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Generalized assignment-type problems a powerful modeling scheme

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Practice and Theory of Automated Timetabling II (PATAT 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1408))

Abstract

Assignment-type problems and their generalized versions appear to be powerful modeling tools. In this paper we formulate several combinatorial problems and timetabling and scheduling applications as such problems. Neighborhood search techniques are very appropriate for dealing with these problems. Four different methods (descent method, Tabu search method, exchange procedure, and simulated annealing) and several restarting strategies are reviewed. Finally, we indicate how population-based techniques can be used to deal with these problems.

This research was supported by NSERC grant OGP 0008312, FCAR grant ER-1654, and FRSQ grant 930913

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References

  1. Aubin, J., Ferland, J.A.: A Large Scale Timetabling Problem. Computers and Operations Research 16 (1989), 67–77.

    Article  MATH  MathSciNet  Google Scholar 

  2. Berrada, I., Ferland, J.A., Michelon, P.: A Multi-Objective Approach to Nurse Scheduling with both Hard and Soft Constraints. Socio-Economic Planning Science 30 (1996), 183–193.

    Article  Google Scholar 

  3. Charest, M., Ferland, J.A.: Preventive Maintenance Scheduling of Power Generating Units. Annals of Operations Research 41 (1993), 185–206.

    Article  MATH  Google Scholar 

  4. Costa, D.: Méthodes de résolution constructives, séquentielles et évolutives pour des problèmes d’affectations sous contraintes. Doctoral dissertation, Department of Mathematics, école Polytechnique Fédérale de Lausanne, Lausanne, Switzerland (1995).

    Google Scholar 

  5. Costa, D.: An Evolutionary Tabu Search Algorithm and the NHL Scheduling Problem. INFOR 33 (1995), 161–178.

    MATH  Google Scholar 

  6. Davis, L.: Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York (1991).

    Google Scholar 

  7. Ferland, J.A., Berrada, I., Nabli, I., Ahiod, B., Michelon, P., Gascon, V.: Generalized Assignment-Type Goal Programming Problem and Application to Nurse Scheduling. Publication #1112, Département d’informatique et de recherche opérationnelle, Université de Montréal, Montréal, Canada (1998).

    Google Scholar 

  8. Ferland, J.A., Fleurent, C.: Computer Aided Scheduling for a Sport League. INFOR 29 (1991), 14–25.

    Google Scholar 

  9. Ferland, J.A., Hertz, A., Lavoie, A.: An Object-Oriented Methodology for Solving Assignment-Type Problems with Neighborhood Search Techniques. Operations Research 44 (1996), 347–359.

    Article  MATH  MathSciNet  Google Scholar 

  10. Ferland, J.A., Ichoua, S., Lavoie, A., Gagné, E.: Scheduling Medical School Students’ Internships Using Tabu Search Methods with Intensification and Diversification. Publication #1068, département d’informatique et de recherche opérationnelle, Université de Montréal, Montréal, Canada (1998).

    Google Scholar 

  11. Ferland, J.A., Lavoie, A.: Exchange Procedures for Timetabling Problems. Discrete Applied Mathematics 35 (1992), 237–253.

    Article  MATH  Google Scholar 

  12. Fleurent, C., Ferland, J.A.: Object-Oriented Implementation of Heuristic Search Methods for Graph Coloring, Maximum Clique, and Satisfiability. DIMACS Series in Discrete Mathematics and Theoretical Computer Science 26 (1996), 619–652.

    MATH  Google Scholar 

  13. Fleurent, C., Ferland, J.A.: Genetic and Hybrid Algorithms for Graph Coloring. Annals of Operations Research 63 (1996), 437–461.

    Article  MATH  Google Scholar 

  14. Fleurent, C., Ferland, J.A.: Genetic Hybrids for the Quadratic Assignment Problem. DIMACS Series in Discrete Mathematics and Theoretical Computer Science 16 (1994), 173–187.

    MATH  MathSciNet  Google Scholar 

  15. Glover, F.: Future Paths for Integer Programming and Links to Artificial Intelligence. Computer and Operations Research 13 (1986), 533–549.

    Article  MATH  MathSciNet  Google Scholar 

  16. Glover, F. and Laguna, M.: Tabu Search. In: Reeves, C. (ed): Combinatorial Problems. Blackwell Scientific Publishing, New-York (1993), 70–150.

    Google Scholar 

  17. Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading Massachusetts (1989).

    MATH  Google Scholar 

  18. Hansen, P.: The Steepest Ascent, Mildest Descent Heuristic for Combinatorial Programming. Congress on Numerical Methods in Combinatorial Optimization, Capri, Italy (1986).

    Google Scholar 

  19. Hertz, A., DeWerra, D.: Using Tabu Search Techniques for Graph Coloring. Computing 39 (1987), 345–351.

    Article  MATH  MathSciNet  Google Scholar 

  20. Hillier, F.S., Lieberman, G.J.: Introduction to Operations Resarch. 5th edn. McGraw-Hill, New York (1990).

    Google Scholar 

  21. Johnson, D.S., Aragon, C.R., McGeoch, L.A., Shevon, C.: Optimisation by Simulated Annealing: An Experimental Evaluation; Part I, Graph Partitioning. Operations Research 37 (1989), 865–892.

    MATH  Google Scholar 

  22. Kelly, J.P., Lagana, M., Glover, F.: A Study of Diversification Strategies for the Quadratic Assignment Problem. Computers and Operations Research 21 (1994), 885–893.

    Article  MATH  Google Scholar 

  23. Reeves, C. (ed.): Modern Heuristic Techniques for Combinatorial Problems. Blackwell Scientific Publishing, New York (1993).

    MATH  Google Scholar 

  24. Robert, V.: La confection d’horaires par décomposition en sous-problèmes d’affectation. Doctoral dissertation, Department of Mathematics, école Polytechnique Fédérale de Lausanne, Lausanne, Switzerland (1996).

    Google Scholar 

  25. Ross, C.T., Soland, R.M.: A Branch and Bound Algorithm for the Generalized Assignment Problem. Mathematical Programming 3 (1975), 91–103.

    Article  MathSciNet  Google Scholar 

  26. Sherali, H.D.: Equivalent Weights for Lexicographic Multi-Objective Programs: Characterizations and Computations. European Journal of Operational Research 11 (1981), 367–379.

    Article  MathSciNet  Google Scholar 

  27. Steuer, R.E.: Multiple Criteria Optimization: Theory, Computation, and Application. Krieger, Malabar Florida (1989).

    MATH  Google Scholar 

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Edmund Burke Michael Carter

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© 1998 Springer-Verlag Berlin Heidelberg

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Ferland, J.A. (1998). Generalized assignment-type problems a powerful modeling scheme. In: Burke, E., Carter, M. (eds) Practice and Theory of Automated Timetabling II. PATAT 1997. Lecture Notes in Computer Science, vol 1408. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055881

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  • DOI: https://doi.org/10.1007/BFb0055881

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  • Print ISBN: 978-3-540-64979-3

  • Online ISBN: 978-3-540-49803-2

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