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A Path Relinking Approach for the Multi-Resource Generalized Quadratic Assignment Problem

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4638))

Abstract

We consider the multi-resource generalized quadratic assignment problem (MR-GQAP), which has many applications in various fields such as production scheduling, and constitutes a natural generalization of the generalized quadratic assignment problem (GQAP) and the multi-resource generalized assignment problem (MRGAP). We propose a new algorithm PR-CS for this problem that proves highly effective. PR-CS features a path relinking approach, which is a mechanism for generating new solutions by combining two or more reference solutions. It also features an ejection chain approach, which is embedded in a neighborhood construction to create more complex and powerful moves. Computational comparisons on benchmark instances show that PR-CS is more effective than existing algorithms for GQAP, and is competitive with existing methods for MRGAP, demonstrating the power of PR-CS for handling these special instances of MR-GQAP without incorporating special tailoring to exploit these instances.

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References

  1. Cordeau, J., Gaudioso, M., Laporte, G., Moccia, L.: A memetic heuristic for the generalized quadratic assignment problem. INFORMS Journal on Computing 18, 433–443 (2006)

    Article  MathSciNet  Google Scholar 

  2. Gavish, B., Pirkul, H.: Algorithms for the multi-resource generalized assignment problem. Management Science 37, 695–713 (1991)

    Article  MATH  Google Scholar 

  3. Glover, F.: Genetic algorithms and scatter search: unsuspected potentials. Statistics and Computing 4, 131–140 (1994)

    Article  Google Scholar 

  4. Glover, F.: Tabu search for nonlinear and parametric optimization (with links to genetic algorithms. Discrete Applied Mathematics 49, 231–255 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  5. Glover, F.: Ejection chains, reference structures and alternating path methods for traveling salesman problems, Research Report, University of Colorado, Boulder, CO. Discrete Applied Mathematics 65, 223–253 (1996)

    Google Scholar 

  6. Ibaraki, T., Ohashi, T., Mine, H.: A heuristic algorithm for mixed-integer programming problems. Mathematical Programming Study 2, 115–136 (1974)

    Google Scholar 

  7. Laguna, M., Martí, R.: Scatter Search: Methodology and Implementations in C. Kluwer Academic Publishers, Boston (2003)

    Google Scholar 

  8. Lee, C., Ma, Z.: The generalized quadratic assignment problem, Technical Report. Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, Canada (2003)

    Google Scholar 

  9. Martí, R., Laguna, M., Glover, F.: Principles of scatter search. European Journal of Operational Research 169, 359–372 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  10. Nonobe, K., Ibaraki, T.: A tabu search approach to the CSP (constraint satisfaction problem) as a general problem solver. European Journal of Operational Research 106, 599–623 (1998)

    Article  MATH  Google Scholar 

  11. Voss, S.: Heuristics for nonlinear assignment problems. In: Pardalos, P.M., Pitsoulis, L.S. (eds.) Nonlinear Assignment Problems, pp. 175–215. Kluwer Academic Publishers, Dordrecht (2000)

    Google Scholar 

  12. Yagiura, M., Ibaraki, T., Glover, F.: An ejection chain approach for the generalized assignment problem. INFORMS Journal on Computing 16, 133–151 (2004)

    Article  MathSciNet  Google Scholar 

  13. Yagiura, M., Iwasaki, S., Ibaraki, T., Glover, F.: A very large-scale neighborhood search algorithm for the multi-resource generalized assignment problem. Discrete Optimization 1, 87–98 (2004)

    Article  MATH  MathSciNet  Google Scholar 

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Thomas Stützle Mauro Birattari Holger H. Hoos

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© 2007 Springer-Verlag Berlin Heidelberg

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Yagiura, M. et al. (2007). A Path Relinking Approach for the Multi-Resource Generalized Quadratic Assignment Problem. In: Stützle, T., Birattari, M., H. Hoos, H. (eds) Engineering Stochastic Local Search Algorithms. Designing, Implementing and Analyzing Effective Heuristics. SLS 2007. Lecture Notes in Computer Science, vol 4638. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74446-7_9

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  • DOI: https://doi.org/10.1007/978-3-540-74446-7_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74445-0

  • Online ISBN: 978-3-540-74446-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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