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New algorithms for coupled tasks scheduling – asurvey

Published online by Cambridge University Press:  10 December 2012

Jacek Blazewicz ,
Grzegorz Pawlak ,
Michal Tanas  and
Wojciech Wojciechowicz
Jacek Blazewicz
Affiliation:
Institute of Bioorganic Chemistry, Polish Academy of Sciences, ul. Z. Noskowskiego 12/14, 61-704 Poznan, Poland. jblazewicz@cs.put.poznan.pl Institute of Computing Science, Poznan University of Technology, ul. Piotrowo 2, 60-965 Poznan, Poland
Grzegorz Pawlak
Affiliation:
Institute of Computing Science, Poznan University of Technology, ul. Piotrowo 2, 60-965 Poznan, Poland
Michal Tanas
Affiliation:
Computer Science Division, Physics Faculty, Adam Mickiewicz University, ul. Umultowska 85, 61-614 Poznan, Poland
Wojciech Wojciechowicz
Affiliation:
Institute of Computing Science, Poznan University of Technology, ul. Piotrowo 2, 60-965 Poznan, Poland
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Abstract

The coupled tasks scheduling problem is a class of scheduling problems introduced forbeam steering software of sophisticated radar devices, called phased arrays. Due toincreasing popularity of such radars, the importance of coupled tasks scheduling isconstantly growing. Unfortunately, most of the coupled tasks problems are NP-hard, andonly a few practically usable algorithms for such problems were found. This paper providesa survey of already known complexity results of various variants of coupled tasksproblems. Then, it complements previous results by providing experimental results of twonew polynomial algorithms for coupled tasks scheduling, which are: an exact algorithm for1|(1,4,1),strictchains|Cmax problem,and a fast heuristic algorithm for more general1|(1,2k, 1), strictchains|Cmaxproblem, where k ∈ ℕ.

Keywords

Coupled tasksschedulingcomplexity theoryheuristic algorithms
Type
Research Article
Information
RAIRO - Operations Research , Volume 46 , Issue 4 , October 2012 , pp. 335 - 353
Copyright
© EDP Sciences, ROADEF, SMAI, 2012

