This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
An Inherently Parallel Method for Heuristic Problem-Solving: Part II-Example Applications
October 1995 (vol. 6 no. 10)
pp. 1016-1028

Abstract—This paper presents the application of Parallel Dynamic Interaction (PDI) to three real problem domains: the flow-shop scheduling problem, the job-shop scheduling problem and the vertex cover problem. Specific examples are provided as to how the general PDI framework, introduced in Part I of this paper, can be applied to a particular problem. The results of an empirical study of 90 example instances of these problems indicate that PDI consistently out-performs previously published heuristics for the vertex cover problem, and can typically generate solutions within a few percent of optimal for flow-shop and job-shop problems. Out of the 76 examples for which the optimal solution could be determined, PDI was able to produce results averaging within 4% of optimal. In over 30% of the cases, PDI was able to find the optimal solution. In no case did the PDI solution deviate more than 15% from optimal. It is also seen that the time taken by PDI to arrive at these solutions is negligible compared to that taken by conventional search techniques. This provides strong empirical evidence that PDI is capable of generating high quality solutions to exponentially and super-exponentially hard problems in reasonably short periods of time.

[1] M. Garey and D.S. Johnson,Computers and Intractability.San Francisco: Freeman, 1979.
[2] E. Horowitz and S. Sahni,Algorithms: Design and Analysis.Potomac, Md.: Computer Science Press, 1978.
[3] T. Gonzalez and S. Sahni,“Flowshop and jobshop schedules: Complexity and approximation,” Operations Research, vol. 26, pp. 36-52, Jan.-Feb. 1978.
[4] M. O’hEigeartaigh,J.K. Lenstra,, and A.H.G. Rinnooy Kan, eds., Combinatorial Optimization: Annotated Bibliographies.New York: John Wiley, 1985.
[5] A. Kusiak,Intelligent Manufacturing Systems.Englewood Cliffs, N.J.: Prentice Hall, 1990.
[6] S. French,, Sequencing and Scheduling: An Introduction to the Mathematics ofthe Job-Shop.Chichester, England: Ellis Horwood Ltd., 1982.
[7] K.E. Baker,Introduction to Sequencing and Scheduling.New York: John Wiley, 1974.
[8] S.M. Johnson,“Optimal two- and three-stage production schedules with setuptimes,” Naval Research Logistics Quarterly, vol. 1, no. 1, pp. 61-68, 1954.
[9] J. Blazewicz,“Scheduling under resource constraints_deterministic models,” Annals of Operations Research, vol. 7, no. 1-4, 1986.
[10] M.R. Garey,D.S. Johnson,, and R. Sethi,“The complexity of flowshop and jobshop scheduling,” Mathematics of Operations Research, vol. 1, no. 2, pp. 117-129, 1976.
[11] J.G. Shanthikumar and Y.B. Wu,“Decomposition approaches in permutation scheduling with application to the M-machine flow shop schedulingproblems,” European J. of Operations Research, vol. 19, pp. 125-141, 1985.
[12] B.J. Lagweg,L.K. Lenstra,, and R. Kan,“A general bounding scheme for permutation flow shop problem,” Operations Research, vol. 26, pp. 53-67, 1978.
[13] G. Li and B.W. Wah,“Computational efficiency of parallel approximate branch-and-bound algorithms,” Proc. 1984 Int’l Conf. on Parallel Processing, pp. 473-480, 1984.
[14] T.H. Lai and S. Sahni,“Anomalies in parallel branch-and-bound algorithms,” Proc. 1983 Int’l Conf. on Parallel Processing, pp. 183-190, 1983.
[15] B.W. Wah and Y.Q. Ma,“MANIP—a parallel computer system for implementing branch-and-bound algorithms,” Proc. 8th Ann. Symp. on Computer Architecture, pp. 239-262, 1982.
[16] I. Pramanick,“Parallel dynamic interaction—an inherently parallel problemsolving methodology,” PhD thesis, Department of Electrical and Computer Engineering.,The University of Iowa, May 1991.
[17] G.L. Nemhauser and L.E. Trotter,“Vertex packings: Structural properties and algorithms,” Mathematical Programming, vol. 8, pp. 232-248, 1975.
[18] E. Balas and H. Samuelsson,“A node covering algorithm,” Naval Research Logistics Quarterly, vol. 24, no. 2, pp. 213-233, 1977.
[19] R. Bar-Yehuda and S. Even,“On approximating a vertex cover for planar graphs,” Proc. 14th Ann. ACM Symp. on Theory of Computing, pp. 303-309, May 1982.
[20] R. Levinson,“Towards more optimal vertex covers,” Technical Report UCSC-CRL-89-03, Computer Research Laboratory,Univ. of California at Santa Cruz, Mar. 1989.
[21] R. Bar-Yehuda and S. Even,“A local-ratio theorem for approximating the weighted vertex cover problem,” Annals of Discrete Mathematics, vol. 25, pp. 27-46, 1985.
[22] R. Bar-Yehuda and S. Even,“A linear-time approximation algorithm for the weighted vertex cover problem,” J. of Algorithms, vol. 2, pp. 198-203, 1981.
[23] B. Monien and E. Speckenmeyer,“Some further approximation algorithms for the vertex cover problem,” Lecture Notes in Computer Science, vol. 159, pp. 341-349, 1983.
[24] D.S. Hochbaum,“Approximation algorithms for the set covering and vertex cover problems,” SIAM J. of Computing, vol. 11, no. 3, pp. 555-556, Aug. 1982.
[25] R. Bar-Yehuda,“Approximating vertex covers,” private communication, Aug. 1990.
[26] V. Chvatal,“A greedy heuristic for the set-covering problem,” Mathematics of Operations Research, vol. 4, no. 3, pp. 233-235, Aug. 1979.
[27] F. Brglez,D. Bryan,, and K. Kozminski,“Combinational Profiles of sequential benchmark circuits,” Proc. Int’l Symp. on Circuits and Systems, pp. 1,929-1,934, May 1989.
[28] I. Pramanick,“Application of a parallel heuristic framework to the set covering problem,” Proc. 1992 Int’l Conf. on Parallel Processing, pp. III-185-III-189, Aug. 1992.
[29] G. Jain,B. Ramkumar,, and J. Kuhl,“A control strategy based on heuristic techniques for the parallel execution of logic programs,” Proc. Eighth Int’l Parallel Processing Symp., pp. 311-315, Apr. 1994.

Index Terms:
Super-exponential complexity, flow-shop sched-uling, job-shop scheduling, vertex cover, heuristics.
Citation:
Ira Pramanick, Jon G. Kuhl, "An Inherently Parallel Method for Heuristic Problem-Solving: Part II-Example Applications," IEEE Transactions on Parallel and Distributed Systems, vol. 6, no. 10, pp. 1016-1028, Oct. 1995, doi:10.1109/71.473512
Usage of this product signifies your acceptance of the Terms of Use.