Abstract
This work explores the use of parallel computing to solve multilocal optimization problems with Stretched Simulated Annealing (SSA), a method that combines simulated annealing with a stretching function technique. Several approaches to the parallelization of SSA are explored, based on different strategies for the refinement of the initial feasible region in subregions and its allocation to the processors involved. The parallel approaches, collectively named as PSSA (Parallel SSA), make viable what would otherwise be unfeasible with traditional sequential computing: an efficient search of the subregions that allows to find many more optima in a reasonable amount of time. To prove the merits of PSSA, several experimental metrics and numerical results are presented for a set of benchmark problems.
Keywords
- Initial Feasible Region
- Homogeneous Decomposition
- Heterogeneous Decomposition
- Hartman Function
- Homogeneous Subdomains
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.
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- 1.
Ignoring the time to spawn and coordinate all SSA instances, and post-process results.
References
Chelouah, R., Siarry, P.: A continuous genetic algorithm designed for the global optimization of multimodal functions. J. Heuristics 6, 191–213 (2000)
Eriksson, P., Arora, J.: A comparison of global optimization algorithms applied to a ride comfort optimization problem. Struct. Multidiscip. Optim. 24, 157–167 (2002)
Floudas, C.: Recent advances in global optimization for process synthesis, design and control: enclosure of all solutions. Comput. Chem. Eng. vol. 23, S963–S973 (1999)
Guibas, L.J., Sedgewick, R.: A dichromatic framework for balanced trees. In: Proceedings of the 19th Annual Symposium on Foundations of Computer Science, Ann Arbor, pp. 8–21 (1978)
Hedar, A.R.: Global Optimization Test Problems (2015). http://www-optima.amp.i.kyoto-u.ac.jp/member/student/hedar/Hedar_files/TestGO.htm
High-Performance Portable MPI (2015) – http://www.mpich.org/
Ingber, L.: Very fast simulated re-annealing. Math. Comput. Model. 12, 967–973 (1989)
Kernighan, B.W., Ritchie, D.M.: The C Programming Language, 2nd edn. Prentice Hall, Englewood Cliffs (1988). ISBN 0-13-110362-8
Kiseleva, E., Stepanchuk, T.: On the efficiency of a global non-differentiable optimization algorithm based on the method of optimal set partitioning. J. Glob. Optim. 25, 209–235 (2003)
León, T., Sanmatías, S., Vercher, H.: A multi-local optimization algorithm. Top 6(N. 1), 1–18 (1998)
Message Passing Interface Forum (2015) – http://www.mpi-forum.org/
Parsopoulos, K., Plagianakos, V., Magoulas, G., Vrahatis, M.: Objective function stretching to alleviate convergence to local minima. Nonlinear Anal. 47, 3419–3424 (2001)
Parsopoulos, K., Vrahatis, M.: Recent approaches to global optimization problems through particle swarm optimization. Nat. Comput. 1, 235–306 (2002)
Pereira, A.I., Fernandes, E.M.G.P.: A reduction method for semi-infinite programming by means of a global stochastic approach. Optimization 58, 713–726 (2009)
Pereira, A.I., Ferreira, O., Pinho, S.P., Fernandes, E.M.G.P.: Multilocal programming and applications. In: Zelinka, I., Snasel, V., Abraham, A. (eds.) Handbook of Optimization. Intelligent Systems Series, pp. 157–186. Springer, Berlin/New York (2013)
Pereira, A.I., Fernandes, E.M.G.P.: Constrained Multi-global optimization using a penalty stretched simulated annealing framework. In: Numerical Analysis and Applied Mathematics. AIP Conference Proceedings, Crete, vol. 1168, pp. 1354–1357 (2009)
Pereira, A.I., Fernandes, E.M.G.P.: Comparative study of penalty simulated annealing methods for multiglobal programming. In: 2nd International Conference on Engineering Optimization, Lisbon (2010)
Price, C.: Non-linear Semi-infinite Programming. University of Canterbury (1992)
Rauber, T., Runger, G.: Parallel Programming for Multicore and Cluster Systems. Springer (2010). ISBN 978-3-642-04817-3
Ribeiro, T., Rufino, J., Pereira, A.I.: PSSA: parallel stretched simulated annealing. In: Proceedings of the 2011’ International Conference on Numerical Analysis and Applied Mathematics, Halkidiki, pp. 783–786 (2011)
Salhi, S., Queen, N.: A hybrid algorithm for identifying global and local minima when optimizing functions with many minima. Eur. J. Oper. Res. 155, 51–67 (2004)
Snir, M., Otto, S.W., Huss-Lederman, S., Walker, D.W.: MPI-The Complete Reference (Volume 1). MIT, Cambridge (1988). ISBN 0-262-69215-5
The GNU C Library (2015) – http://www.gnu.org/software/libc/manual/
TOP500 Supercomputer Sites (2015) – http://www.top500.org
Tsoulos, I., Lagaris, I.: Gradient-controlled, typical-distance clustering for global optimization (2004). www.optimization.org
Tu, W., Mayne, R.: Studies of multi-start clustering for global optimization. Int. J. Numer. Methods Eng. 53, 2239–2252 (2002)
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Rufino, J., Pereira, A.I. (2015). Solving Multilocal Optimization Problems with Parallel Stretched Simulated Annealing. In: Almeida, J., Oliveira, J., Pinto, A. (eds) Operational Research. CIM Series in Mathematical Sciences, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-20328-7_21
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DOI: https://doi.org/10.1007/978-3-319-20328-7_21
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