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Classical Techniques

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Search Methodologies

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Abstract

The purpose of this chapter is to provide an introduction to three classical search techniques—branch and bound, dynamic programming and network flow programming—all of which have a well established record in the solution of both classical and practical problems. All three have their origins in, or prior to, the 1950s and were the result of a surge in interest in the use of mathematical techniques for the solution of practical problems. The timing was in part due to developments in Operations Research in World War II, but was also spurred by increasing competition in the industrial sector and the promise of readily accessible computing power in the foreseeable future.

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References

  • Abdullah S, Ahmadi S, Burke EK, Dror M and Mc Collum B (2007) A tabu-based large neighbourhood search methodology for the capacitated examination timetabling problem. J Oper Res Soc 58:1494–1502

    Article  Google Scholar 

  • Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows: theory, algorithms and applications. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Ahuja RK, Ergun O, Orlin JB, Punnen AO (2002) A survey of very large-scale neighbourhood search techniques. Discret Appl Math 123:75–102

    Article  Google Scholar 

  • Anderson DR, Sweeney DJ, Williams TA (1997) Introduction to management science: quantitative approaches to decision making. West Publishing, Eagan

    Google Scholar 

  • Balakrishnan VK (1997) Schaum’s outline of graph theory (Schaum’s Outline Series). Schaum Publishers, Mequon

    Google Scholar 

  • Balas E, Christofides N (1981) A restricted Lagrangian approach to the travelling salesman problem. Math Prog 21:19–46

    Article  Google Scholar 

  • Beasley JE (1985) An exact two-dimensional non-guillotine cutting tree-search procedure. Oper Res 33:49–64

    Article  Google Scholar 

  • Bellman R (1957) Dynamic programming. Princeton University Press, Princeton

    Google Scholar 

  • Bouzaher A, Braden JB, Johnson GV (1990) A dynamic programming approach to a class of non-point source pollution control problems. Manage Sci 36:1–15

    Article  Google Scholar 

  • Bron C, Kerbosch J (1973) Finding all cliques of an un-directed graph—alg 457. Commun ACM 16:575–577

    Article  Google Scholar 

  • Brown JR (1972) Chromatic scheduling and the chromatic number problem. Manage Sci 19:456–463

    Article  Google Scholar 

  • Christofides N, Whitlock C (1977) An algorithm for two-dimensional cutting problems. Oper Res 25:30–44

    Article  Google Scholar 

  • Clarke SR, Norman JM (1999) To run or not?: some dynamic programming models in cricket. J Oper Res Soc 50:536–545

    Google Scholar 

  • Cotta C, Aldana JF, Nebro AJ, Troya JM (1995) Hybridising genetic algorithms with branch and bound techniques for the resolution of the TSP. In: Poras CC et al (eds) Proceedings of the international conference on artificial neural networks and genetic algorithms, Ales, pp 277–280

    Google Scholar 

  • Dantzig GB, (1951) Maximization of a linear function of variables subject to linear inequalities. In: Koopmans TC (ed) Activity analysis of production and allocation. Wiley, New York

    Google Scholar 

  • Dijkstra EW (1959) A note on two problems in connection with graphs. Numer Math 1:269

    Article  Google Scholar 

  • Dowsland KA (1987) An exact algorithm for the pallet loading problems. EJOR 31:78–84

    Article  Google Scholar 

  • Dowsland KA (1998) Nurse scheduling with tabu search and strategic oscillation. EJOR 106:393–407

    Article  Google Scholar 

  • Dowsland KA, Thompson JM (2000) Solving a nurse scheduling problem with knapsacks, networks and tabu search. J Oper Res Soc 51:825–833

    Google Scholar 

  • Dowsland KA, Herbert EA, Kendall G (2006) Using tree search bounds to enhance a genetic algorithm approach to two rectangle packing problems. EJOR 168:390–402

    Article  Google Scholar 

  • Erlenkotter D (1978) A dual-based procedure for uncapacitated facility location. Oper Res 26:992–1009

    Article  Google Scholar 

  • Fernandes S, Lourenço HR (2007) Hybrids combining local search heuristics with exact algorithms. In: Rodriguez F, MĂ©lian B, Moreno JA, Moreno JM (eds) Proc V Congreso Español sobre MetaheurĂ­sticas, Algoritmos Evolutivos y Bioinspirados, MAEB’2007, Tenerife, 14–16 Feb 2007, pp 269–274

    Google Scholar 

  • Findlay PL, Kobbacy KAH, Goodman DJ (1989) Optimisation of the daily production rates for an offshore oil field. J Oper Res Soc 40:1079–1088

    Google Scholar 

  • Fisher ML (1985) An applications oriented guide to Lagrangian relaxation. Interfaces 15:10–21

