This Article 
 Bibliographic References 
 Add to: 
An Inherently Parallel Method for Heuristic Problem-Solving: Part I-General Framework
October 1995 (vol. 6 no. 10)
pp. 1006-1015

Abstract—The class of NP-hard problems contains many problems of considerable practical importance. The complexity of these problems is so overwhelming that exhaustive search of the solution space is not possible even using massively parallel search techniques, particularly for problems of super-exponential complexity such as flow-shop and job-shop scheduling. This two-part paper discusses a novel, inherently parallel heuristic solution technique. Part I presents this technique, known as Parallel Dynamic Interaction (PDI), as a general solution framework that is applicable to a number of computationally intractable problems, and gives details of its general methodology.

From a parallel processing standpoint, PDI is interesting because it is inherently based upon the dynamic interplay between simultaneously executing subproblems. As such, PDI has no direct serial analog, and is not directly amenable to conventional parallel processing speedup analysis. This may provide an indication that parallel processing can offer opportunities beyond simply speeding up the solution of sequentially specified algorithms. From a practical problem-solving perspective, PDI shows promise as a method capable of generating high quality solutions to exponentially and super-exponentially hard problems. For large problems, PDI is often able to find a near-optimal solution many orders of magnitude faster than the time taken for a conventional parallel branch-and-bound search to find a solution of comparable quality. The successful application of PDI to three NP-hard problems is described in Part II of this paper.

[1] G. Li and B.W. Wah,“Computational efficiency of parallel approximate branch-and-bound algorithms,” 1984 International Conf. on Parallel Processing, pp. 473-480, Aug. 1984.
[2] T.S. Abdelrahman and T.N. Mudge,“Parallel branch and bound algorithms on hypercube multiprocessors,” Proc. 3rd. Conf. on Hypercube Concurrent Computers and Applications, pp. 1,492-1,499, 1988.
[3] K. Almquist,R.J. Anderson, and E.D. Lazowska,“The Measured performance of parallel dynamic programming implementations,” Proc. 1989 International Conf. on Parallel Processing, pp. III-76-III-79, Aug. 1989.
[4] S.H.S. Huang,H. Liu, and V. Viswanathan,“A sub-linear parallel algorithm for some dynamic programming problems,” Proc. 1990 International Conf. on Parallel Processing, vol. 3, pp. 261-264, Aug. 1990.
[5] V.M. Lo,S. Rajopadhye,S. Gupta,D. Keldsen,M.A. Mohamed, and J. Telle,“Mapping divide-and-conquer algorithms to parallel architectures,” Proc. 1990 International Conf. on Parallel Processing, vol. 3, pp. 128-135, Aug. 1990.
[6] M. Garey and D.S. Johnson,Computers and Intractability,San Francisco, Freeman, 1979.
[7] E. Horowitz and S. Sahni,Algorithms: Design and Analysis, Potomac, Maryland, Computer Science Press, 1978.
[8] P. Banerjee, M.H. Jones, and J.S. Sargent, “Parallel Simulated Annealing Algorithms for Cell Placement on Hypercube Multiprocessors,” IEEE Trans. Parallel and Distributed Systems, vol. 1, no. 1, Jan. 1990.
[9] T. Gonzalez and S. Sahni,“Flowshop and jobshop schedules: Complexity and approximation,” Operations Research, vol. 26, pp. 36-52, Jan.-Feb. 1978.
[10] M. O’Heigeartaigh, J.K. Lenstra andA.H.G. Rinnooy Kan, eds., Combinatorial Optimization: Annotated Bibliographies, Wiley, 1985.
[11] I. Pramanick,“Parallel dynamic interaction—an inherently parallel problemsolving methodology,” PhD thesis, Department of Electrical and Computer Engineering.,The University of Iowa, May 1991.
[12] D.W. Etherington,“Formalizing nonmonotonic reasoning systems,” Artificial Intelligence, pp. 41-85, vol. 31, 1987.
[13] S. French,Sequencing and Scheduling: An Introduction to the Mathematics of the Job-Shop, Chichester, Ellis Horwood Ltd., 1982.

Index Terms:
NP-hard problems, heuristic problem solving, inherently parallel, dynamic interaction, locally applied heuristics.
Ira Pramanick, Jon G. Kuhl, "An Inherently Parallel Method for Heuristic Problem-Solving: Part I-General Framework," IEEE Transactions on Parallel and Distributed Systems, vol. 6, no. 10, pp. 1006-1015, Oct. 1995, doi:10.1109/71.473511
Usage of this product signifies your acceptance of the Terms of Use.