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Reliable Computing

, Volume 1, Issue 1, pp 77–91 | Cite as

A parallel interval method implementation for global optimization using dynamic load balancing

  • Jerry Eriksson
  • Per Lindström
Parallel Algorithms for Interval Computations

Abstract

During the past few years the interest paid to global optimization has rapidly increased. One of the main reasons is the new technology of parallel computers which offer computational power capable of solving global optimization problems in reasonable time. The method studied in this work is based on interval analysis which provides a reliable way for solving the problem. Despite the fact that the method contains a high degree of potential parallelism, it is not straight forward to parallelize due to its irregular and unpredictable computational behaviour. This paper deals with the problem of balancing the load dynamically, both with respect to the quantity and to the quality of the tasks. Efficient strategies are proposed and implemented on an Intel iPSC/2 hypercube. Since the sequential algorithm is used as a base it will be modified to suit the parallel algorithm.

Keywords

Mathematical Modeling Computational Mathematic Global Optimization Industrial Mathematic Dynamic Load 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Реализация параллельното интервального метода для глобальной оптимизации с динамичецким бадансированием нагрузки

Abstract

В течение ностедних нескольких пег ннтерес к нроблеме глобальной онтимнзанин быстро возрастал. Олна нз основных врнчин этого — нобые технологии параллельных компьютеров, обеспечнваюппе аостаточвую вычнслительную мощность для решения залач глоза глобальной онтнмизации за разумное время. Мегол, рассмотренный в данной работе, оснонан на интервальном анализе, которьй овеснечивает надежный нуть решения залачи. Несмотря на значительную до←ю нотенниадьного параллелизма в зтом метоле, его параллелизация ирелставляет собой хетрнвиальную залачу нз-за нерегулярного и непрелсказуемого хола вычислений. Настоящая рабога рассматривает проб←ему динамического балаисирования иагрузки с учетом как качества, так и количества залач. Преллаіаются зффектнiвные стратетии решения в оиисывается их реализация на гинеркуве Intel iPSC/2. ПосколЧjку в качестве вiсходного исиользуется нонользуется иослеловательный алгоритм, он будет модифниирован, что нозводит всхользовать ето как иараллельный.

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References

  1. [1]
    Caprani, O. and Madsen, K.Experiments with interval methods for nonlinear systems. Technical report. Institute fur Angewandte Mathematik, Universität Frieburg i. Br., Copenhagen, 1981.Google Scholar
  2. [2]
    Caprani, O. and Madsen, K.Introduktion til interval analyse. Institute of Datalogy, University of Copenhagen, 1981.Google Scholar
  3. [3]
    Eriksson, J.Improvements of the interval method for solving the global optimization problem. UMINF-report. Information Processing, University of Umeå, 1991.Google Scholar
  4. [4]
    Eriksson, J.Parallel global optimzation using interval analysis. UMINF-report, Information Processing. University of Umeå, 1991.Google Scholar
  5. [3]
    Eriksson, J.Improvements of the interval method for solving the global optimzation, problem. UMINF-report. Information Processing, University of Umeå, 1991.Google Scholar
  6. [4]
    Eriksson, J.Parallel global optimzation using interval analysis. UMINF-report, Information Processing, University of Umeå, 1991.Google Scholar
  7. [5]
    Eriksson, J.Parallel global optimization using interval analysis on iPSC/2 (Draft). UMINF-report, Information Processing, University of Umeå, 1990.Google Scholar
  8. [6]
    Felten, E. W.Best-first branch-and-bound on a hypercube. In: “Conference on Hypercube Concurrent Computers and Applications, 1”, ACM, 1988, pp. 1500–1504.Google Scholar
  9. [7]
    Hansen, E.Global optimization using interval analysis—the multi-dimensional case. Numerische Mathematik34 (1980), pp. 247–270.MATHMathSciNetCrossRefGoogle Scholar
  10. [8]
    Krawczyk, R.Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken. Computing4 (1969), pp. 187–201.MATHMathSciNetGoogle Scholar
  11. [9]
    Lai and Sahni.Anomalies in parallel branch-and-bound algorithms. Communications of the ACM27 (6) (1984), pp. 594–602.MathSciNetCrossRefGoogle Scholar
  12. [10]
    Lin, F. C. and Keller, R. M.Gradient model: a demand-driven load balancing scheme. In: “IEEE Conf. on Distributed Systems”, 1984, pp. 337–357.Google Scholar
  13. [11]
    Moore, R. E.A computational lest for convergence of iterative methods for nonlinear systems. SIAM Journal on Numerical Analysis15 (6) (1978), pp. 1194–1196.MATHMathSciNetGoogle Scholar
  14. [12]
    Moore, R. E.A test for existence of solutions to nonlinear systems. SIAM Journal on Numerical Analysis14 (4) (1977), pp. 611–615.MATHMathSciNetCrossRefGoogle Scholar
  15. [13]
    Moore, R. E.Interval analysis. Prentice Hall, Englewood Cliffs, 1966.Google Scholar
  16. [14]
    Ranka, S., Won, Y., and Sahni, S.Programming a hypercube multicomputer. IEEE Software, 1988, pp. 69–77.Google Scholar
  17. [15]
    Ratschek, H. and Rokne, J.New computer methods for global optimization. Ellis Horwood, Chichester, 1988.Google Scholar
  18. [16]
    Ratchek, H. and Voller, R. L.What can interval analysis do for global optimization. J. of Global Optimization1 (2) (1991), pp. 111–130.Google Scholar
  19. [17]
    Thoft-Christensen, J.Global optimering på paralleldalamal. Masters thesis. Numerical Institute in Copenhagen, 1989.Google Scholar
  20. [18]
    Walster, G. W., Hansen, E., and Sengupta, S.Test results for a global optimization algorithm. In: Boggs, Byrd, and Schnabel (eds) “Numerical Optimization”, SIAM J. on Scientific and 72–287.Google Scholar

Copyright information

© J. Eriksson, P. Lindström 1995

Authors and Affiliations

  • Jerry Eriksson
    • 1
  • Per Lindström
    • 1
  1. 1.Institute of Information ProcessingUniversity of UmeåUmeåSweden

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