Abstract
This paper deals with the mathematical modelling of a scheduling problem in a heterogeneous CPU/FPGA architecture with heterogeneous communication delays in order to minimize the makespan, \(C_{max}\). This study was motivated by the quality of the available solvers for Mixed Integer Program. The proposed model includes the communication delay constraints in a heterogeneous case, depending on both tasks and computing units. These constraints are linearized without adding any extra variables and the obtained linear model is reduced to speed-up the solving with CPLEX up to 60 times. Computational results show that the proposed model is promising. For an average sized problem of up to 50 tasks and five computing units the solving time under CPLEX is a few seconds.
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References
Ait El Cadi, A., (2004). Automatisation de la parallélisation de systèmes complexes avec application l’environnement Matlab/Simulink., Thèse (M.Sc.A.)-École Polytechnique de Montréal.
Ali, H., & El-Rewini, H., (1990). An optimal algorithm for scheduling interval ordered tasks with communication on N processor, University of Nebraska at Omaha, Math. And Computer Science Department, Technical. Report, 9120
Baker, K. R., & Trietsch, D. (2009). Principles of sequencing and scheduling. London: Wiley.
Banharnsakun, A., Sirinaovakul, B., & Achalakul, T. (2012). Job shop scheduling with the best-so-far ABC. Engineering Applications of Artificial Intelligence, 25(3), 583593.
Cakici, E., & Mason, S. J. (2007). Parallel machine scheduling subject to auxiliary resource constraints. Production Planning and Control, 18, 217225.
Catalyurek, U. V., Boman, E. G., Devine, K. D., Bozda, D., Heaphy, R. T., & Riesen, L. A. (2009). A repartitioning hypergraph model for dynamic load balancing. Journal of Parallel and Distributed Computing, 69, 711–724.
Chen, W. H., & Lin, C. S. (2000). A hybrid heuristic to solve a task allocation problem. Computers and Operations Research, 27(3), 287–303.
Chrétienne, P., & Picouleau, C. (1995). Scheduling with communication delays: A survey. In P. Chrétienne, E. G. Coffman, J. K. Lenstra, & Z. Liu (Eds.), Scheduling theory and its applications (p. 6590). New York: Wiley.
Darte, A., Robert, Y., & Vivien, F. (2000). Scheduling and automatic parallelization. Boston: Birkhäuser.
Dauzère-Pérès, S., & Sevaux, M. (2003). Using Lagrangean relaxation to minimize the weighted number of late jobs on a single machine. Naval Research Logistics, 50(3), 273288.
Davidović, T., Liberti, L., Maculan, N., & Mladenović, N., (2007). Towards the optimal solution of the multiprocessor scheduling problem with communication delays. In MISTA proceedings.
Davidović, T., Hansen, P., & Mladenović, N. (2005). Permutation-based genetic, tabu and variable neigh-borhood search heuristics for multiprocessor scheduling with communication delays. Asia-Pacific Journal of Operational Research, 22(3), 297326.
El-Rewini, H., Ali, H. H., & Lewis, T. G. (1994). Task scheduling in parallel and distributed systems. Englewood Cliffs, NJ: Prentice-Hall.
Flynn, M. (1972). Some computer organizations and their effectiveness. IEEE Transactions on Computers, 100(9), 948–960.
Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: A guide to the theory of NP-completeness. San Fran-cisco: WH Freeman & Co.
Gen, M., & Lin, L. (2014). Multiobjective evolutionary algorithm for manufacturing scheduling problems: State-of-the-art survey. Journal of Intelligent Manufacturing, 25(5), 849866.
Hao, X., Gen, M., Lin, L., & Suer, G. A. (2015). Effective multiobjective EDA for bi-criteria stochastic job-shop scheduling problem. Journal of Intelligent Manufacturig. doi:10.1007/s10845-014-1026-0.
Harris, J. M. (2000). Combinatorics and graph theory. New York: Springer.
Hartmann, S., & Briskorn, D. (2010). A survey of variants and extensions of the resource-constrained oroject scheduling problem. European Journal of Operational Research, 207, 1–14.
Huong, G. N. T., Na, Y., & Kim, S. W. (2011). Applying frame layout to hardware design in FPGA for seamless support of cross calls in CPU–FPGA coupling architecture. Microprocessors and Microsystems, 35, 462–472.