    Article  Google Scholar 

  • Floyd RW (1962) Algorithm 97—shortest path. Commun ACM 5:345

    Article  Google Scholar 

  • Ford LR, Fulkerson DR (1956) Maximal flow through a network. Can J Math 18:399–404

    Article  Google Scholar 

  • Fulkerson DR (1961) An out-of-kilter method for minimal cost flow problems. SIAM J Appl Math 9:18–27

    Article  Google Scholar 

  • Garfinkel RS, Nemhauser GL (1969) The set partitioning problem: set covering with equality constraints. Oper Res 17:848–856

    Article  Google Scholar 

  • Glover F, Laguna M (1997) Tabu search. Kluwer, Dordrecht

    Book  Google Scholar 

  • Glover F, Glover R, Lorenzo J, Mcmillan C (1982) The passenger mix problem in the scheduled airlines. Interfaces 12:73–79

    Article  Google Scholar 

  • Golumbic MC (1980) Algorithmic graph theory and perfect graphs. Academic, New York

    Google Scholar 

  • Gutin GM (1999) Exponential neighbourhood local search for the travelling salesman problem. Comput OR 26, 313–320

    Article  Google Scholar 

  • Hayes M, Norman JM (1984) Dynamic programming in orienteering—route choice and the siting of controls. J Oper Res Soc 35:791–796

    Google Scholar 

  • Held M, Karp RM (1970) The travelling salesman problem and minimum spanning trees. Oper Res 18:1138–1162

    Article  Google Scholar 

  • Hindi KS, Fleszar K, Charalambous C (2003) An effective heuristic for the CLSP with setup times. J Oper Res Soc 54:490–498

    Article  Google Scholar 

  • Jarvinen P, Rajala J, Sinervo H (1972) A branch and bound algorithm for seeking the p-median. Oper Res 20:173

    Article  Google Scholar 

  • Johnson TB (1968) Optimum pit mine production scheduling. Technical report, University of California, Berkeley

    Google Scholar 

  • Kamarkar NK (1984) A new polynomial-time algorithm for linear programming. Combinatorica 4:373–395

    Article  Google Scholar 

  • Khachiyan LG, (1979) A polynomial algorithm in linear programming. Dokl. Akad. Nauk SSSR 244:1093–1096 (in Russian) (English transl.: Sov Math Dokl 20:191–194 (1979))

    Google Scholar 

  • Little JDC, Murty KG, Sweeney DW, Karel C (1963) An algorithm for the travelling salesman problem. Oper Res 11:972–989

    Article  Google Scholar 

  • Martello S, Toth P (1981) A branch and bound algorithm for the zero-one multiple knapsack problem. Discret Appl Math 3:275–288

    Article  Google Scholar 

  • Martello S, Toth P (1990) Knapsack problems: algorithms and computer implementations. Wiley, New York

    Google Scholar 

  • Mamer JW, Smith SA (1982) Optimising field repair kits based on job completion rate. Manage Sci 28:1328–1334

    Article  Google Scholar 

  • Minty GJ (1960) Monotone networks. Proc R Soc 257A:194–212

    Google Scholar 

  • Nagar A, Heragu SS, Haddock J (1995) A meta-heuristic algorithm for a bi-criteria scheduling problem. Ann OR 63:397–414

    Article  Google Scholar 

  • Potts CN, van de Velde SL (1995) Dynasearch—iterative local improvement by dynamic programming. Part 1: the TSP. Technical report, University of Twente

    Google Scholar 

  • Ross GT, Soland RM (1975) A branch and bound algorithm for the generalised assignment problem. Math Prog 8:91–103

    Article  Google Scholar 

  • Tamura H, Hirahara A, Hatono I, Umano M (1994) An approximate solution method for combinatorial optimisation—hybrid approach of genetic algorithm and Lagrangian relaxation method. Trans Soc Instrum Control Eng 130:329–336

    Google Scholar 

  • Zykov AA (1949) On some properties of linear complexes. Math Sb 24:163–188

    Google Scholar 

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Author information

Authors and Affiliations

  1. Gower Optimal Algorithms Ltd, Swansea, UK

    Kathryn A. Dowsland

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  1. Kathryn A. Dowsland
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Correspondence to Kathryn A. Dowsland .

Editor information

Editors and Affiliations

  1. Computing Science and Mathematics, University of Stirling, Scotland, United Kingdom

    Edmund K. Burke

  2. Research and Knowledge Transfer, University of Nottingham, Malaysia & UK, Semenyih, Malaysia

    Graham Kendall

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Dowsland, K.A. (2014). Classical Techniques. In: Burke, E., Kendall, G. (eds) Search Methodologies. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-6940-7_2

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