A Novel Permutation Based Solution Representation Technique for Vehicle Routing Problems on GPUs

Abstract

In this study, the vehicle routing problem (VRP) which is a well-known NP-hard combinatorial optimization problem is handled on graphic processing units (GPUs). Solving any kind of VRP is extremely hard when the instance size is large. For this reason, researchers tend to solve the VRP with meta-heuristics. Although, many well-designed meta-heuristics produce near-optimal solutions in reasonable time, still a challenge to solve large scale instances. To accomplish this issue, researchers need novel, fast and wisely designed parallel operators for the proposed algorithms. Furthermore, the success of these operators directly depends on the way the solution is represented. This paper offers a new permutation based solution representation technique (π+) for vehicle routing problems on GPUs. Results show that proposed technique can be used in many algorithms to accelerate computations.

Keywords

• vehicle routing problem
• parallel programming
• GPU

Araç Rotalama Problemleri için Grafik İşlem Birimleri Üzerinde Yeni Bir Çözüm Gösterim Tekniği

Abstract

Bu çalışmada, NP-Hard kombinatorik optimizasyon problemlerinden olan araç rotalama problemi (ARP), grafik işlem birimleri (GPU) üzerinde ele alınmıştır. Problem boyutunun büyümesiyle birlikte ARP'nin herhangi bir türünü optimal olarak çözmek oldukça zorlaşmaktadır. Araştırmacılar bu yüzden metasezgisel yöntemlere yönelmektedir. Her ne kadar bu metasezgisel algoritmalar kabul edilebilir sürelerde optimale yakın sonuçlar üretse de büyük boyutlu problemler için bu durum farklıdır. Bu durumu aşmak için, araştırmacılar önerilen algoritmalar için yeni, hızlı ve akıllıca tasarlanmış paralel operatörlere ihtiyacı bulunmaktadır. Bu operatörlerin başarısı doğrudan çözümün temsil edilme şekline bağlıdır. Bu makale, ARP'yi GPU'lar üzerinde etkin bir şekilde ele alabilmek için yeni bir permütasyon tabanlı çözüm gösterim tekniği (π +) sunmaktadır. Sonuçlar, önerilen tekniğin hesaplamaları hızlandırmak için birçok algoritmada kullanılabileceğini göstermektedir.

Keywords

• Araç rotalama problemi
• Paralel programlama
• GPU

References

1. Gilbert Laporte, The vehicle routing problem: An overview of exact and approximate algorithms, European Journal of Operational Research, vol. 5 no. 3, pp. 345-358, 1992.
2. G. Dantzig ve J. Ramser, The Truck Dispatching Problem, Management Science, vol 6, pp. 80-91, 1959.
3. P. Toth ve D. Vigo, The granular tabu search and its application to the vehicle-routing problem, Informs Journal on Computing, vol. 15, no. 4, 2003.
4. D. Pisinger ve S. Ropke, A general heuristic for vehicle routing problems, Computers & Operations Research, vol 34, pp. 2403-2435, 2007.
5. S. N. Kumar ve R. Panneerselvam, A Survey on the Vehicle Routing Problem and Its Variants, Intelligent Information Management, vol. 4, pp. 66-74, 2012.
6. E. Taillard, . P. Badeau, . M. Gendreau, . F. Guertin ve J.-Y. Potvin, A Tabu Search Heuristic for the Vehicle Routing Problem with Soft Time Windows, Transportation Science, vol 31, no. 2, pp. 101-195, 1997.
7. K. Fleszar, I. Osman ve K. Hindi, Avariable neighbourhood search for the open vehicle routing problem, European Journal of Operational Research, vol. 195, pp. 803-809, 2009.
8. Bin Yu, Zhong-Zhen Yang, Baozhen Yao, An improved ant colony optimization for vehicle routing problem, European Journal of Operational Research, vol. 196, no. 1, pp. 171-176, 2009.

9. S. Tsutsui ve N. Fujimoto, Solving Quadratic Assignment Problems by Genetic Algorithms with GPU Computation: A Case Study, GECCO, Montreal, 2009.
10. S. Tsutsui ve N. Fujimoto, Fast QAP Solving by ACO with 2-opt Local Search on a GPU, IEEE Section Congres, San Francisco, 2011.
11. M. Czapinski, An effective Parallel Multistart Tabu Search for Quadratic Assignment Problem CUDA platform, J. Parallel Distrib. Comput. , vol. 73, pp. 1461-1468, 2013.
12. E. Özçetin, G. Öztürk, A Parallel Iterated Local Search Algorithm on GPUs for Quadratic Assignment Problem, International Journal of Engineering Technologies, vol. 4, no. 2, pp. 123-127, 2018.
13. E. Özçetin, G. Öztürk, A Hybrid Genetic Algorithm for the Quadratic Assignment Problem on Graphics Processing Units, Anadolu University Journal of Science and Technology-A Applied Sciences and Engineering, vol. 17, no. 1, pp. 167-180, 2016.
14. J. M. Cecilia, J. M. Garcia, A. Nisbet, M. Amos ve M. Ujaldon, Enhancing data parallelism for Ant Colony Optimization on GPUs, J. Parallel Distrib. Comput. , vol. 73, pp. 42-51, 2013.
15. A. Delevacq, P. Delisle, M. Gravel ve M. Krajecki, Parallel Ant Colony Optimization on Graphics Processing Units, J. Parallel Distrib. Comput. , vol. 73, pp. 52-61, 2013.
16. C. Shulz, Efficient local search on the GPU—Investigations on the vehicle routing problem, J. Parallel Distrib. Comput., vol. 73, no.1, pp. 14-31, 2013.
17. C. Groer, B. Golden ve E. Wasil, A Parallel Algorithm for the Vehicle Routing Problem, INFORMS Journal on Computing, vol. 23, pp. 315-330, 2011.
18. J. Szymon ve Z. Dominik, Solving Multi-criteria Vehicle Routing Problem by Parallel Tabu Search on GPU, Procedia Computer Science, vol. 18, pp. 2529-2532, 2013.
19. T. Davidović, P. Hansen, N. Mladenovic, Permutation-based genetic, tabu, and variable neighborhood search heuristics for multiprocessor scheduling with communication delays, Asia Pacific Journal of Operational Research, vol. 22, no.3, 2005.
20. A. Klöckner, N. Pinto, Y. Lee, B. Catanzaro, P. Ivanov ve A. Fasih, PyCUDA and PyOpenCL: A scripting-based approach to GPU run-time code generation, Parallel Computing, vol. 38, no. 3, pp. 157-174, 2012.