INTELLIGENT WATER DROPS ALGORITHM

The following papers introduce a relatively new algorithm called the Intelligent Water Drops Algorithm developed by Hamed Shah Hosseini in 2007 based on the processes that happen in the natural river systems and the actions and reactions that take place between water drops in the river and the changes that happen in the environment that river is flowing. (Image grabbed from photographymad.com)

1. Problem Solving by Intelligent Water Drops. H. Hosseini. Proceedings of the 2007 IEEE Congress on Evolutionary Computation. 2007.

2. The Intelligent Water Drops Algorithm : A Nature-Inspired Swarm-Based Optimization Algorithm. H. Hosseini. Int. J. Bio-Inspired Computation. Vol 1, Nos 1/2. 2009.

This link provides a list of applications of IWD.

LENNARD - JONES CLUSTER OPTIMIZATION

The following papers show the extensive studies done on the optimization of Lennard-Jones clusters starting from one of the earliest studies on LJ clusters by Northby using lattice-based searches towards usage of Genetic Algorithms methods, Ant Colony Optimization and Particle Swarm Optimization. (Image grabbed from http://en.wikipedia.org/wiki/Lennard-Jones_potential)

1. Structure and Binding of Lennard Jones Clusters : 13 <= N <= 147. J. Northby. The Journal of Chemical Physics. 87, 6166. 1987.

2. Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard Jones Clusters containing up to 110 atoms. D. Wales and J. Doye. Journal of Physical Chemistry. 101 (28), pp 5111–5116. 1997.

3. The Search for Minimum Potential Energy Structures of Small Atomic Clusters. Application of the Ant Colony Algorithm. P. Raczynski and Z. Gburski. Materials Science Poland. Vol 23, pp 599-606. 2005.

4. Using Ant Colony Optimization to Find Low Energy Atomic Cluster Structures. P. Tomson and G.W. Greenwood. Evolutionary Computation, IEEE. Vol 3, pp 2677 - 2682. 2005.

5. Fast Global Optimization of Difficult Lennard-Jones Clusters. M. Locatelli and F. Schoen. Computational Optimization and Applications. Vol 21, pp 55-70. 2000.

6. Genetic Algorithm for Structural Cluster Optimization. M. D. Wolf, and U. Landman. J. Phys. Chem. Vol 102, pp 6129 - 6137. 1998.

7. Minimizing Lennard-Jones potential using a real coded Genetic algorithm and Particle Swarm Optimization. K. Deep, V. Katiyar and Shashi. World Journal of Modelling and Simulation. Vol 7, pp 312 - 320. 2011.

8. Global Geometry optimization of atomic clusters using a Modified Genetic Algorithm in SpaceFixed Coordinates. J. Niesse and H. Mayne. The Journal of Chemical Physics. 105, 4700. 1996.

BINARY LENNARD JONES CLUSTER OPTIMIZATION

The importance of Binary Lennard Jones (LJ) to alloy clusters and the ability to tailordefine the structure with a choice of atom types and composition is the reason it is widely studied. The following papers show different optimization methods which successfully found putative global optima of Binary LJ clusters. (Image grabbed from J of Chem Inf and Modelling)

1. Global Optimization of Binary Lennard-Jones Clusters Using Three Perturbation Operators. Y. Tao, X. Ruchu, and H. Wenqi. J. Chem. Inf and Modelling. Vol 51 (3), pp 572–577.

2. Mapping the Magic Numbers in Binary Lennard-Jones Clusters. J. Doye and L. Meyer. Phys. Rev. Lett. Vol 95, pp. 063401-063405.

MORSE CLUSTER OPTIMIZATION

The papers listed below investigates on the simple model of potential energy of atoms with varying width of the potential affecting structure of the cluster. It has been argued to be a more appropriate / accurate model for understanding real-life clusters compared to to Lennard Jones potential model. (Image grabbed from Paper #3 below, J. Doye and co-workers 1995)

1. Structural consequences of the range of the interatomic potential: a menagerie of clusters. J.P.K. Doye and D.J. Wales, J. Chem. Soc., Faraday Trans. Vol 93, pp. 4233-4244 (1997). Postcript .

2. Global Optimization of Morse Clusters by Potential Energy Transformation. J. Doye, R. Leary, M. Locatelli and F. Schoen. INFORMS J. Computing. Vol 16, pp. 371-379.

3. The effect of the range of the potential on the structures of clusters. J. Doye, D. Wales and R. Stephen Berry. J. Chem. Phys. Vol 103, pp. 4234-4249 (1995).

JANUS CLUSTERS

(Image grabbed from Granick Research Group http://groups.mrl.illinois.edu/granick/)

1. A numerical study of one-patch colloidal particles: from square-well to Janus. Phys. Chem. Chem. Phys. Vol 12, pp. 11869-11877 (2010).

2. Controlling crystallization and its abscence: proteins, colloids and patchy models. Phys. Chem. Chem. Phys. Vol 9, pp. 2197-2205 (2009).

LIMITED MEMORY BFGS

The following papers show the mathematics behind the numerical optimization method called L-BFGS based on Broyden-Fletcher-Goldfarb-Shanno method for solving nonlinear unconstrained optimization problems. (Image grabbed from http://research.microsoft.com)

 

1. Updating Quasi-Newton Matrices with Limited Storage. J. Nocedal. Mathematics of Computation. Vol 35, pp 773 - 782. 1980.

2. On the Limited Memory BFGS Method for Large Scale Optimization. Mathematical Programming. Vol 45, pp 503 - 528. 1989.