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Properties of Some Combinatorial Optimization Problems and Their Effect on the Performance of Integer Programming and Constraint Logic Programming

Published: 01 August 1998 Publication History

Abstract

<P>The comparative performance of Integer Programming (IP) and Constraint Logic Programming (CLP) is explored by examining a number of models for four different combinatorial optimization applications. Computational results show contrasting behavior for the two approaches, and an analysis of performance with respect to problem and model characteristics is presented. The analysis shows that tightness of formulation is of great benefit to CLP where effective search reduction results in problems that can be solved quickly. In IP, if the linear feasible region does not identify the corresponding integer polytope, the problem may be difficult to solve. The paper identifies other characteristics of model behavior and concludes by examining ways in which IP and CLP may be incorporated within hybrid solvers.</P>

References

[1]
R. K. AHUJA, T.L. MAGNANTI, and J. B. ORLIN, 1993. Network Flows: Theory, Algorithms and Applications, Prentice Hall, Englewood Cliffs, New Jersey.
[2]
K. R. BAKER, 1974. Introduction to Sequencing and Scheduling, John Wiley, New York.
[3]
CPLEX OPTIMIZATION, INC, 1992. Using the CPLEX Callable Library and CPLEX Mixed Integer Library, CPLEX Optimization, Inc, Suite 279, 930 Tahoe Blvd., Bldg. 802, Incline Village, NV 89451-9436, USA.
[4]
K. DARBY-DOWMAN and J. LITTLE, 1997. A Golf Scheduling Problem, Technical Report, Department of Mathematics and Statistics, Brunel University, Uxbridge, Middlesex, England.
[5]
K. DARBY-DOWMAN, J. LITTLE, G. MITRA, and M. ZAFFALON, 1997. Constraint Logic Programming and Integer Programming Approaches and Their Collaboration in Solving an Assignment Scheduling Problem, Constraints, An International Journal 1:3, 245-264.
[6]
K. DARBY-DOWMAN and G. MITRA, 1985. An Extension of Set Partitioning with Application to Scheduling Problems, European Journal of Operational Research 21, 200-205.
[7]
EUROPEAN COMPUTER RESEARCH CENTRE, 1994. ECLiPSe User Guide, ECRC GmbH, Arabellastr. 17, Munich, Germany.
[8]
M. FISHER, 1995. Vehicle Routing, Chapter 1 in, Handbooks in Operations Research and Management Science Vol. 8, M. O. Ball, T. L. Magnanti, C. L. Monma, and G. L. Nemhauser (eds), Elsevier Science B.V., Amsterdam.
[9]
L. R. FOULDS and J. M. WILSON, 1997. A Variation of the Generalized Assignment Problem Arising in the New Zealand Dairy Industry, Annals of Operations Research 69, 105-114.
[10]
K. L. HOFFMAN and M. PADBERG, 1993. Solving Airline Crew Scheduling Problems by Branch and Cut, Management Science 39:6, 657-682.
[11]
J. KRARUP and P. PRUZAN, 1983. The Simple Plant Location Problem: Survey and Synthesis, European Journal of Operational Research 12, 36-81.
[12]
S. MARTELLO and P. TOTH, 1990. Knapsack Problems: Algorithms and Computer Implementations, John Wiley, Chichester.
[13]
G. MITRA and K. DARBY-DOWMAN, 1985. CRU-SCHED--A Computer Based Bus Crew Scheduling System Using Integer Programming, in Computer Scheduling of Public Transport 2, J.M. Rousseau (ed), Elsevier Science B.V., Amsterdam.
[14]
R. RODOSEK, M.G. WALLACE, and M. T. HAJIAN, 1996. A New Approach to Integrate Mixed Integer Programming with CLP, Proceedings of the CP96 Workshop on Constraint Programming Applications: An Inventory and Taxonomy, 45-54, Cambridge, Massachusetts.
[15]
D. M. RYAN and B. A. FOSTER, 1981. An Integer Programming Approach to Scheduling, in Computer Scheduling of Public Transport, A. Wren (ed), Elsevier Science B.V., Amsterdam, 269-280.
[16]
J. A. M. SCHREUDER, 1980. Constructing Timetables For Sport Competitions, Mathematical Programming Study 13, 58-67.
[17]
B. M. SMITH, S.C. BRAILSFORD, P.M. HUBBARD, and H. P. WILLIAMS, The Progressive Party Problem: Integer Linear Programming and Constraint Programming Compared, Constraints, An International Journal 1:1/2, 119-138.

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cover image INFORMS Journal on Computing
INFORMS Journal on Computing  Volume 10, Issue 3
August 1998
97 pages

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INFORMS

Linthicum, MD, United States

Publication History

Published: 01 August 1998

Author Tags

  1. Combinatorial optimization
  2. Mathematical programming
  3. computational performance
  4. constraint logic programming
  5. integer programming
  6. search strategies

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