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Optimisation

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Industrial Applications of Neural Networks

Part of the book series: Research Reports ESPRIT ((ANNIE,volume 1))

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Abstract

The published work on the application of neural networks to optimisation problems is dominated by the travelling salesman problem. Since Hopfield’s paper (1985) there have been many attempts to produce solutions to this problem using neural and conventional methods.

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References

  • Aarts E H L and van Laarhoven P J M (1985) Statistical cooling: a general approach to combinatorial optimisation problems. Philips Journal of Research 40, 193–226

    MathSciNet  Google Scholar 

  • Aarts E H L and Korst J H M (1987) Boltzmann machines and their applications. Proc of Parallel Architectures and Languages, European Conference, Eindhoven, The Netherlands, June 1987

    Google Scholar 

  • Aarts E H L and Horst J H M (1989) Simulated annealing and Boltzmann machines. Wiley & Sons

    MATH  Google Scholar 

  • Adorf H M and Johnston M D (1990) A discrete stochastic neural network algorithm for constraint satisfaction problems. International Conference on Neural Networks, San Diego CA, USA, June 1990 3, 917–924

    Article  Google Scholar 

  • Angeniol B, De la Croix Vaubois G and Le Texier Y (1988) Self-organising feature maps and the TSP. Neural Networks 1, 289–293

    Article  Google Scholar 

  • Baker E and Fisher M (1981) Computational results for very large air crew scheduling problems. The International Journal of Management Science 9, 6, 613–618

    Google Scholar 

  • Balas E (1965) An additive algorithm for solving linear programs with zero-one variables. Operations Research 13, 517–546

    Article  MathSciNet  Google Scholar 

  • Balas E and Padberg M W (1976) Set partitioning: A survey. SIAM Review 18, 4, 710–760

    Article  MATH  MathSciNet  Google Scholar 

  • Balas E and Samuelson H (1973) Finding a minimum node cover in an arbitrary graph. MSRR 325, Carnegie-Mellon Univ, Pittsburgh, USA

    Google Scholar 

  • Baba E (1980) Cutting plans from conditional bounds: A new approach to set covering. Math Plug 12, 19–36

    Google Scholar 

  • Balas E and Ho A (1980) Set covering algorithms using cutting plans, heuristics and subgradient optimisation: A computational study. Mathematical Programming 12, 37–60

    MATH  MathSciNet  Google Scholar 

  • Bodin L, Golden B, Assad A and Ball M (1983) Routing and scheduling of vehicles and crews - the state of the art. Computer and Operations Research 10, 2, Special Issue

    Google Scholar 

  • Bodin L D, Kydes A S and Rosenfield D B (-) Approximation techniques for automated manpower scheduling. Research paper, UPS/UMTA-1, SUNY, Stony Brook, New York, USA

    Google Scholar 

  • Burr D J (1988) An improved elastic net method for the TSP. IEEE Int Con on Neural Networks I, 69–75, San Diego CA, USA, 1988

    Google Scholar 

  • Christofides N (1975) Graph theory: An algorithmic approach. Academic Press

    Google Scholar 

  • Christofides N and Korman S (1975) A computational survey of methods for the set coveting problem. Management Science 21, 5, 591–599

    Article  MATH  MathSciNet  Google Scholar 

  • Chvatal V (1979) A greedy heuristic for the set covering problem. Mathematics of Operations Research 4, 3, 233–235

    Article  MATH  MathSciNet  Google Scholar 

  • Couvrey B and Yansouni B (1977) A method of estimating manpower levels at an airport. ACIFORS Symposium Proceedings, Germany, 340–355

    Google Scholar 

  • Crainic T (1978) The crew scheduling problem of an aviation company. Publication 122, Centre de Recherche sur les Transports, Université de Montreal, Canada

    Google Scholar 

  • Dahl E (1987) Neural network algorithm for an NP-complete problem: Map and graph colouring. Proc IEEE First Int Conf on Neural Networks, San Diego CA, USA, 1987

    Google Scholar 

  • Dantzig G B and Wolfe P (1960) Decomposition principle for linear programming. Operations Research 8, 1, 100–111

    Article  Google Scholar 

  • Délorme J (1974) Contribution to the resolution of the covering problem: truncating methods. Thèse de Docteur Ingénieur, Université Paris V I

    Google Scholar 

  • Durbin R and Willshaw D (1987) An analogue approach to the TSP using an elastic net method. Nature, 326, 689–691

    Article  Google Scholar 

  • Etcheberry J (1977) The set covering problem: A new implicit enumeration algorithm. Operations Research 25, 5, 760–772

    Article  MATH  MathSciNet  Google Scholar 

  • Foo Y and Takefuji Y (1988) Integer linear programming neural networks for job-shop scheduling. Proceedings of the IEEE Int Conf on Neural Networks, San Diego CA, USA, 1988

    Google Scholar 

  • Garfinkel R S and Nemhauser G L (1969) The set partitioning problem: Set covering with equality constraints. Operations Research 17, 848–856

    Article  MATH  Google Scholar 

  • Gomory R E (1958) Outline for an algorithm for integer solution to linear programs. Bulletin of the American Mathematical Society 64, 5

    Article  MathSciNet  Google Scholar 

  • Hegde S U, Sweet J L and Levy W B (1988) Determination of parameters in a Hopfield/tank computational network IEEE International Conference on Neural Networks, II, 291–298, San Diego CA, USA, 1988

    Google Scholar 

  • Ho A C (1982) Worst case analysis of a class of set covering heuristics. Math Prog 23, 170–180

    Article  MATH  Google Scholar 

  • Hopfield J J (1982) Neural networks and physical systems with emergent collective computational abilities. USA Proc National Academy of Sciences 79, 2554–2558

