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Solving Multilocal Optimization Problems with Parallel Stretched Simulated Annealing

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Operational Research

Part of the book series: CIM Series in Mathematical Sciences ((CIMSMS,volume 4))

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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.

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  1. 1.

    Ignoring the time to spawn and coordinate all SSA instances, and post-process results.


  1. Chelouah, R., Siarry, P.: A continuous genetic algorithm designed for the global optimization of multimodal functions. J. Heuristics 6, 191–213 (2000)

    Article  MATH  Google Scholar 

  2. Eriksson, P., Arora, J.: A comparison of global optimization algorithms applied to a ride comfort optimization problem. Struct. Multidiscip. Optim. 24, 157–167 (2002)

    Article  Google Scholar 

  3. 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)

    Article  Google Scholar 

  4. 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)

    Google Scholar 

  5. Hedar, A.R.: Global Optimization Test Problems (2015).

  6. High-Performance Portable MPI (2015) –

  7. Ingber, L.: Very fast simulated re-annealing. Math. Comput. Model. 12, 967–973 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kernighan, B.W., Ritchie, D.M.: The C Programming Language, 2nd edn. Prentice Hall, Englewood Cliffs (1988). ISBN 0-13-110362-8

    Google Scholar 

  9. 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)

    Article  MATH  MathSciNet  Google Scholar 

  10. León, T., Sanmatías, S., Vercher, H.: A multi-local optimization algorithm. Top 6(N. 1), 1–18 (1998)

    Google Scholar 

  11. Message Passing Interface Forum (2015) –

  12. Parsopoulos, K., Plagianakos, V., Magoulas, G., Vrahatis, M.: Objective function stretching to alleviate convergence to local minima. Nonlinear Anal. 47, 3419–3424 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  13. Parsopoulos, K., Vrahatis, M.: Recent approaches to global optimization problems through particle swarm optimization. Nat. Comput. 1, 235–306 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. 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)

    Article  MATH  MathSciNet  Google Scholar 

  15. 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)

    Chapter  Google Scholar 

  16. 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)

    Google Scholar 

  17. 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)

    Google Scholar 

  18. Price, C.: Non-linear Semi-infinite Programming. University of Canterbury (1992)

    Google Scholar 

  19. Rauber, T., Runger, G.: Parallel Programming for Multicore and Cluster Systems. Springer (2010). ISBN 978-3-642-04817-3

    Google Scholar 

  20. 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)

    Google Scholar 

  21. 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)

    Article  MATH  MathSciNet  Google Scholar 

  22. 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

    Google Scholar 

  23. The GNU C Library (2015) –

  24. TOP500 Supercomputer Sites (2015) –

  25. Tsoulos, I., Lagaris, I.: Gradient-controlled, typical-distance clustering for global optimization (2004).

  26. Tu, W., Mayne, R.: Studies of multi-start clustering for global optimization. Int. J. Numer. Methods Eng. 53, 2239–2252 (2002)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to José Rufino .

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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.

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