Abstract
In this paper, we propose a decentralized parallel computation model for global optimization using interval analysis. The model is adaptive to any number of processors and the workload is automatically and evenly distributed among all processors by alternative message passing. The problems received by each processor are processed based on their local dominance properties, which avoids unnecessary interval evaluations. Further, the problem is treated as a whole at the beginning of computation so that no initial decomposition scheme is required. Numerical experiments indicate that the model works well and is stable with different number of parallel processors, distributes the load evenly among the processors, and provides an impressive speedup, especially when the problem is time-consuming to solve.
Similar content being viewed by others
References
Hansen P, Jaumard B. Lipschitz optimization. In Handbook of Global Optimization, Horst R, Pardalos P M (eds.), Dordrecht: Kluwer Academic Pulishers, 1995, pp.407–493.
Özdamar L, Demirhan M B. Experiments with new stochastic global optimization search techniques. Computers and Operations Research, 2000, 27(9): 841–865.
Hansen E. Global Optimization Using Interval Analysis. New York: Marcel Dekker, 1992.
Kearfott R B. Rigorous Global Search: Continuous Problems. Dordrecht: Kluwer Academic Publisher, 1996.
Pintér J. Branch and bound algorithms for solving global optimization problems with lipschitzian structure. Optimization, 1988, 19: 101–110.
Tang Z B. Adaptive partitioned random search to global optimization. IEEE Transactions on Automatic Control, 1994, 39(11): 2235–2244.
Ratschek H, Rokne J. Interval methods. In Handbook of Global Optimization, Horst R, Pardalos P M (eds.), Kluwer Academic Publishers, 1995, pp.751–828.
Skillicorn D B, Talia D. Models and languages for parallel computation. ACM Computing Surveys, 1998, 30(2): 123–169.
Skelboe S. Computation of rational interval functions. BIT Numerical Mathematics, 1974, 14(1): 87–95.
Hansen E, Sengupta S. Global constrained optimization using interval analysis. In Interval Mathematics, Nickel K (ed.), Berlin: Springer-Verlag, 1980, pp.25–47.
Moore R E. Interval Analysis. Engelwood Cliffs: Prentice Hall, 1966.
Ratz D, Csendes T. On the selection of subdivision directions in interval branch-and-bound methods for global optimization. Journal of Global Optimization, 1995, 7(2): 183–207.
Casado L G, García I, Csendes T. A heuristic rejection criterion in interval global optimization algorithms. BIT Numerical Mathematics, 2001, 41(4): 683–692.
Casado L G, Martínez J A, García I. Experiments with a new selection criterion in a fast interval optimization algorithm. Journal of Global Optimization, 2001, 19(3): 247–264.
Csendes T. New subinterval selection criteria for interval global optimization. Journal of Global Optimization, 2001, 19(3): 307–327.
Pedamallu C S, Özdamar L, Csendes T, Vinkó T. Efficient interval partitioning for constrained global optimization. Journal of Global Optimization, 2008, 42(3): 369–384.
Sun M. A fast memoryless interval-based algorithm for global optimization. Journal of Global Optimization, 2010, 47(2): 247–271.
Henriksen T, Madsen K. Use of a depth-first strategy in parallel global optimization. Technical Report 92-10, Institute of Numerical Analysis, Technical University of Denmark, Lyngby, 1992.
Eriksson J, Lindstrom P. A parallel interval method implementation for global optimization using dynamic load balancing. Reliable Computing, 1995, 1(1): 77–91.
Benyoub A, Daoudi E M. Parallelization of the continuous global optimization problem with inequality constraints by using interval arithmetic. In Proc. the 9th International Conference on High-Performance Computing and Networking, June 2001, pp.595–602.
Ibraev S. A new parallel method for verified global optimization [PhD Thesis]. University of Wuppertal, Germany, 2001.
Gau C Y, Stadtherr M A. Parallel interval-Newton using message passing: Dynamic load balancing strategies. In Proc. the 2001 ACM/IEEE Conference on Supercomputing, Denver, Colorado, Nov. 2001, Article No.23.
Berner S. Parallel methods for verified global optimization practice and theory. Journal of Global Optimization, 1996, 9(1): 1–22.
Message Passing Interface Forum. MPI: The message passing interface standard. 1994, http://www.mpi-forum.org, 2011.
Wu Y, Kumar A. Interval subdivision strategies for constrained optimization. In Proc. the International Conference of Numerical Analysis and Applied Mathematics, Sept. 2005, pp.593–596.
Ratschek H, Rokne J. New Computer Methods for Global Optimization. Ellis Horwood Limited, 1988.
Floudas C A, Pardalos P M, Adjiman C S, Esposito W R, Gümüs Z H, Harding S T, Klepeis J L, Meyer C A, Schweiger C A. Handbook of Test Problems in Local and Global Optimization. Kluwer Academic Publishers, 1999.
Michalewicz Z. Genetic Algorithms + Data Structures = Evolution Programs. Springer, 1996.
Törn A, Žilinskas A. Global Optimization. Berlin: Springer-Verlag, 1989.
Mäkelä M M, Neittaanmäki P. Nonsmooth Optimization. World Scientific, 1992.
CUTEr. CUTEr: A constrained and unconstrained testing environment, revisited. http://cuter.rl.ac.uk/, 2011.
Knüppel O. PROFILE/BIAS — A fast interval library. Computing, 1994, 53: 277–287.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wu, Y., Kumar, A. A Parallel Interval Computation Model for Global Optimization with Automatic Load Balancing. J. Comput. Sci. Technol. 27, 744–753 (2012). https://doi.org/10.1007/s11390-012-1260-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11390-012-1260-x