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Multi-Objective Particle Swarm Optimisation for Molecular Transition State Search

  • Conference paper
EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 175))

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Abstract

This paper describes a novel problem formulation and specialised Multi- Objective Particle Swarm Optimisation (MOPSO) algorithm to discover the reaction pathway and Transition State (TS) of small molecules. Transition states play an important role in computational chemistry and their discovery represents one of the big challenges in computational chemistry. This paper presents a novel problem formulation that defines the TS search as a multi-objective optimisation (MOO) problem. A proof of concept of a modified multi-objective particle swarm optimisation algorithm is presented to find solutions to this problem.While still at a prototype stage, the algorithm was able to find solutions in proximity to the actual TS in many cases. The algorithm is demonstrated on a range of molecules with qualitatively different reaction pathways. Based on this evaluation, possible future developments will be discussed.

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References

  1. Baker, J.: An algorithm for the location of transition states. Journal of Computational Chemistry 7(4), 385–395 (1986)

    Article  Google Scholar 

  2. Burger, S.K., Liu, Y., Sarkar, U., Ayers, P.W.: Moving least-squares enhanced shepard interpolation for the fast marching and string methods. The Journal of Chemical Physics 130, 24103 (2009)

    Article  Google Scholar 

  3. Burger, S.K., Yang, W.: Quadratic string method for determining the minimum-energy path based on multiobjective optimization. The Journal of Chemical Physics 124(5), 54109 (2006)

    Article  Google Scholar 

  4. Burger, S.K., Yang, W.: Sequential quadratic programming method for determining the minimum energy path. The Journal of Chemical Physics 127(16), 164107 (2007)

    Article  Google Scholar 

  5. Cerjan, C.J., Miller, W.H.: On finding transition states. The Journal of Chemical Physics 75(6), 2800–2806 (1981)

    Article  Google Scholar 

  6. Coello, C.A.C., Lechuga, M.S.: MOPSO: A Proposal for Multiple Objective Particle Swarm Optimization. In: Proceedings of the 2002 Congress on Evolutionary Computation, CEC 2002, vol. 2, IEEE Computer Society (2002)

    Google Scholar 

  7. Coutsias, E.A., Seok, C., Dill, K.A.: Using quaternions to calculate rmsd. Journal of Computational Chemistry 25(15), 1849–1857 (2004)

    Article  Google Scholar 

  8. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)

    Article  Google Scholar 

  9. Del Campo, J.M., Köster, A.M.: A hierarchical transition state search algorithm. The Journal of Chemical Physics 129, 024107 (2008)

    Article  Google Scholar 

  10. Dewar, M.J.S., Healy, E.F., Stewart, J.J.P.: Location of transition states in reaction mechanisms. Journal of the Chemical Society, Faraday Transactions 2: Molecular and Chemical Physics 80(3), 227–233 (1984)

    Google Scholar 

  11. Dey, B., Bothwell, S., Ayers, P.: Fast marching method for calculating reactive trajectories for chemical reactions. Journal of Mathematical Chemistry 41, 1–25 (2007), doi:10.1007/s10910-006-9060-6

    Article  MathSciNet  MATH  Google Scholar 

  12. Dey, B.K., Janicki, M.R., Ayers, P.W.: Hamilton-jacobi equation for the least-action/least-time dynamical path based on fast marching method. The Journal of Chemical Physics 121(14), 6667–6679 (2004)

    Article  Google Scholar 

  13. Weinan, E., Ren, W., Vanden-Eijnden, E.: String method for the study of rare events. Phys. Rev. B 66, 052301 (2002)

    Google Scholar 

  14. Eberhart, R., Simpson, P., Dobbins, R.: Computational intelligence PC tools. Academic Press Professional, Inc., San Diego (1996)

    Google Scholar 

  15. Elber, R., Karplus, M.: A method for determining reaction paths in large molecules: Application to myoglobin. Chemical Physics Letters 139(5), 375–380 (1987)

