Multi-modal Valley-Adaptive Memetic Algorithm for Efficient Discovery of First-Order Saddle Points

  • Mostafa Ellabaan
  • Xianshun Chen
  • Nguyen Quang Huy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7673)


First-order saddle point represents an important landmark on the problem landscape. This point lies along the minimum energy path connecting two minima, more specifically at the point with maximum energy on the path. Unlike minima or maxima, to identify first-order saddle points require both maximization and minimization tasks. Finding such points is extremely difficult. In this paper, we present a real-coded memetic algorithm for locating first-order saddle points. The proposed algorithm leverage the advantage of valley- adaptive clearing scheme in maintaining multiple solutions and Schlegel algorithm in achieving fast and precise convergence. Empirical results shown that the proposed algorithms achieve more than 90% with converge speed of more than 100 fold when comparing to its evolutionary compeers.


Multi-Modal optimization memetic algorithm Saddle points 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Lim, K.K., Ong, Y.S., Lim, M.H., Chen, X., Agarwal, A.: Hybrid ant colony algorithms for path planning in sparse graphs. Soft Computing-A Fusion of Foundations, Methodologies and Applications 12(10), 981–994 (2008)Google Scholar
  2. 2.
    Toda, M.: Transition State Theory Revisited. Wiley-Interscience, City (2002)Google Scholar
  3. 3.
    Jones, D., Sleeman, B.: Differential equations and mathematical biology. CRC Press (2003)Google Scholar
  4. 4.
    Ellabaan, M.M.H., Ong, Y.S., Lim, M.H., Kuo, J.-L.: Finding Multiple First Order Saddle Points Using a Valley Adaptive Clearing Genetic Algorithm. In: Proceedings of the IEEE International Symposium on Computational Intelligence in Robotics and Automation (CIRA 2009), Daejeon, Korea (2009)Google Scholar
  5. 5.
    Trygubenko, S., Wales, D.: A Doubly Nudged Elastic Band Method for Finding Transition States. Chem. Phy. 120(5), 2082–2094 (2004)CrossRefGoogle Scholar
  6. 6.
    Reddy, C.K., Chiang, H.D.: Stability boundary based method for finding saddle points on potential energy surfaces. J. Comput. Biol. 13(3), 745–766 (2006)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Goodrow, A., Bell, A.T., Head-Gordon, M.: Transition state-finding strategies for use with the growing string method. Journal of Chemical Physics 130, 24 (2009)CrossRefGoogle Scholar
  8. 8.
    del Campo, J.M., Koster, A.M.: A hierarchical transition state search algorithm. Journal of Chemical Physics 129(2), 12 (2008)Google Scholar
  9. 9.
    Henkelman, G., Jonsson, H.: A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. Chem. Phy. 15(111), 7010–7022 (1999)Google Scholar
  10. 10.
    Olsen, R.A., Kroes, G.J., Henkelman, G., Arnaldsson, A., Jonsson, H.: Comparison of methods for finding saddle points without knowledge of the final states. Journal of Chemical Physics 121(20), 9776–9792 (2004)CrossRefGoogle Scholar
  11. 11.
    Bungay, S.D., Poirier, R.A., Charron, R.J.: Optimization of transition state structures using genetic algorithms. J. Math. Chem. 28(4), 389–401 (2000)CrossRefzbMATHGoogle Scholar
  12. 12.
    Chaudhury, P., Bhattacharyya, S.P.: A simulated annealing based technique for locating first-order saddle points on multidimensional surfaces and constructing reaction paths: several model studies. Theochem-J. Mol. Struct. 429, 175–186 (1998)CrossRefGoogle Scholar
  13. 13.
    Chaudhury, P., Bhattacharyya, S.P., Quapp, W.: A genetic algorithm based technique for locating first-order saddle point using a gradient dominated recipe. Chem. Phys. 253(2-3), 295–303 (2000)CrossRefGoogle Scholar
  14. 14.
    Nguyen, Q.H., Ong, Y.S., Lim, M.H.: A Probabilistic Memetic Framework. IEEE Transactions on Evolutionary Computation 13(3), 604–623 (2009)CrossRefGoogle Scholar
  15. 15.
    Chen, X., Ong, Y.S., Lim, M.-H., Tan, K.C.: A Multi-Facet Survey on Memetic Computation. IEEE Transactions on Evolutionary Computation 15(5), 591–607 (2011)CrossRefGoogle Scholar
  16. 16.
    Ong, Y.S., Lim, M., Chen, X.: Memetic Computation:Past, Present & Future Research Frontier. IEEE Computational Intelligence Magazine 5(2), 24–31 (2010)CrossRefGoogle Scholar
  17. 17.
    Lim, M.-H., Gustafson, S., Krasnogor, N., Ong, Y.-S.: Editorial to the first issue. Memetic Computing 1(1), 1–2 (2009)CrossRefGoogle Scholar
  18. 18.
    Kok, S., Sandrock, C.: Locating and Characterizing the Stationary Points of the Extended Rosenbrock Function. Evolutionary Computation 17(3), 437–453 (2009)CrossRefGoogle Scholar
  19. 19.
    Vitela, J.E., Castaños, O.: A real-coded niching memetic algorithm for continuous multimodal function optimization. In: IEEE Congress on Evolutionary Computation (2008)Google Scholar
  20. 20.
    Ellabaan, M.M.H., Ong, Y.S.: Valley-Adaptive Clearing Scheme for Multimodal Optimization Evolutionary Search. In: The 9th International Conference on Intelligent Systems Design and Applications (ISDA 2009), Pisa, Italy (2009)Google Scholar
  21. 21.
    Shir, O.M., Emmerich, M., Bäck, T.: Adaptive niche radii and niche shapes approaches for niching with the CMA-ES. Evolutionary Computation 18(1), 97–126 (2010)CrossRefGoogle Scholar
  22. 22.
    Ellabaan, M.M.H., Ong, Y.S.: Experiences on memetic computation for locating transition states in biochemical applications. In: Proceedings of the GECCO, Philadelphia, Pennsylvania, USA (2012)Google Scholar
  23. 23.
    Ellabaan, M., Ong, Y.S., Nguyen, Q.C., Kuo, J.-L.: Evolutionary Discovery of Transition States in Water Clusters. Journal of Theoretical and Computational Chemistry 11(5) (2012)Google Scholar
  24. 24.
    Ellabaan, M.M., Handoko, S.D., Ong, Y.S., Kwoh, C.K., Bahnassy, S.A., Elassawy, F.M., Man, H.Y.: A tree-structured covalent-bond-driven molecular memetic algorithm for optimization of ring-deficient molecules. Computers & Amp; Mathematics with ApplicationsGoogle Scholar
  25. 25.
    Le, M.N., Ong, Y.S., Jin, Y., Sendhoff, B.: A Unified Framework for Symbiosis of Evolutionary Mechanisms with Application to Water Clusters Potential Model Design. IEEE Computational Intelligence Magazine 7(1), 20–35 (2012)CrossRefGoogle Scholar
  26. 26.
    Nguyen, Q.C., Ong, Y.S., Soh, H., Kuo, J.-L.: Multiscale Approach to Explore the Potential Energy Surface of Water Clusters (H2O)n n ≤ 8. The Journal of Physical Chemistry A 112(28), 6257–6261 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mostafa Ellabaan
    • 1
  • Xianshun Chen
    • 1
  • Nguyen Quang Huy
    • 1
  1. 1.Center of Computational Intelligence, School of Computer EngineeringNanyang Technological UniversitySingapore

Personalised recommendations