholar
• Rauch H. E. , Winarske T. Neural networks for routing communications traffic. IEEE Control Systems Magazine (1988) April 26 31 Crossref, Google Scholar
• Ravikumar C. P. , Vedi N. Heuristic and neural algorithms for mapping tasks to a reconfigurable array. Microprocessing and Microprogramming (1995) 41 137 151 Crossref, Google Scholar
• Modern Heuristic Techniques for Combinatorial Problems (1993) (Blackwell Scientific Publications, Oxford) Google Scholar
• Ritter H. , Schulten K. , Reeves C. R. Kohonen's self-organizing maps: Exploring their computational capabilities. Proc. IEEE Internat. Conf. Neural Networks (1988) 1 109 116 Crossref, Google Scholar
• Romano R. , Maimon O. , Furst M. Neural net implementation for assigning a product to a production line. Proc. IEEE Internat. Joint Conf. Neural Networks (1989) 2 577 . (abstract only) Crossref, Google Scholar
• Roysam B. , Bhattacharjya A. K. Hierarchically structured unit-simplex transformations for parallel distributed optimization problems. IEEE Trans. Neural Networks (1992) 3 108 124 Crossref, Google Scholar
• Satyanarayana S. , Tsividis Y. P. , Graf H. P. A reconfigurable VLSI neural network. IEEE J. Solid-State Circuits (1992) 27 67 81 Crossref, Google Scholar
• Schaffer J. D. , Whitley D. , Eshelman L. J. Combinations of genetic algorithms and neural networks. A survey of the state of the art. Proc. Internat. Workshops Combinations Genetic Algorithms and Neural Networks (1992) 1 37 Crossref, Google Scholar
• Schaller H. N. Problem solving by global optimization: The rolling stone neural network. Proc. Internat. Joint Conf. Neural Networks (1993) 2 Nagoya 1481 1484 Crossref, Google Scholar
• Sharda R. Neural networks for the MS/OR analyst: An application bibliography. Interfaces (1994) 24 116 130 Link, Google Scholar
• Sheu B. , Chou E. , Tsai R. , Chen D. , Palaniswami M. , Attikiouzel Y. , Marks II R. J. , Fogel D. , Fukada T. VLSI neural networks: Design challenges and opportunities. Computational Intelligence (1995) (IEEE Press, New York) 261 271 Google Scholar
• Smith K. Solving the generalized quadratic assignment problem using a self-organising process. Proc. IEEE Internat. Conf. Neural Networks (1995) 4 Perth 1876 1879 Crossref, Google Scholar
• Smith K. , Palaniswami M. , Krishnamoorthy M. A hybrid neural approach to combinatorial optimization. Comput. Oper. Res. (1996) 23 597 610 Crossref, Google Scholar
• Smith K. An argument for abandoning the traveling salesman problem as a neural network benchmark. IEEE Trans. Neural Networks (1996) 7 1542 1544 Crossref, Google Scholar
• Smith K. , Palaniswami M. , Krishnamoorthy M. Traditional heuristic versus Hopfield neural network approaches to a car sequencing problem. Eur. J. Oper. Res. (1996) 93 300 316 Crossref, Google Scholar
• Smith K. , Palaniswami M. Static and dynamic channel assignment using neural networks. IEEE J. Selected Areas Comm. (1997) 15 238 249 Crossref, Google Scholar
• Smith K. , Krishnamoorthy M. , Palaniswami M. Neural versus traditional approaches to the location of interacting hub facilities. Location Sci. (1996) 4 155 171 Crossref, Google Scholar
• Szu H. Fast TSP algorithm based on binary neuron output and analog input using zero-diagonal interconnect matrix and necessary and sufficient conditions of the permutation matrix. Proc. IEEE Internat. Conf. Neural Networks (1988) 2 259 266 Crossref, Google Scholar
• Szu H. , Hartley R. Fast simulated annealing. Phys. Lett. A (1987) 122 157 162 Crossref, Google Scholar