    Article  Google Scholar 

  16. Fieldsend, J., Singh, S.: A multi-objective algorithm based upon particle swarm optimisation. In: Proceedings of The UK Workshop on Computational Intelligence, pp. 34–44 (2002)

    Google Scholar 

  17. Fournier, R., Bulusu, S., Chen, S., Tung, J.: Using swarm intelligence for finding transition states and reaction paths. The Journal of Chemical Physics 135(10), 104117 (2011)

    Article  Google Scholar 

  18. Frisch, M.J., et al.: Gaussian 03, Revision C.02. Gaussian, Inc., Wallingford (2004)

    Google Scholar 

  19. Goodrow, A., Bell, A.T., Head-Gordon, M.: Development and application of a hybrid method involving interpolation and ab initio calculations for the determination of transition states. The Journal of Chemical Physics 129(17), 174109 (2008)

    Article  Google Scholar 

  20. Goodrow, A., Bell, A.T., Head-Gordon, M.: Transition state-finding strategies for use with the growing string method. The Journal of Chemical Physics 130(24), 244108 (2009)

    Article  Google Scholar 

  21. Goudos, S.K., Zaharis, Z.D., Kampitaki, D.G., Rekanos, I.T., Hilas, C.S.: Pareto optimal design of dual-band base station antenna arrays using multi-objective particle swarm optimization with fitness sharing. IEEE Transactions on Magnetics 45(3), 1522–1525 (2009)

    Article  Google Scholar 

  22. Henkelman, G., Jónsson, H.: Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. The Journal of Chemical Physics 113(22), 9978–9985 (2000)

    Article  Google Scholar 

  23. Henkelman, G., Uberuaga, B.P., Jónsson, H.: A climbing image nudged elastic band method for finding saddle points and minimum energy paths. The Journal of Chemical Physics 113(22), 9901–9904 (2000)

    Article  Google Scholar 

  24. Janson, S., Merkle, D., Middendorf, M.: Molecular docking with multi-objective particle swarm optimization. Applied Soft Computing 8(1), 666–675 (2008)

    Article  MathSciNet  Google Scholar 

  25. Jin, N., Rahmat-Samii, Y.: Particle swarm optimization for antenna designs in engineering electromagnetics. J. Artif. Evol. App., 9:1–9:10 (January 2008)

    Google Scholar 

  26. Jones, J.E.: On the determination of molecular fields. ii. from the equation of state of a gas. Proceedings of the Royal Society of London. Series A 106(738), 463–477 (1924)

    Article  Google Scholar 

  27. Kabsch, W.: A solution for the best rotation to relate two sets of vectors. Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography 32(5), 922–923 (1976)

    Article  Google Scholar 

  28. Kabsch, W.: A discussion of the solution for the best rotation to relate two sets of vectors. Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography 34(5), 827–828 (1978)

    Article  Google Scholar 

  29. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks, vol. 4 (1995)

    Google Scholar 

  30. Li, X.: A Non-Dominated Sorting Particle Swarm Optimizer for Multiobjective Optimization. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2723, pp. 37–48. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  31. Maeda, S., Ohno, K.: Global mapping of equilibrium and transition structures on potential energy surfaces by the scaled hypersphere search method: applications to ab initio surfaces of formaldehyde and propyne molecules. The Journal of Physical Chemistry A 109(25), 5742–5753 (2005), PMID: 16833907

    Article  Google Scholar 

  32. Moore, J., Chapman, R.: Application of particle swarm to multiobjective optimization. Technical report, Department of Computer Science and Software Engineering, Auburn University (1999)

    Google Scholar 

  33. Mostaghim, S., Teich, J.: Strategies for finding good local guides in multi-objective particle swarm optimizationoptimization. In: Proceedings of the 2003 IEEE Swarm Intelligence Symposium, SIS 2003, pp. 26–33. IEEE Computer Society (2003)

    Google Scholar 

  34. Peters, B., Heyden, A., Bell, A.T., Chakraborty, A.: A growing string method for determining transition states: Comparison to the nudged elastic band and string methods. The Journal of Chemical Physics 120(17), 7877–7886 (2004)

