Partitions selection strategy for set of clustering solutions

Clustering is a difficult task: there is no single cluster definition and the data can have more than one underlying structure. Pareto-based multi-objective genetic algorithms (e.g., MOCK Multi-Objective Clustering with automatic K-determination and MOCLE-Multi-Objective Clustering Ensemble) were proposed to tackle these problems. However, the output of such algorithms can often contains a high number of partitions, becoming difficult for an expert to manually analyze all of them. In order to deal with this problem, we present two selection strategies, which are based on the corrected Rand, to choose a subset of solutions. To test them, they are applied to the set of solutions produced by MOCK and MOCLE in the context of several datasets. The study was also extended to select a reduced set of partitions from the initial population of MOCLE. These analysis show that both versions of selection strategy proposed are very effective. They can significantly reduce the number of solutions and, at the same time, keep the quality and the diversity of the partitions in the original set of solutions. (C) 2010 Elsevier B.V. All rights reserved.

Continuous GRASP with a local active-set method for bound-constrained global optimization

Global optimization seeks a minimum or maximum of a multimodal function over a discrete or continuous domain. In this paper, we propose a hybrid heuristic-based on the CGRASP and GENCAN methods-for finding approximate solutions for continuous global optimization problems subject to box constraints. Experimental results illustrate the relative effectiveness of CGRASP-GENCAN on a set of benchmark multimodal test functions.

A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation

We present a variable time step, fully adaptive in space, hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions. The method is based on the hybrid level set/front-tracking approach proposed in [H. D. Ceniceros and A. M. Roma, J. Comput. Phys., 205, 391400, 2005]. Geometric, interfacial quantities are computed from front-tracking via the immersed-boundary setting while the signed distance (level set) function, which is evaluated fast and to machine precision, is used as a fluid indicator. The surface tension force is obtained by employing the mixed Eulerian/Lagrangian representation introduced in [S. Shin, S. I. Abdel-Khalik, V. Daru and D. Juric, J. Comput. Phys., 203, 493-516, 2005] whose success for greatly reducing parasitic currents has been demonstrated. The use of our accurate fluid indicator together with effective Lagrangian marker control enhance this parasitic current reduction by several orders of magnitude. To resolve accurately and efficiently sharp gradients and salient flow features we employ dynamic, adaptive mesh refinements. This spatial adaption is used in concert with a dynamic control of the distribution of the Lagrangian nodes along the fluid interface and a variable time step, linearly implicit time integration scheme. We present numerical examples designed to test the capabilities and performance of the proposed approach as well as three applications: the long-time evolution of a fluid interface undergoing Rayleigh-Taylor instability, an example of bubble ascending dynamics, and a drop impacting on a free interface whose dynamics we compare with both existing numerical and experimental data.