117,141 research outputs found
Performance evaluation on optimisation of 200 dimensional numerical tests - results and issues
Abstract: Many tasks in science and technology require optimisation. Resolving such tasks could bring great benefits to community. Multidimensional problems where optimisation parameters are hundreds and more face unusual computational limitations. Algorithms, which perform well on low number of dimensions, when are applied to high dimensional space suffers insuperable difficulties. This article presents an investigation on 200 dimensional scalable, heterogeneous, real-value, numerical tests. For some of these tests optimal values are dependent on dimensionsâ number and virtually unknown for variety of dimensions. Dependence on initialisation for successful identification of optimal values is analysed by comparison between experiments with start from random initial locations and start from one location. The aim is to: (1) assess dependence on initialisation in optimisation of 200 dimensional tests; (2) evaluate tests complexity and required for their resolving periods of time; (3) analyse adaptation to tasks with unknown solutions; (4) identify specific peculiarities which could support the performance on high dimensions (5) identify computational limitations which numerical methods could face on high dimensions. Presented and analysed experimental results can be used for further comparison and evaluation of real value methods
Performance evaluation on optimisation of 200 dimensional numerical tests - results and issues
Abstract: Many tasks in science and technology require optimisation. Resolving such tasks could bring great benefits to community. Multidimensional problems where optimisation parameters are hundreds and more face unusual computational limitations. Algorithms, which perform well on low number of dimensions, when are applied to high dimensional space suffers insuperable difficulties. This article presents an investigation on 200 dimensional scalable, heterogeneous, real-value, numerical tests. For some of these tests optimal values are dependent on dimensionsâ number and virtually unknown for variety of dimensions. Dependence on initialisation for successful identification of optimal values is analysed by comparison between experiments with start from random initial locations and start from one location. The aim is to: (1) assess dependence on initialisation in optimisation of 200 dimensional tests; (2) evaluate tests complexity and required for their resolving periods of time; (3) analyse adaptation to tasks with unknown solutions; (4) identify specific peculiarities which could support the performance on high dimensions (5) identify computational limitations which numerical methods could face on high dimensions. Presented and analysed experimental results can be used for further comparison and evaluation of real value methods
Semiclassical instanton approach to calculation of reaction rate constants in multidimensional chemical systems
The semiclassical instanton approximation is revisited in the context of its application to the calculation of chemical reaction rate constants. An analytical expression for the quantum canonical reaction rate constants of multidimensional systems is derived for all temperatures from the deep tunneling to high-temperature regimes. The connection of the derived semiclassical instanton theory with several previously developed reaction rate theories is shown and the numerical procedure for the search of instanton trajectories is provided. The theory is tested on seven different collinear symmetric and asymmetric atom transfer reactions including heavy-light-heavy, light-heavy-light and light-light-heavy systems. The obtained thermal rate constants agree within a factor of 1.5â2 with the exact quantum results in the wide range of temperatures from 200 to 1500 K
Calibration of semi-analytic models of galaxy formation using Particle Swarm Optimization
We present a fast and accurate method to select an optimal set of parameters
in semi-analytic models of galaxy formation and evolution (SAMs). Our approach
compares the results of a model against a set of observables applying a
stochastic technique called Particle Swarm Optimization (PSO), a self-learning
algorithm for localizing regions of maximum likelihood in multidimensional
spaces that outperforms traditional sampling methods in terms of computational
cost. We apply the PSO technique to the SAG semi-analytic model combined with
merger trees extracted from a standard CDM N-body simulation. The
calibration is performed using a combination of observed galaxy properties as
constraints, including the local stellar mass function and the black hole to
bulge mass relation. We test the ability of the PSO algorithm to find the best
set of free parameters of the model by comparing the results with those
obtained using a MCMC exploration. Both methods find the same maximum
likelihood region, however the PSO method requires one order of magnitude less
evaluations. This new approach allows a fast estimation of the best-fitting
parameter set in multidimensional spaces, providing a practical tool to test
the consequences of including other astrophysical processes in SAMs.Comment: 11 pages, 4 figures, 1 table. Accepted for publication in ApJ.
Comments are welcom
On multidimensional solitons and their legacy in contemporary Atomic, Molecular and Optical physics
This viewpoint relates to an article by B A Malomed, D Mihalache, F Wise, and L Torner (2005 J. Opt. B: Quantum Semiclass. Opt. 7 R53âR72) and was published as part of a series of viewpoints celebrating 50 of the most inïŹuential papers published in the Journal of Physics series, which is celebrating its 50th anniversary.Postprint (published version
- âŠ