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References

Références

Ageev, A.A. and Baburin, A.E., Approximation algorithms for uet scheduling problems with exact delays. Oper. Res. Lett. 35 (2007) 533–540. Google Scholar
Ahr, D., Bekesi, J., Galambos, G., Oswald, M. and Reinelt, G., An exact algorithm for scheduling identical coupled tasks. Math. Methods Oper. Res. 59 (2004) 193–203. Google Scholar
K. Baker, Introduction to Sequencing and Scheduling. J. Wiley, New York (1974).
Baptiste, P., A note on scheduling identical coupled tasks in logarithmic time. Disc. Appl. Math. 158 (2010) 583–587. Google Scholar
Bekesi, J., Galambos, G., Oswald, M. and Reinelt, G., Improved analysis of an algorithm for the coupled task problem with uet jobs. Oper. Res. Lett. 37 (2009) 93–96. Google Scholar
Blazewicz, J., Dell’Olmo, P., Drozdowski, M. and Speranza, M.G., Scheduling multiprocessor tasks on three dedicated processors. Inform. Process. Lett. 41 (1992) 275–280. Google Scholar
Blazewicz, J., Drabowski, M. and Weglarz, J., Scheduling independent 2-processors tasks to minimize schedule length. Inf. Process. Lett. 18 (1984) 267–273. Google Scholar
Blazewicz, J., Ecker, K., Kis, T., Potts, C.N., Tanas, M. and Whitehead, J., Scheduling of coupled tasks with unit processing times. J. sched. 13 (2010) 453–461. Google Scholar
Blazewicz, J., Ecker, K., Kis, T. and Tanas, M., A note on the complexity of scheduling coupled tasks on a single processor. J. Brazil. Comput. Soc. 7 (2002) 23–27. Google Scholar
J. Blazewicz, K. Ecker, E. Pesch, G. Schmidt and J. Weglarz, Handbook of Scheduling. From Theory to Applications. Springer Verlag (2007).
Blazewicz, J., Pawlak, G. and Walter, B., Scheduling production tasks in a two stage FMS. Int. J. Prod. Res. 40 (2002) 4341–4352. Google Scholar
Brauner, N., Finke, G., Lehoux-Lebacque, V., Potts, C. and Whitehead, J., Scheduling of coupled tasks and one-machine no-wait robotic cells. Comput. Oper. Res. 36 (2009) 301–307. Google Scholar
P. Brucker, Scheduling Algorithms. Springer Verlag, Berlin, 3rd edition (2001).
Brucker, P. and Knust, S., Complexity results for single-machine problems with positive finish-start time-lags. Osnabrück Schriften zur Mathematik 202 (1998) 299–316. Google Scholar
Ecker, K. and Tanas, M., Complexity of scheduling of coupled tasks with chains precedence constraints and constant even length of the gap. Found. Comput. Decision Sci. 32 (2007) 199–212. Google Scholar
Ecker, K. and Tanas, M., Complexity of scheduling of coupled tasks with chains precedence constraints and constant even length of the gap. J. Oper. Res. Soc. 63 (2012) 524–529. Google Scholar
Elshafei, M., Sherali, H.D. and Smith, J.C., Radar pulse interleaving for multi-target tracking. Naval Res. Logist. 51 (2004) 79–94. Google Scholar
Farina, A. and Neri, P., Multitarget interleaved tracking for phased array radar. IEEE Proc. Part F : Comm. Radar Signal Process 127 (1980) 312–318. Google Scholar
Graham, R.L., Lawler, E.L., Lenstra, J.K. and Rinnooy Kan, A.H.G., Optimization and approximation in deterministic sequencing and scheduling : A survey. Ann. Discrete Math. 5 (1979) 287–326. Google Scholar
J.N.D. Gupta, Single facility scheduling with two operations per job and time-lags. Technical Paper (1994).
Gupta, J.N.D., Comparative evaluation of heuristic algorithms for the single machine scheduling problem with two operations per job and time-lags. J. Glob. Optim. 9 (1996) 239–50. Google Scholar
Heinselman, P.L., Preignitz, D.L., Manross, K.L. and Smith, T.M. and Adams, R.W., Rapid sampling of severe storms by the national weather radar testbed phased array radar. Weather Forecast. 23 (2008) 808–824. Google Scholar
A. Izquierdo-Fuente and J.R. Casar-Corredera. Optimal radar pulse scheduling using neural networks. In IEEE International Conference on Neural Networks 7 (1994) 4588–4591.
Lehoux-Lebacque, V., Brauner, N. and Finke, G., Identical coupled tasks scheduling : polynomial complexity of the cyclic case. Les Cahiers Leibnitz 179 (2009). Google Scholar
J. Leung, editor. Handbook of Scheduling. Chapman and Hall (2004).
McNaughton, R., Scheduling with deadlines and loss functions. Manage. Sci. 6 (1959) 1–12. Google Scholar
Orman, A.J. and Potts, C.N., On the complexity of coupled tasks scheduling. Disc. Appl. Math. 72 (1997) 141–154. Google Scholar
Orman, A.J., Potts, C.N., Shahani, A.K. and Moore, A.R., Scheduling for the control of a multifunctional radar system. Eur. J. Oper. Res. 90 (1996) 13–25. Google Scholar
Orman, A.J., Shahani, A.K. and Moore, A.R., Modelling for the control of a complex radar system. Comput. Oper. Res. 25 (1998) 239–249. Google Scholar
Potts, C.N. and Whitehead, J.D., Heuristics for a coupled-operation scheduling problem. J. Oper. Res. Soc. 58 (2007) 1375–1388. Google Scholar
Shapiro, R.D., Scheduling coupled tasks. Nav. Res. Logist. Quart. 27 (1980) 477–481. Google Scholar
M.I. Skolnik, Introduction to Radar Systems. McGraw Hill, London (1980).
M. Tanas, Scheduling of Coupled Tasks. PhD thesis, Technische Universitat Clausthal (2004).
J.D. Whitehead, Scheduling and layout in flexible manufacturing systems. Ph.D. thesis, University of Southampton (2002).
W. Yu, The Two-machine Flow Shop Problem with Delays and the One-machine Total Tardiness Problem Ph.D. Thesis. Technische Universiteit Eindhoven (1996).
Yu, W., Hoogeveen, H. and Lenstra, J.K., Minimizing makespan in a two-machine flow shop with delays and unit-time operations is np-hard. J. Sched. 7 (2004) 333–348. Google Scholar