Abstract
In the paper, we investigate theoretical and practical aspects of distributed computing for simulated annealing algorithms applied to the problem of scheduling l jobs on m machines. Given n = l · m, the total number of tasks, O(n 3) processors and an upper bound Λ = Λ(l, m) of the objective function, the expected run-times of parallelized versions of our heuristics [14] are O(n · log n · log Λ) for the exponential cooling schedule and O(n2 · log3/2 n · m1/2 · log Λ) for the hyperbolic one. For Markov chains of constant length, the results imply a polylogarithmic run-time O(log n · log(l + m)) for the exponential schedule, where we employ Λ ≤ O(l + m), see Leighton et al. [10]. We implemented a distributed version of our sequential heuristics and first computational experiments on benchmark instances are presented.
Research partially supported by the Strategic Research Programme at CUHK under Grant No. SRP 9505, by a Hong Kong Government RGC Earmarked Grant, Ref.No. CUHK 4367/99E, and by the Germany/Hong Kong Joint Research Scheme under Grant Nos. D/9800710, GHK 99/02 and GHK 00/08.
On leave from IBM T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, N.Y., U.S.A.
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References
E.H.L. Aarts. Local Search in Combinatorial Optimization. Wiley & Sons, 1998.
E.H.L. Aarts and J.H.M. Korst. Simulated Annealing and Boltzmann Machines: A Stochastic Approach. Wiley & Sons, 1989.
M. Besch, H. Bi, P. Enskonatus, G. Heber, M. Wilhelmi. High-level Data Parallel Programming in PROMOTER. Proc. Intern. Workshop on High-level Parallel Programming Models and Supportive Environments, pp. 47–54, 1997.
H. Bi, M. Kessler, H. W. Pohl, M. Tief. Promise-High-level Data-parallel Programming Environment. Proc. 3 rd Workshop on Advanced Parallel Processing Technologies, pp. 207–211, 1999.
M.R. Garey and D.S. Johnson. Complexity Results for Multiprocessor Scheduling under Resource Constraints. SIAM Journal on Computing, 4(4):397–411, 1975.
A. Gibbons and W. Rytter. Efficient Parallel Algorithms. Cambridge University Press, 1988.
D. Helmbold and E. Mayr. The Two Processor Scheduling is in NC. SIAM Journal on Computing, 18:1140–1148, 1989.
H. Jung, P. Spirakis, and M. Serna. A Parallel Algorithm for the Two Processor Constrained Scheduling. Proc. 18 th ICALP, pp. 417–425, 1991.
S. Lawrence, Resource Constrained Project Scheduling: An Experimental Investigation of Heuristic Scheduling Techniques (Supplement), Technical report, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, Pennsylvania, 1984.
F.T. Leighton, B.M. Maggs, and A.W. Richa, Fast Algorithms for Finding O(Congestion + Dilation) Packet Routing Schedules. Combinatorica, 19:375–401, 1999.
J.F. Muth, G.L. Thompson, and P.R. Winters, editors. Industrial Scheduling. Prentice-Hall, Englewood Cliffs, N.J., 1963.
M. Perregaard and J. Clausen. Parallel Branch-and-Bound Methods for the Job-Shop Scheduling Problem. Annals of Operations Research, 83:137–160, 1998.
B. Roy and B. Sussmann. Les problèmes d’Ordonnancement avec Constraints Disjonctives. Note DS No.9 bis. SEMA, 1964.
K. Steinhöfel, A. Albrecht, and C.K. Wong. Two Simulated Annealing-Based Heuristics for the Job Shop Scheduling Problem. European Journal of Operational Research, 118(3):524–548, 1999.
K. Steinhöfel, A. Albrecht, and C.K. Wong. On Parallel Heuristics for the Job Shop Scheduling Problem. In: S.Q. Zheng (ed.), Proc. Intern. Conf. on Parallel and Distributed Computing and Systems, pp. 806–811, 1999.
Storer, R.H., Wu, S.D., and Vaccari, R., New Search Spaces for Sequencing Problems with Application to Job Shop Scheduling, Management Science, 38:1495–1509, 1992.
E. Taillard. Parallel Taboo Search Techniques for the Job-Shop Scheduling Problem. ORSA Journal on Computing, 6:108–117, 1994.
P.J.M. Van Laarhoven, E.H.L. Aarts, and J.K. Lenstra. Job Shop Scheduling by Simulated Annealing. Operations Research, 40(1):113–125, 1992.
U.V. Vazirani and V.V. Vazirani. The Two Processor Scheduling is in Random NC. SIAM Journal on Computing, 16:747–759, 1987.
M.G.A. Verhoeven, H.M.M. ten Eikelder, B.J.M. Aarts and E.H.L. Aarts. Sequential and Parallel Local Search Algorithms for Job Shop Scheduling. Meta-Heuristics (Advances and Trends in Local Search Paradigms for Optimization), pp. 359–371, 1999.
D.P. Williamson, L.A. Hall, J.A. Hoogeveen, C.A.J. Hurkens, J.K. Lenstra, S.V. Sevast’janov, and D.B. Shmoys. Short Shop Schedules. Operations Research, 45:288–294, 1997.
Yamada, T. and Nakano, R., A Genetic Algorithm Applicable to Large-Scale Job Shop Problems, In: R. Manner and B. Manderick (eds.), Proc. 2 nd International Conf. on Parallel Problem Solving from Nature, North-Holland, Amsterdam, 1992, pp. 281–290.
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Albrecht, A., Der, U., Steinhöfel, K., Wong, CK. (2000). Distributed Simulated Annealing for Job Shop Scheduling. In: Schoenauer, M., et al. Parallel Problem Solving from Nature PPSN VI. PPSN 2000. Lecture Notes in Computer Science, vol 1917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45356-3_24
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