    Article  Google Scholar 

  35. Schlegel, H.B.: Exploring potential energy surfaces for chemical reactions: an overview of some practical methods. Journal of Computational Chemistry 24(12), 1514–1527 (2003)

    Article  Google Scholar 

  36. Schrödinger, E.: An undulatory theory of the mechanics of atoms and molecules. Physical Review 28(6), 1049–1070 (1926)

    Article  MATH  Google Scholar 

  37. Sharaf, A.M., El-Gammal, A.A.A.: A multi objective multi-stage particle swarm optimization mopso search scheme for power quality and loss reduction on radial distribution system. In: International Conference on Renewable Energies and Power Quality, ICREPQ (2009)

    Google Scholar 

  38. Sheppard, D., Terrell, R., Henkelman, G.: Optimization methods for finding minimum energy paths. The Journal of Chemical Physics 128(13), 134106 (2008)

    Article  Google Scholar 

  39. Shi, Y., Eberhart, R.: A modified particle swarm optimizer. In: The 1998 IEEE International Conference on Evolutionary Computation Proceedings, IEEE World Congress on Computational Intelligence, pp. 69–73 (1998)

    Google Scholar 

  40. Stacey, A., Jancic, M., Grundy, I.: Particle swarm optimization with mutation. In: The 2003 Congress on Evolutionary Computation, CEC 2003, vol. 2, pp. 1425–1430. IEEE (2003)

    Google Scholar 

  41. Trygubenko, S.A., Wales, D.J.: A doubly nudged elastic band method for finding transition states. The Journal of Chemical Physics 120(5), 2082–2094 (2004)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute for Integrated and Intelligent Systems, Griffith University, Queensland, Australia

    Jan Hettenhausen & Andrew Lewis

  2. School of Information Technology, York University, Toronto, Canada

    Stephen Chen

  3. Faculty of Business, Technology and Sustainable Development, Bond University, Queensland, Australia

    Marcus Randall

  4. Department of Chemistry, York University, Toronto, Canada

    René Fournier

Authors
  1. Jan Hettenhausen
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  2. Andrew Lewis
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  3. Stephen Chen
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  4. Marcus Randall
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  5. René Fournier
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Corresponding author

Correspondence to Jan Hettenhausen .

Editor information

Editors and Affiliations

  1. , Computer Science Department, CINVESTAV-IPN, Col. San Pedro Zacatenco 2508, Mexico City, 07360, Mexico

    Oliver Schütze

  2. , Computer Science Department, CINVESTAV-IPN, Col. San Pedro Zacatenco 2508, Mexico City, 07360, Mexico

    Carlos A. Coello Coello

  3. , Computer Science and Communications, University of Luxembourg, rue Richard Coudenhove-Kalergi 6, Luxembourg, 1359, Luxembourg

    Alexandru-Adrian Tantar

  4. Computer Science and Communications, Research Unit, University of Luxembourg, rue Richard Coudenhove-Kalergi 6, Luxembourg, L-1359, Luxembourg

    Emilia Tantar

  5. Computer Science, and Communications, University of Luxembourg, rue Richard Coudenhove-Kalergi 6, Luxembourg, L-1359, Luxembourg

    Pascal Bouvry

  6. Bordeaux Mathematical Institute, INRIA Bordeaux-Sud Ouest, Université Bordeaux I, cours de la Libération 351, Talence Cedex, 33405, France

    Pierre Del Moral

  7. Bâtiment Leyteire, UFR Sciences et Modélisation, Université Bordeaux II, 3ter place de la Victoire, Bordeaux, 33000, France

    Pierrick Legrand

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Hettenhausen, J., Lewis, A., Chen, S., Randall, M., Fournier, R. (2013). Multi-Objective Particle Swarm Optimisation for Molecular Transition State Search. In: Schütze, O., et al. EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II. Advances in Intelligent Systems and Computing, vol 175. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31519-0_27

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  • DOI: https://doi.org/10.1007/978-3-642-31519-0_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31518-3

  • Online ISBN: 978-3-642-31519-0

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