    Article  MathSciNet  Google Scholar 

  • Hopfield J J and Tank D W (1985) Neural computation of decisions optimisation problems. Biological Cybernetics 52, 141–152

    MATH  MathSciNet  Google Scholar 

  • Hu T C (1972) Integer programming and network flows. Addison Wesley

    Google Scholar 

  • Karmarkar N (1984) A new polynomial time algorithm for linear programming. Combinatorica 4, 373–395

    Article  MATH  MathSciNet  Google Scholar 

  • Karp R (1972) Reducibility among combinatorial problems. Complexity of computer computations, 85–103, Plenum Press, New York, USA

    Google Scholar 

  • Khachian L G (1979) A polynomial algorithm for linear programming. Dolklady Akad Nauk USSR, 244(5) 1093–1096. Translated in Soviety Math Dolcady 20, 191–194

    Google Scholar 

  • Kirkpatrick S, Gelatt C and Vecchi M (1983) Optimisation by simulated annealing. Science, 220: 671

    Article  MATH  MathSciNet  Google Scholar 

  • Lemke C E, Salkin H M and Spielberg K (1971) Set covering by single-branch enumeration with linear programming subproblems. Operational Research 19, 998–1022

    MATH  MathSciNet  Google Scholar 

  • Lin S (1965) Computer solutions of the TSP. Bell Tech Journal 44, 2245–2269

    MATH  Google Scholar 

  • Lundy M and Mees A (1986) Convergence of an annealing algorithm. Math Prog, 34, 111–124

    Article  MATH  MathSciNet  Google Scholar 

  • Metropolis N, Rosenbiuth A, Rosenbluth M, Teller A and Teller E (1953) Equation of state calculations by fast computing machines. J ChemPhysics 21, 1087–1092

    Google Scholar 

  • Marsten R E (1974) An algorithm for large set partitioning problems. Management Science 20, 5, 774–787

    Article  MATH  MathSciNet  Google Scholar 

  • Mitra D, Romeo F and Sangiovanni-Vincentelli A (1986) Convergence and fine time behaviour of simulated annealing. Advances in Applied Probability 18, 747

    Article  MATH  MathSciNet  Google Scholar 

  • Nicoletti B, Natali L and Scalas M (1976) Manpower staffing at an airport: Generalised set covering problem. 1976 ACIFORS Symposium Proceedings, Miami, Florida, USA, 473–503

    Google Scholar 

  • Peretto P and Niez J J (1986) Stochastic dynamics of neural networks. IEEE Transaction Systems, Man and Cybernetics 16, 1

    Article  MathSciNet  Google Scholar 

  • Pierce J C (1968) Applications of combinatorial programming to a class of all-zero-one integer programming problems. Management Science 15, 191–209

    Article  MathSciNet  Google Scholar 

  • Pierce J F and Lasky J S (1973) Improved combinatorial programming algorithms for a class of allzero-one integer programing problems. Management Science 19, 528–543

    Article  MATH  MathSciNet  Google Scholar 

  • Rubin J (1973) A technique for the solution of massive set covering problems with application to airline crew scheduling. Transp Sci 7, 1 34–48

    Article  Google Scholar 

  • Salkin H M and Koncal R D (1973) Set covering by an all integer algorithm: Computational experience. J Assoc Comput Math 20, 189–193

    MATH  Google Scholar 

  • Salkin H (1975) Integer programming. Addison-Wesley

    Google Scholar 

  • Saylor J and Stork D (1986) Parallel analogue neural networks for tree searching. AIP Conference Proceedings 151: Neural networks for computing

    Google Scholar 

  • Segal M (1974) The operator-scheduling problem: A network-flow approach. Operations Research 22, 808–823

    Article  MATH  Google Scholar 

  • Spitzer M (1961) Solution to the crew scheduling problem. AGIFORS symposium, October 1961

    Google Scholar 

  • Szu H and Hartley R L (-) Simulated annealing with Cauchy probability. Optics letter

    Google Scholar 

  • Thiriez H (1969) Airline crew scheduling: A group theoretic approach. PhD dissertation, MIT, October 1969

    Google Scholar 

  • Vasko F J and Wilson G R (1984) An efficient heuristic for large set covering problems. Naval Research Logistics Quarterly 31, 163–171

    Article  MATH  Google Scholar 

  • Vasko F J and Wolf F E (1988) Solving set covering problems on a personal computer. Computer Operations Research 15 (2) 115–121

    Article  MATH  MathSciNet  Google Scholar 

  • Wilhelm E (1975) Overview of the Rucus package driver run cutting program. Workshop on Automated Techniques for Scheduling of Vehicle Operators for Urban Public Transportation Services, Chicago Ill, USA

    Google Scholar 

  • Wilson G V and Pawley G S (1988) On the stability of the TSP algorithm of Hopfield and Tank. Biol Cyber, 58, 63–70

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Harwell Laboratory, AEA Technology, OX11 0RA, Didcot, Oxon, UK

    Ian F. Croall & John P. Mason

Authors
  1. Ian F. Croall
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  2. John P. Mason
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Editors and Affiliations

  1. Harwell Laboratory, AEA Technology, OX11 0RA, Didcot, Oxon, UK

    Ian F. Croall  & John P. Mason  & 

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© 1992 ECSC — EEC — EAEC, Brussels — Luxembourg

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Croall, I.F., Mason, J.P. (1992). Optimisation. In: Croall, I.F., Mason, J.P. (eds) Industrial Applications of Neural Networks. Research Reports ESPRIT, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84837-7_6

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  • DOI: https://doi.org/10.1007/978-3-642-84837-7_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55875-0

  • Online ISBN: 978-3-642-84837-7

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