Hwang, R., Gen, M., & Katayama, H. (2008). A comparison of multiprocessor task scheduling algorithms with communication costs. Computers & Operations Research, 35, 976993.
Isaak, G. (1994). Scheduling rooted forests with communication delays. Order, 11, 309316.
Jong-Kook, K., Shivle, S., Siegel, H. J., Maciejewski, A. A., Braun, T. D., Schneider, M., et al. (2007). Dynamically mapping tasks with priorities and multiple deadlines in a heterogeneous environment. Journal of Parallel and Distributed Computing, 67, 154169.
Knuth, D. E. (1997). The art of computer programming (3rd ed., Vol. 1). Boston: Addison-Wesley.
Koné, O., Artigues, C., Lopez, P., & Mongeau, M. (2011). Event-based MILP models for resource-constrained project scheduling problems. Computers & Operations Research, 38, 3–13.
Korkhov, V. V., Moscicki, J. T., & Krzhizhanovskaya, V. V. (2009). Dynamic workload balancing of parallel applications with user-level scheduling on the grid. Future Generation Computer Systems, 25, 28–34.
Long, Q., Lin, J., & Sun, Z. (2011). Agent scheduling model for adaptive dynamic load balancing in agent-based distributed simulations. Simulation Modelling Practice and Theory, 19, 1021–1034.
Luo, P., L, K., & Shi, Z. (2007). A revisit of fast greedy heuristics for mapping a class of independent tasks onto heterogeneous computing systems. Journal of Parallel and Distributed Computing, 67, 695714.
Luo, H., Zhang, A., & Huang, G. Q. (2013). Active scheduling for hybrid flowshop with family setup time and inconsistent family formation. Journal of Intelligent Manufacturing, 26, 1–19.
Murty, K. G. (1994). Operations research: Deterministic optimization models. Englewood Cliffs, NJ: Prentice-Hall.
Pinedo, M. (2002). Scheduling: Theory, algorithms, and systems (2nd ed.). New Jersey: Prentice-Hall.
Prastein, M., (1987). Precedence-constrained scheduling with minimum time and communication, MS Thesis, University of Illinois at Urbana-Champaign.
Rayward-Smith, V. J. (1987). UET scheduling with unit interprocessor communication delays. Discrete Applied Mathematics, 18, 557.
Sousa, J. P., & Wolsey, L. A. (1992). A time-indexed formulation of nonpreemptive single machine scheduling problems. Mathematical Programming, 54, 353367.
Unlu, Y., & Mason, S. J. (2010). Evaluation of mixed integer programming formulations for non-preemptive parallel machine scheduling problems. Computers & Industrial Engineering, 58, 785800.
Urban, T. L. (1998). Note. Optimal balancing of U-shaped assembly lines. Management Science, 44(5), 738–741.
Vázquez, E. P., Calvo, M. P., & Ordóñez, P. M. (2013). Learning process on priority rules to solve the RCMPSP. Journal of Intelligent Manufacturing, 26, 1–16.
Venugopalan, S., & Sinnen, O. (2012). Optimal linear programming solutions for multiprocessor scheduling with communication delays. In Y. Xiang, I. Stojmenovic, B. O. Apduhan, G. Wang, K. Nakano, & A. Zomaya (Eds.), Algorithms and architectures for parallel processing (Vol. 7439, p. 129138). Heidelberg: Springer.
Zhang, S., & Wong, T. N. (2014). Integrated process planning and scheduling: An enhanced ant colony optimization heuristic with parameter tuning. Journal of Intelligent Manufacturing. doi:10.1007/s10845-014-1023-3.
Zhang, W., Xu, W., Liu, G., & Gen, M. (2015). An effective hybrid evolutionary algorithm for stochastic multiobjective assembly line balancing problem. Journal of Intelligent Manufacturing. doi:10.1007/s10845-015-1037-5.
Zhang, W., Gen, M., & Jo, J. B. (2014). Hybrid sampling strategy-based multiobjective evolutionary algorithm for process planning and scheduling problem. Journal of Intelligent Manufacturing, 25(5), 881897.
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Ait El Cadi, A., Souissi, O., Ben Atitallah, R. et al. Mathematical programming models for scheduling in a CPU/FPGA architecture with heterogeneous communication delays. J Intell Manuf 29, 629–640 (2018). https://doi.org/10.1007/s10845-015-1075-z
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DOI: https://doi.org/10.1007/s10845-015-1075-z