Genetic algorithms for numerical optimization

Genetic algorithms (GAs) are stochastic adaptive algorithms whose search method is based on simulation of natural genetic inheritance and Darwinian striving for survival. They can be used to find approximate solutions to numerical optimization problems in cases where finding the exact optimum is prohibitively expensive, or where no algorithm is known. However, such applications can encounter problems that sometimes delay, if not prevent, finding the optimal solutions with desired precision. In this paper we describe applications of GAs to numerical optimization, present three novel ways to handle such problems, and give some experimental results.     

A comparison between genetic algorithms and the RAND method for solving the joint replenishment problem

The purpose of this paper is to compare the performance of genetic algorithms (GAs) and the best available heuristic, known as the RAND, for solving the joint replenishment problem (JRP). An important feature of the JRP which makes it suitable for GAs is that it can be formulated as a problem having one continuous decision variable and a number of integer decision variables equal to the number of products being produced or ordered. Experiments on randomly generated problems indicate that GAs can provide better solutions to the JRP than the RAND for some problems, and at worst can almost match the performance of the RAND from a practical point of view for the rest of the problems. GAs never converged to solution with a total cost of more than 0.08% of the total cost of the RAND for 1600 randomly generated problems. In addition, GAs have the advantages of: (i) being easy to implement (e.g. less than 200 lines of code); (ii) having a code which is easy to understand and modify; and (iii) dealing easily with constrained JRPs which are neglected by most of the available methods including the RAND, in spite of their importance in practice.     

Non-standard methods in evolutionary computation

The paper presents non-standard methods in evolutionary computation and discusses their applicability to various optimization problems. These methods maintain populations of individuals with nonlinear chromosomal structure and use genetic operators enhanced by the problem specific knowledge.     

The Downfall of Gomułka

Marina Tsvetaeva’s 1934 “Chërt” (The Devil) forms a central part of the cycle of autobiographical prose she wrote in emigration. This article assembles clues to the hidden origins of the Devil she describes in prose about her grandfathers, some of it censored in pre-1990 editions of her works. Tsvetaeva’s Devil is not simply metaphysical: it has the unusual appearance of a Great Dane. Though she goes on to trace its appearances in the literature and culture of her childhood, some of its physical features (eyes, nose, colour and posture) link it with other people in her life. The vivid details of the Devil suggest relationships, though peculiarly mediated ones, to members of her own family, especially her maternal grandfather, Aleksandr Danilovich Mein. The poet describes herself using Pushkin’s poem “Utoplennik” to camouflage her own sense of self from her mother. Much of the rest of “The Devil” describes her recognition of the Devil in varying symbolic or even phonetic guises, tracing how the poet stayed faithful to him even after he ceased to appear visibly, how she found and read his symbols in surrounding reality—e.g., card games, toys, rituals for finding lost objects—and in unexpected, otherwise respectable, parts of society, including her own grandfather. As always, Tsvetaeva creates a story that affirms her identity as a poet and illustrates the work she had to do to achieve that identity.     

Change-point detection in a shape-restricted regression model

A regression model with a possible structural change and with a small number of measurements is considered. A priori information about the shape of the regression function is used to formulate the model as a linear regression model with inequality constraints and a likelihood ratio test for the presence of a change-point is constructed. The exact null distribution of the test statistic is given. Consistency of the test is proved when the noise level goes to zero. Numerical approximations to the powers against various alternatives are given and compared with the powers of the k-linear-r-ahead recursive residuals tests and CUSUM tests. Performance of four different estimators of the change-point is studied in a Monte Carlo experiment. An application of the procedures to some real data is also presented.     

Intake Fraction Variability Between Air Pollution Emission Sources Inside an Urban Area

The cost‐effective mitigation of adverse health effects caused by air pollution requires information on the contribution of different emission sources to exposure. In urban areas the exposure potential of different sources may vary significantly depending on emission height, population density, and other factors. In this study, we quantified this intraurban variability by predicting intake fraction (iF) for 3,066 emission sources in Warsaw, Poland. iF describes the fraction of the pollutant that is inhaled by people in the study area. We considered the following seven pollutants: particulate matter (PM), nitrogen oxides (NO_x), sulfur dioxide (SO₂), benzo[a] pyrene (BaP), nickel (Ni), cadmium (Cd), and lead (Pb). Emissions for these pollutants were grouped into four emission source categories (Mobile, Area, High Point, and Other Point sources). The dispersion of the pollutants was predicted with the CALPUFF dispersion model using the year 2005 emission rate data and meteorological records. The resulting annual average concentrations were combined with population data to predict the contribution of each individual source to population exposure. The iFs for different pollutant‐source category combinations varied between 51 per million (PM from Mobile sources) and 0.013 per million (sulfate PM from High Point sources). The intraurban iF variability for Mobile sources primary PM emission was from 4 per million to 100 per million with the emission‐weighted iF of 44 per million. These results propose that exposure due to intraurban air pollution emissions could be decreased more effectively by specifically targeting sources with high exposure potency rather than all sources.     

The effect of dance therapy on the balance of women over 60 years of age: The influence of dance therapy for the elderly

Dance therapy is a physical activity that can lead to balance improvement in older adults. The aim of the study was to evaluate the effects of dance therapy on balance and risk of falls in older women. Twenty-four older women (mean age 66.4 years old) attended dance sessions for three months. Pretest/posttests were completed using the Postural Stability Test, the Limits of Stability Test, and the Fall Risk Test M-CTSIB. Results showed the Limits of Stability Test was significantly higher (17.5%) after dance classes. Regular use of dance therapy shows promise in improving balance by increasing the limits of stability.     

Matrix geometric approach for random walks: Stability condition and equilibrium distribution

ABSTRACT

In this paper, we analyze a sub-class of two-dimensional homogeneous nearest neighbor (simple) random walk restricted on the lattice using the matrix geometric approach. In particular, we first present an alternative approach for the calculation of the stability condition, extending the result of Neuts drift conditions^[30 Neuts, M.F., Matrix-geometric Solutions in Stochastic Models: An Algorithmic Approach; The Johns Hopkins University Press: Baltimore, 1981. [Google Scholar]^] and connecting it with the result of Fayolle et al. which is based on Lyapunov functions.^[13 Fayolle, G.; Iasnogorodski, R.; Malyshev, V., Random Walks in the Quarter Plane; Springer-Verlag: New York, 1999. [Google Scholar]^] Furthermore, we consider the sub-class of random walks with equilibrium distributions given as series of product forms and, for this class of random walks, we calculate the eigenvalues and the corresponding eigenvectors of the infinite matrix R appearing in the matrix geometric approach. This result is obtained by connecting and extending three existing approaches available for such an analysis: the matrix geometric approach, the compensation approach and the boundary value problem method. In this paper, we also present the spectral properties of the infinite matrix R.