New MIP model for Multiprocessor Scheduling Problem with Communication Delays
In this chapter, we consider The Multiprocessor Scheduling Problem with Communication Delays. We propose a new Mixed Integer Program (MIP) formulation for this problem taking into account the precedence constraints and the communication delays—delays that depend on the network and the tasks. The new proposed formulation reduces both the number of variables and the number of constraints, when compared to the best mathematical programming formulations from the literature. We summarize the mathematical formulation in a previous work and, in the present chapter; we added extra results to show the quality of the new model. The aim of the extended tests is to assess the quality of this model from one side and from the other side to show which parameters affect the performance of our model, especially the network architecture, the communication, and the number of task impacts. The results are significant but there are still some open problems to solve.
KeywordsMultiprocessors Task scheduling Communication delay Mixed Integer Program CPLEX
The authors would like to gratefully thank the IRT (Institut de recherche technologique) Railenium for the financial support to achieve this research. Also, the authors thank the International Chair Professor N. Mladenović, for his contribution to this work. This Chair position at the University of Valenciennes is cofunded by the region Nord-Pas-de-Calais and the IRT Railenium. This research is conducted within or partially covered by the framework of the grant num. BR05236839 “Development of information technologies and systems for stimulation of personality’s sustainable development as one of the bases of development of digital Kazakhstan”.
- 1.Ait El Cadi, A.: Automatisation de la parallèlisation de systémes complexes avec application à l’environnement Matlab/Simulink. MS Thesis, École Polytechnique de Montréal (2004)Google Scholar
- 2.Ait El Cadi, A., Ben Atitallah, R., Hanafi, S., Mladenović, N., Artiba, A.: New MIP model for multiprocessor scheduling problem with communication delays. Optimization Letters, 11(6), 1091–1107 (2017)Google Scholar
- 3.Ali, H.H., El-Rewini, H.: An optimal algorithm for scheduling interval ordered tasks with communication on N processor, University of Nebraska at Omaha, Mathematics and Computer Science Department, Technical Report, 91-20 (1990)Google Scholar
- 8.Chrétienne, P., Picouleau, C.: Scheduling with communication delays: a survey. In: Chrétienne, P., Coffman, E.G., Lenstra, J.K., Liu, Z. (eds.) Scheduling Theory and Its Applications, pp. 65–90. Wiley, New York (1995)Google Scholar
- 13.Davidović, T., Liberti, L., Maculan, N., Mladenović, N.: Towards the optimal solution of the multiprocessor scheduling problem with communication delays. In: MISTA Proceedings (2007)Google Scholar
- 28.Prastein, M.: Precedence-constrained scheduling with minimum time and communication. MS Thesis, University of Illinois at Urbana-Champaign (1987)Google Scholar
- 33.Venugopalan, S., Sinnen, O.: Optimal linear programming solutions for multiprocessor scheduling with communication delays. In: Xiang, Y., Stojmenovic, I., Apduhan, B.O., Wang, G., Nakano, K., Zomaya, A. (eds.) Algorithms and Architectures for Parallel Processing, vol. 7439, pp. 129–138. Springer, Heidelberg (2012)CrossRefGoogle Scholar