Karesel atama problemleri için tavlama benzetimi paralelleştirme yöntemlerinin karşılaştırılması

Öz

Karesel atama problemi (KAP), NP-hard sınıfındaki en zor kombinatoryal optimizasyon problemlerinden birisidir. Problemin zorluğundan dolayı birçok araştırmacı bu tip atama problemini çalışılmaktadır. Bu çalışmada tavlama benzetimi yöntemi MATLAB platformunda paralelleştirilerek iyi bilinen bir KAP Kütüphanesi olan QAPLIB’den alınan 36 örnek problemi çözmek için kullanılmıştır. Değişik paralelleştirme yöntemlerinin performansları kullanılan problemler için karşılaştırılmıştır. Sonuç olarak seri tavlama benzetimi yöntemiyle karşılaştırıldığında, paralel yöntemlerin uygun parametreler kullanıldığında daha hızlı sonuç verdiği görülmüştür.

Anahtar Kelimeler

• Karesel atama problemi,Paralel programlama,Tavlama benzetimi,Optimizasyon

Comparison of simulated annealing parallelization methods for quadratic assignment problems

Abstract

Quadratic assignment problem (QAP) is one of the most difficult combinatorial optimization problems in the NP-hard class. Due to the difficulty of the problem, many researchers have been studying this type of assignment problem. In this work, simulated annealing method is parallelized on MATLAB platform and is used to solve 36 problems from QAPLIB which is a well-known QAP library. The performance of different parallelization methods is compared for the problems used. As a result, when compared with the serial simulated annealing method, it is seen that the parallel methods give faster results when the appropriate parameters are used.

Keywords

• Quadratic assignment problem,Parallel programming,Simulated annealing,Optimization

References

1. Koopmans TC, Beckmann M. “Assignment problems and the location of economic activities”. Econometrica, 25(1), 53-76, 1957.
2. Loiola EM, de Abreu NMM, Boaventura-Netto PO, Hahn P, Querido T. “A survey for the quadratic assignment problem”. Europian Journal of Operational Research, 176(2), 657-690, 2007.
3. Paul G. “Comparative performance of tabu search and simulated annealing heuristics for the quadratic assignment problem”. Operations Research Letters, 38(6), 577-581, 2010.
4. Onbaşoǧlu E, Özdamar L. “Parallel simulated annealing algorithms in global optimization”. Journal of Global Optimization, 19(1), 27-50, 2001.
5. Ferreiro AM, García JA, López-Salas JG, Vázquez C. “An efficient implementation of parallel simulated annealing algorithm in GPUs”. Journal of Global Optimization, 57(3), 863-890, 2013.
6. Laursen PS. “Parallel heuristic search-introductions and a new approach”. Solving Combinatorial Optimization Problems in Parallel. Editors: Ferreira A, Pardalos P. Lecture Notes in Computer Science, 1054, 248-274, 1996.
7. Holmqvist K, Migdalas A, Pardalos PM. Parallelized Heuristics for Combinatorial Search. Editors: Migdalas A, Pardalos PM, Storøy S. Parallel Computing in Optimization, 269-294, Boston, MA, USA, Springer, 1997.
8. Hussin MS, Stützle T. “Tabu search vs. simulated annealing as a function of the size of quadratic assignment problem instances”. Computers & Operation Research, 43, 286-291, 2014.

9. Said GAENA, Mahmoud AM, El-Horbaty ESM. “A comparative study of meta-heuristic algorithms for solving quadratic assignment problem”. International Journal of Advanced Computer Science and Applications, 5(1), 1-6, 2014.
10. Karami M, Niroomand S, Mirzaei N, Vizvari B. “Analysis and performance measurement of existing solution methods of quadratic assignment problem”. International Journal of Electronics, Mechanical and Mechatronics Engineering, 3(2), 557-570, 2014.
11. Ghandeshtani KS, Mollai N, Seyedkashi SMH, Neshati MM. “New simulated annealing algorithm for quadratic assignment problem”. ADVCOMP 2010: The Fouth International Conference on Advanced Engineering Computing and Applications in Sciences, Florence, Italy, 25-30 October 2010.
12. Wang JC. “A multistart simulated annealing algorithm for the quadratic assignment problem”. 3rd International Conference on Innovations in Bio-Inspired Computing and Applications, Kaohsiung, Taiwan, 26-28 September 2012.
13. Kovac M. “Solving quadratic assignment problem in parallel using local search with simulated annealing elements”. The International Conference on Digital Technologies 2013, Zilina, Slovakia 29-31 May 2013.
14. Kaviani MA, Abbasi M, Rahpeyma B, Yusefi MM. “A hybrid tabu search-simulated annealing method to solve quadratic assignment problem”. Decision Science Letters, 3(3), 391-396, 2014.
15. Paul G. “A GPU implementation of the simulated annealing heuristic for the quadratic assignment problem”. Computing Research Repository, arXiv: 1208.2675, 2012.
16. Rao SS. Engineering Optimization Theory and Practice. 4th ed. New Jersey, USA, Wiley, 2009.
17. Chen H, Flann NS, Watson DW. “Parallel genetic simulated annealing: a massively parallel SIMD algorithm”. IEEE Transactions on Parallel and Distributed Systems, 9(2), 126-136, 1998.
18. Burkard RE, Çela E, Karisch SE, Rendl F. "QAPLIB”. http://anjos.mgi.polymtl.ca/qaplib/ (09.05.2017).
19. Nugent CE, Vollmann TE, Ruml J. “An experimental comparison of techniques for the assignment of facilities to locations”. Operations Research, 16(1), 150-173, 1968.
20. Skorin-Kapov J. “Tabu search applied to the quadratic assignment problem”. ORSA Journal of Computing, 2(1), 33-45, 1990.
21. Burkard RE, Karisch SE, Rendl F. “QAPLIB A quadratic assignment problem library”. Journal of Global Optimization, 10(4), 391-403, 1997.
22. Li Y, Pardalos PM. “Generating quadratic assignment test problems with known optimal permutations”. Computational Optimization and Applications, 1(2), 163-184, 1992.