RAMP: A New Metaheuristic Framework for Combinatorial Optimization

  • César Rego
Chapter
Part of the Operations Research/Computer Science Interfaces Series book series (ORCS, volume 30)

Abstract

We propose a new metaheuristic framework embodied in two approaches, Relaxation Adaptive Memory Programming (RAMP) and its primal-dual extension (PD-RAMP). The RAMP method, at the first level, operates by combining fundamental principles of mathematical relaxation with those of adaptive memory programming, as expressed in tabu search. The extended PD- RAMP method, at the second level, integrates the RAMP approach with other more advanced strategies. We identify specific combinations of such strategies at both levels, based on Lagrangean and surrogate constraint relaxation on the dual side and on scatter search and path relinking on the primal side, in each instance joined with appropriate guidance from adaptive memory processes. The framework invites the use of alternative procedures for both its primal and dual components, including other forms of relaxations and evolutionary approaches such as genetic algorithms and other procedures based on metaphors of nature.

Keywords

RAMP Scatter Search Surrogate Constraints Lagrangean Relaxation Cross-Parametric Relaxation Subgradient Optimization Adaptive Memory Metaheuristics Combinatorial Optimization 
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References

  1. Duarte, R., C. Rego and D. Gamboa (2004) “A Filter and Fan Approach for the Job Shop Scheduling Problem: A Preliminary Study,” in Proceedings: International Conference on Knowledge Engineering and Decision Support, 401–406.Google Scholar
  2. Glover, F. (1965) “A Multiphase-Dual Algorithm for the Zero-One Integer Programming Problem,” Operations Research, 13:879–919.MATHMathSciNetGoogle Scholar
  3. Glover, F. (1968) “Surrogate Constraints,” Operations Research, 16(4):741–749.MATHMathSciNetGoogle Scholar
  4. Glover, F. (1975) “Surrogate Constraint Duality in Mathematical Programming,” Operations Research, 23(3):434–451.MATHMathSciNetGoogle Scholar
  5. Glover, F. (1997) “A Template for Scatter Search and Path Relinking,” in Lecture Notes in Computer Science, 1363, J.K. Hao, E. Lutton, E. Ronald, M. Schoenauer, D. Snyers (Eds.), 13–54.Google Scholar
  6. Greenberg, H.J. and W.P. Pierskalla (1970) “Surrogate Mathematical Proramming,” Operations Research, 18:1138–1162.MathSciNetGoogle Scholar
  7. Greistorfer, P., C. Rego and B. Alidaee “Simple Filter-and-Fan Approach for the Facility Location Problem,” Research Report, Hearin Center for Enterprise Science, School of Business Administration, University of Mississippi, USA.Google Scholar
  8. Held, M., P. Wolfe and H.P. Crowder (1975) “Validation of Subgradient Optimization,” Mathematical Programming, 6:62–88.CrossRefMathSciNetGoogle Scholar
  9. Lorena, L.A.N. and M.G. Narciso (1999) “Lagrangean/Surrogate Relaxations for the Generalized Assignment Problems,” European Journal of Operational Research, 114(1): 165–177.CrossRefMATHGoogle Scholar
  10. Lorena, L.A.N. and F.B. Lopes (1994) “A Surrogate Heuristic for Set Covering Problems,” European Journal of Operational Research, 79:138–150.CrossRefMATHGoogle Scholar
  11. Martello, S., D. Pisinger and P. Toth (2000), “New Trends in Exact Algorithms for the 0-1 Knapsack Pproblem,” European Journal of Operational Research, 123:325–332.CrossRefMathSciNetMATHGoogle Scholar
  12. Pisinger, D. (1999a) “Core problems in Knapsack Algorithms,” Operations Research, 47:570–575.MATHMathSciNetCrossRefGoogle Scholar
  13. Pisinger, D. (1999b) “An Exact Algorithm for Large Multiple Knapsack Problems”, European Journal of Operational Research, 114:528–541.CrossRefMATHGoogle Scholar
  14. Pisinger, D. (2004) “Where are the hard knapsack problems?,” Computers and Operations Research, to appear.Google Scholar
  15. Poljak, B.T. (1969) “Minimization of Unsmooth Functionals,” USSR Computational Mathematics and Mathematical Physics, 9:14–29.CrossRefGoogle Scholar
  16. Rego, C. and F. Glover (2002) “Local Search and Metaheuristics for the Traveling Salesman Problem,” in book The Traveling Salesman Problem and its Variations, G. Gutin and A. Punnen Editors, Kluwer Academic Publishers, 309–368.Google Scholar
  17. Rego, C., H. Li, and F. Glover (2004) “Adaptive and Dynamic Search Neighborhoods for Protein Folding in a 2D-HP Lattice Model”, Research Report, Hearin Center for Enterprise Science, School of Business Administration, University of Mississippi, USA.Google Scholar
  18. Rego, C., L. Sagbansua, B. Alidaee, and F. Glover (2004) “RAMP and Primal-Dual RAMP Algorithms for the Multi-Resource Generalized Assignment Problem,” Research Report, Hearin Center for Enterprise Science, School of Business Administration, University of Mississippi, USA.Google Scholar
  19. Yagiura, M., T. Ibaraki, and F. Glover (2004a) “A Path Relinking Approach with Ejection Chains for the Generalized Assignment Problem,” European Journal of Operational Research, to appear.Google Scholar
  20. Yagiura, M., T. Ibaraki and F. Glover (2004b) “An Ejection Chain Approach for the Generalized Assignment Problem,” INFORMS Journal on Computing, 16(2):133–151.CrossRefMathSciNetGoogle Scholar
  21. Yagiura, M., S. Iwasaki, T. Ibaraki and F. Glover (2004) “A Very Large-Scale Neighborhood Search Algorithm for the Multi-Resource Generalized Assignment Problem,” Discrete Optimization, 1:87–98.CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2005

Authors and Affiliations

  • César Rego
    • 1
  1. 1.Hearin Center for Enterprise Science, School of Business AdministrationUniversity of MississippiUniversityUSA

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