• Tagliarini G. A. , Page E. W. Solving constraint satisfaction problems with neural networks. Proc. IEEE Internat. Conf. Neural Networks (1987) 3 741 747 Google Scholar
• Takada T. , Sanou K. , Fukumara S. A neural-network systems for solving an assortment problem in the steel-industry. Ann. Oper. Res. (1995) 57 265 281 Crossref, Google Scholar
• Takahashi M. , Kyuma K. , Funada E. 10000 Cell placement optimization using a self-organizing map. Proc. Internat. Joint Conf. Neural Networks (1993) 3 2417 2420 Crossref, Google Scholar
• Takefuji Y. Neural Network Parallel Computing (1992) (Kluwer Academic Publishers, Boston, MA) Crossref, Google Scholar
• Takefuji Y. , Lee K. C. Artificial neural networks for four-coloring map problems and K-colorability problems. IEEE Trans. Circuits and Systems (1991) 38 326 333 Crossref, Google Scholar
• Takefuji Y. , Szu H. Design of parallel distributed cauchy machines. Proc. IEEE Internat. Joint Conf. Neural Networks (1989) 1 529 532 Crossref, Google Scholar
• Tank D. W. , Hopfield J. J. Simple neural optimization networks: An A/D converter, signal decision circuit and a linear programming circuit. IEEE Trans. Circuit Systems (1986) 33 533 541 Crossref, Google Scholar
• Thomae D. A. , Van den Bout D. Encoding logical constraints into neural network cost functions. Proc. Internat. Joint Conf. Neural Networks (1990) 3 San Diego 863 868 Crossref, Google Scholar
• Uesaka Y. Mathematical basis of neural networks for combinatorial optimization problems. Optoelectronics (1993) 8 1 9 Google Scholar
• Unaltuna M. K. , Pitchumani V. Unsupervised competitive learning neural network algorithms for circuit bipartitioning. Proc. World Congress Neural Networks (1994) 1 San Diego 302 307 Google Scholar
• Urahama K. , Nishiyuki H. Neural algorithms for placement problems. Proc. Internat. Joint Conf. Neural Networks (1993) 3 Nagoya 2421 2424 Crossref, Google Scholar
• Vakhutinsky A. I. , Golden B. L. Solving vehicle routing problems using elastic nets. Proc. IEEE Internat. Conf. Neural Networks (1994) 7 4535 4540 Crossref, Google Scholar
• Vakhutinsky A. I. , Golden B. L. A hierarchical strategy for solving traveling salesman problems using elastic nets. J. Heuristics (1995) 1 67 76 Crossref, Google Scholar
• Vaithayanathan S. , Ignizio J. A stochastic neural network for resource constrained scheduling. Comput. Oper. Res. (1992) 19 241 254 Crossref, Google Scholar
• Vaithyanathan S. , Ogmen H. , Ignizio J. Generalized Boltzmann machines for multidimensional knapsack problems. Intelligent Engineering Systems Through Artificial Neural Networks (1994) 4 (Asme Press, New York) 1079 1084 Google Scholar
• Van den Bout D. E. , Miller III T. K. A travelling salesman objective function that works. Proc. IEEE Internat. Conf. Neural Networks (1988) 2 299 303 Crossref, Google Scholar
• Van den Bout D. E. , Miller III T. K. Improving the performance of the Hopfield-Tank neural network through normalization and annealing. Biol. Cybernetics (1989) 62 129 139 Crossref, Google Scholar
• Van den Bout D. E. , Miller III T. K. Graph partitioning using annealed neural networks. IEEE Trans. Neural Networks (1990) 1 192 203 Crossref, Google Scholar
• Van Hentenryck P. Constraint Satisfaction in Logic Programming (1989) (MIT Press, Cambridge, MA) Google Scholar
• Van Vliet R. , Cardon H. , Kohonen T. , Makisara K. , Simula O. , Kangas J. Combining a graph partitioning and a TSP neural network to solve the MTSP. Artificial Neural Networks (1991) 2 (North Holland, Amsterdam) 157 162 Google Scholar
