Advertisement

A Hybrid Optimization GNA Algorithm for the Quadratic Assignment Problem Solving

  • Kefaya QaddoumEmail author
  • Azmi Al Azzam
Conference paper
Part of the Lecture Notes on Data Engineering and Communications Technologies book series (LNDECT, volume 29)

Abstract

The quadratic assignment problem (QAP) was considered one of the most significant combinatorial optimization problems due to its variant and substantial applications in real life such as scheduling, production, computer manufacture, chemistry, facility location, communication, and other fields. QAP is an NP-hard problem that is impossible to be solved in polynomial time when the problem size increases, hence heuristic and metaheuristic approaches are utilized for solving the problem instead of exact methods. Optimization plays a significant role in easing this problem. In this paper, we will provide a solution to optimize QAP. In the QAP problem, there is a total of facilities (departments, company’s,…etc.) that must be located to minimize the flow (amount of material to be exchanged). Thus, the objective function is composed by multiplying both distances between the locations and the flow among these facilities. Global Neighborhood (GNA) Algorithm will be used to optimize the QAP problem, and the solution will also be compared to the well-known Genetic Algorithm (GA).

References

  1. 1.
    Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1, 67–82 (1997)CrossRefGoogle Scholar
  2. 2.
    Glover, F.: The future paths for integer programming and links to artificial intelligence. Comput. Oper. Res. 13(5), 533–549 (1986)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Reeves, C.R.: Modern Heuristic Techniques for Combinatorial Optimization Problems. Blackwell Scientific, Oxford (1993)Google Scholar
  4. 4.
    Lee, K.S., Geem, Z.W.: A new structural optimization method based on the harmony search algorithm. Comput. Struct. 82, 781–798 (2004)CrossRefGoogle Scholar
  5. 5.
    Lee, K.S., Geem, Z.W.: A new meta-heuristic algorithm for continuous engineering optimization. Comput. Methods Appl. Mech. Eng. 194(2005), 3902–3933 (2005)CrossRefGoogle Scholar
  6. 6.
    Omran, M.G., Mahdavi, M.: Global-best harmony search. Appl. Math. Comput. 198, 643–656 (2008)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Rechenberg, I.: Cybernetic solution path of an experimental problem, Royal Aircraft Establishment, Library Translation no. 1122 (1965)Google Scholar
  8. 8.
    Fogel, L.J., Owens, A.J., Walsh, M.J.: Artificial Intelligence Through Simulated Evolution. Wiley, Chichester (1996)zbMATHGoogle Scholar
  9. 9.
    De Jong, K.: Analysis of the behavior of a class adaptive systems, Ph.D. Thesis. University of Michigan, Ann Arbor, MI (1975)Google Scholar
  10. 10.
    Koza, J.R.: Genetic programming: a paradigm for genetically breeding populations of computer programs to solve problems, Report No. STAN-CS-90- 1314. Stanford University, Stanford, CA (1990)Google Scholar
  11. 11.
    Goldberg, D.E.: Genetic Algorithms in Search Optimization and Machine Learning. Addison-Wesley, Boston (1989)zbMATHGoogle Scholar
  12. 12.
    Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)Google Scholar
  13. 13.
    Glover, F.: Heuristic for integer programming using surrogate constraints. Decis. Sci. 8(1), 156–166 (1977)CrossRefGoogle Scholar
  14. 14.
    Dorigo, M., Maniezzo, V., Colorni, A.: The ant system: optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybernet. 26(1), 29–41 (1996)CrossRefGoogle Scholar
  15. 15.
    Kennedy, J., Eberhart, R.: Particle swarm optimization. In: IEEE International Conference on Neural Networks Perth, Australia, pp. 1942–1948 (1995)Google Scholar
  16. 16.
    Geem, Z.W., Kim, J.H., Loganathan, G.: A new heuristic optimization algorithm: harmony search. Simulation 76(2), 60 (2001)CrossRefGoogle Scholar
  17. 17.
    Nakrani, S., Tovey, C.: On honey bees and dynamic server allocation in internet hosting centers. Adapt. Behav. 12(3–4), 223 (2004)CrossRefGoogle Scholar
  18. 18.
    Kirkpatrick, S., Gelatt, C., Vecchi, M.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Rashedi, E., Nezamabadi, H., Saryazdi, S.: GSA: a gravitational search algorithm. Inform. Sci. 179(13), 2232–2248 (2009)CrossRefGoogle Scholar
  20. 20.
    Engelbrecht, A.P.: Fundamentals of Computational Swarm Intelligence. Wiley, Hoboken (2006)Google Scholar
  21. 21.
    Dorigo, M., Gambardella, L.M.: Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans. Evol. Comput. 1(1), 53–66 (1997)CrossRefGoogle Scholar
  22. 22.
    Eberhart, R., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science MHS 1995, pp. 39–43. IEEE (1995)Google Scholar
  23. 23.
    Alazzam, A., Lewis III, H.: A new optimization algorithm for combinatorial problems. (IJARAI) Int. J. Adv. Res. Artif. Intell. 2(5) (2013)Google Scholar
  24. 24.
    Nugent, C.E., Vollman, T.E., Ruml, J.: An experimental comparison of techniques for the assignment of facilities to locations. Operations (1968)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Higher Colleges of TechnologyAbu DhabiUAE

Personalised recommendations