Transform Ranking: a New Method of Fitness Scaling in Genetic Algorithms

The first systematic evaluation of the effects of six existing forms of fitness scaling in genetic algorithms is presented alongside a new method called transform ranking. Each method has been applied to stochastic universal sampling (SUS) over a fixed number of generations. The test functions chosen were the two-dimensional Schwefel and Griewank functions. The quality of the solution was improved by applying sigma scaling, linear rank scaling, nonlinear rank scaling, probabilistic nonlinear rank scaling, and transform ranking. However, this benefit was always at a computational cost. Generic linear scaling and Boltzmann scaling were each of benefit in one fitness landscape but not the other. A new fitness scaling function, transform ranking, progresses from linear to nonlinear rank scaling during the evolution process according to a transform schedule. This new form of fitness scaling was found to be one of the two methods offering the greatest improvements in the quality of search. It provided the best improvement in the quality of search for the Griewank function, and was second only to probabilistic nonlinear rank scaling for the Schwefel function. Tournament selection, by comparison, was always the computationally cheapest option but did not necessarily find the best solutions

Algorithmic differentiation and the calculation of forces by quantum Monte Carlo

We describe an efficient algorithm to compute forces in quantum Monte Carlo using adjoint algorithmic differentiation. This allows us to apply the space warp coordinate transformation in differential form, and compute all the 3M force components of a system with M atoms with a computational effort comparable with the one to obtain the total energy. Few examples illustrating the method for an electronic system containing several water molecules are presented. With the present technique, the calculation of finite-temperature thermodynamic properties of materials with quantum Monte Carlo will be feasible in the near future.Comment: 32 pages, 4 figure, to appear in The Journal of Chemical Physic

QCD critical region and higher moments for three flavor models

One of the distinctive feature of the QCD phase diagram is the possible emergence of a critical endpoint. The critical region around the critical point and the path dependency of the critical exponents is investigated within effective chiral (2+1)-flavor models with and without Polyakov-loops. Results obtained in no-sea mean-field approximations where a divergent vacuum part in the fermion-loop contribution is neglected, are confronted to the renormalized ones. Furthermore, the modifications caused by the back-reaction of the matter fluctuations on the pure Yang-Mills system are discussed. Higher order, non-Gaussian moments of event-by-event distributions of various particle multiplicities are enhanced near the critical point and could serve as a probe to determine its location in the phase diagram. By means of a novel derivative technique higher order generalized quark-number susceptibilities are calculated and their sign structure in the phase diagram is analyzed.Comment: 12 pages, 11 figures. Final PRD version (references and one more equation added

Reading and Upward Bound-Another Look

The major purpose of summer Upward Bound instructional programs is to assist those high school students who have the potential for succeeding in a college or university, but who otherwise would probably not be given the opportunity to enter an institution of higher learning. The generally low academic achievement of many of these students is often due to a variety of factors including poor and ineffective teaching (1), lack of motivation (8), and an environment which is far from conducive to scholarly or academic pursuits. In sum, typical school activities tend to be less than relevant for many of these bright young men and women. The Upward Bound programs are usually designed to aid participating students in overcoming their adverse reactions to learning so that they will be better prepared to further their education

Power-Law Scaling in the Internal Variability of Cumulus Cloud Size Distributions due to Subsampling and Spatial Organization

In this study, the spatial structure of cumulus cloud populations is investigated using three-dimensional snapshots from large-domain LES experiments. The aim is to understand and quantify the internal variability in cloud size distributions due to subsampling effects and spatial organization. A set of idealized shallow cumulus cases is selected with varying degrees of spatial organization, including a slowly organizing marine precipitating case and five more quickly organizing diurnal cases over land. A subdomain analysis is applied, yielding cloud number distributions at sample sizes ranging from severely undersampled to nearly complete. A strong power-law scaling is found in the relation between cloud number variability and subdomain size, reflecting an inverse linear relation. Scaling subdomain size by cloud size yields a data collapse across time points and cases, highlighting the role played by cloud spacing in controlling the stochastic variability. Spatial organization acts on top of this baseline model by increasing the maximum cloud size and by enhancing the variability in the number of smallest clouds. This reflects that the smaller clouds start to live on top of larger-scale thermodynamic structures, such as cold pools, which favor or inhibit their formation. Compositing all continental cumulus cases suggests the existence of a prototype diurnal time dependence in the spatial organization. A simple stochastic expression for cloud number variability is proposed that is formulated in terms of two dimensionless groups, which allows objective estimation of the degree of spatial organization in simulated and observed cumulus cloud populations

Geometric approach to Fletcher's ideal penalty function

Original article can be found at: www.springerlink.com Copyright Springer. [Originally produced as UH Technical Report 280, 1993]In this note, we derive a geometric formulation of an ideal penalty function for equality constrained problems. This differentiable penalty function requires no parameter estimation or adjustment, has numerical conditioning similar to that of the target function from which it is constructed, and also has the desirable property that the strict second-order constrained minima of the target function are precisely those strict second-order unconstrained minima of the penalty function which satisfy the constraints. Such a penalty function can be used to establish termination properties for algorithms which avoid ill-conditioned steps. Numerical values for the penalty function and its derivatives can be calculated efficiently using automatic differentiation techniques.Peer reviewe

A first look at quasi-Monte Carlo for lattice field theory problems

In this project we initiate an investigation of the applicability of Quasi-Monte Carlo methods to lattice field theories in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable calculated by averaging over random observations generated from an ordinary Monte Carlo simulation behaves like N−1/2, where N is the number of observations. By means of Quasi-Monte Carlo methods it is possible to improve this behavior for certain problems to up to N−1. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling.Peer Reviewe