• Verleysen M. , Jespers P. An analog VLSI implementation of Hopfield's neural network. IEEE Micro. (1989) December 46 55 Crossref, Google Scholar
• Vidyasagar M. Location and stability of the high-gain equilibria of nonlinear neural networks. IEEE Trans. Neural Networks (1993) 4 660 672 Crossref, Google Scholar
• Vinod V. V. , Ghose S. , Chakrabarti P. P. Resultant projection neural networks for optimization under inequality constraints. IEEE Trans. Systems, Man, and Cybernetics Part B (1996) 26 509 521 Google Scholar
• Wacholder E. A neural network-based optimization algorithm for the static weapon-target assignment problem. ORSA J. Comput. (1990) 1 232 246 Link, Google Scholar
• Wacholder E. , Han J. , Mann R. C. An extension of the Hopfield-Tank model for solution of the multiple TSP. Proc. IEEE Internat. Conf. Neural Networks (1991) 2 305 325 Google Scholar
• Wacholder E. , Han J. , Mann R. C. A neural network algorithm for the multiple TSP. Biol. Cybernetics (1989) 61 11 19 Crossref, Google Scholar
• Wang J. Analogue neural networks for solving the assignment problem. Electronics lett. (1992) 28 1047 1050 Crossref, Google Scholar
• Wang J. A recurrent neural network for solving the shortest path problem. Proc. IEEE Internat. Sympos. Circuits Systems (1994) 6 319 322 Crossref, Google Scholar
• Wang Q. , Sun X. , Golden B. , Jia J. Using artificial neural networks to solve the orienteering problem. Ann. Oper. Res. (1995) 61 111 120 Crossref, Google Scholar
• Wei Y. C. , Cheng C. K. Ratio cut partitioning for hierarchical designs. IEEE Trans. CAD (1991) July 911 921 Crossref, Google Scholar
• Wilson G. V. , Pawley G. S. On the stability of the tsp algorithm of Hopfield and Tank. Biol. Cybernetics (1988) 58 63 70 Crossref, Google Scholar
• Wong W. S. , Funka-Lea C. A. An elastic net solution to obstacle avoidance tour planning. Proc. Internat. Joint Conf. Neural Networks (1990) 3 San Diego 799 804 Crossref, Google Scholar
• Xu X. , Tsai W. T. Effective neural algorithms for the travelling salesman problem. Neural Networks (1991) 4 193 205 Crossref, Google Scholar
• Yamada S. , Kasai T. An efficient algorithm for the linear assignment problem. Electronics and Comm. Japan, Part 3 (1990) 73 28 36 Crossref, Google Scholar
• Yamamoto A. , Ohta M. , Ueda H. , Ogihara A. , Fukunaga K. Asymmetric neural network and its application to knapsack problem. IEICE Trans. Fundamentals E78-A (1995) 300 305 Google Scholar
• Yao X. Evolutionary artificial neural networks. Internat. J. Neural Systems (1993) 4 203 222 Crossref, Google Scholar
• Yip P. , Takefuji Y. Constrained optimization with use of two-dimensional maximum neurons. Proc. Internat. Conf. Neural Networks (1994) 7 4667 4671 Crossref, Google Scholar
• Zhang L. , Thomopoulos S. C. A. Neural network implementation of shortest path algorithm for traffic routing in communication networks. Proc. Internat. Joint Conf. Neural Networks (1989) 2 Washington, DC 591 . (abstract only) Crossref, Google Scholar
• Zhao S. , Dillon T. S. Parallel distributed implementation of the shortest path algorithm. Proc. Internat. Joint Conf. Neural Networks (1993) 2 Nagoya 1598 1601 Google Scholar
• Zhou D. N. , Cherkassky V. , Baldwin T. R. , Hong D. W. Scaling neural networks for job-shop scheduling. Proc. Internat. Joint Conf. Neural Networks (1990) 3 San Diego 889 894 Crossref, Google Scholar
• Zissimopolous V. , Paschos V. , Pekergin F. On the approximation of NP-complete problems by using the Boltzmann machine method: The case of some covering and packing problems. IEEE Trans. Comput. (1991) 40 1413 1418 Crossref, Google Scholar