Sangit Chatterjee

Genetic algorithms and traveling salesman problems

Abstract A genetic algorithm (GA) with an asexual reproduction plan through a generalized mutation for an evolutionary operator is developed that can be directly applied to a permutation of n numbers for an approximate global optimal solution of a traveling salesman problem (TSP). Schema analysis of the algorithm shows that a sexual reproduction with the generalized mutation operator preserves the global convergence property of a genetic algorithm thus establishing the fundamental theorem of the GA for the algorithm. Avoiding an intermediate step of encoding through random keys to preserve crossover or permuting n and using “fixing” states for legal crossover are the chief benefits of the innovations reported in this paper. The algorithm has been applied to a number of natural and artificial problems and the results are encouraging.

On Measuring Skewness and Elongation in Common Stock Return Distributions: The Case of the Market Index

This article is an exploratory investigation of the distributional properties of market index returns using J. W. Tukeys g and h distributions. Specifically, it is shown that over sufficiently long periods of time, the distribution of the market index is adequately explained as a skewed, elongated (g x h) distribution. Estimates of skewness and elongation are developed that are easy to calculate and are robust with respect to outliers. Functional forms for the appropr iate distributions are provided. The findings reported here have implications for understanding skewness and elongation, developing appropriate portfolio strategies, and devising pricing models incorporating higher moments. Copyright 1988 by the University of Chicago.

Genetic algorithms and their statistical applications: an introduction

Abstract Genetic algorithms (GA) are stochastic optimization tools that work on “Darwinian” models of population biology and are capable of solving for near-optimal solution for multivariable functions without the usual mathematical requirements of strict continuity, differentiability, convexity and other properties. The algorithm begins by choosing a large number of candidate solutions which propagate themselves through a “selection criteria” and are changed by the application of well-developed genetic operators. GAs are applied to problems in statistical estimation and the results are compared to the output of standard software. It is argued that many statistical and mathematical restrictions that usually restrict modeling and analysis can be dispensed with by employing the GA as an optimization technique. The use of GAs for solving discrete optimization problems with applications in statistics for the variable selection problem in regression and other multivariate statistical methods are also discussed.

A Data-Analytic Look at Skewness and Elongation in Common-Stock-Return Distributions

This article explores the nature of skewness and elongation in daily common-stock-return distributions of individual firms using estimates of g (for skewness) and h (for elongation) obtained form Turkeys g and h distributions. Both parametric and nonparametric (bootstrap) estimates of standard errors of the g estimates are computed and compared. Daily return distributions are first examined cross-sectionally over a large sample of firms. The estimates of the skewness parameter exhibit variation across individual firms, but some general trends are evident across industry groups and firm sizes. Return distributions typically seem to be more elongated than the Gaussian distribution. From a time series perspective, both skewness and elongation are persistent in the return distributions of individual firms and vary over a finite range. First-order autocorrelation coefficients of monthly g and h estimates are large and suggest a certain degree of predictability.

Genetic clustering of social networks using random walks

In the era of globalization, traditional theories and models of social systems are shifting their focus from isolation and independence to networks and connectedness. Analyzing these new complex social models is a growing, and computationally demanding area of research. In this study, we investigate the integration of genetic algorithms (GAs) with a random-walk-based distance measure to find subgroups in social networks. We test our approach by synthetically generating realistic social network data sets. Our clustering experiments using random-walk-based distances reveal exceptionally accurate results compared with the experiments using Euclidean distances.

Bootstrapping ARMA Models: Some Simulations

The bootstrap is used to demonstrate the feasibility of obtaining estimates of standard errors of the parameter estimates of ARMA models. The method is applied to simulated data and to two published data sets, and the success of the bootstrap is evaluated. The simulations show the bootstrap to be an effective tool for estimating standard errors for parameter estimates in time series models. The bootstrap estimates of the standard errors are distribution free and valid for small samples.

A review of regression diagnostics for behavioral research

Influential data points can affect the results of a regression analysis; for example, the usual sum mary statistics and tests of significance may be misleading. The importance of regression diagnostics in detecting influential points is discussed, and five statistics are recommended for the applied researcher. The suggested diagnostics were used on a small dataset to detect an influen tial data point, and the effects were analyzed. Colinearity-based diagnostics also are discussed and illustrated on the same dataset. The non- robustness of the least squares estimates in the presence of influential points is emphasized. Diagnostics for multiple influential points, multi variate regression, multicolinearity, nonlinear regression, and other multivariate procedures also are discussed.

Estimation of misclassification probabilities by bootstrap methods

Several methods have been proposed to estimate the misclassification probabilities when a linear discriminant function is used to classify an observation into one of several populations. We describe the application of bootstrap sampling to the above problem. The proposed method has the advantage of not only furnishing the estimates of misclassification probabilities but also provides an estimate of the standard error of estimate. The method is illustrated by a small simulation experiment. It is then applied to three published, well accessible data sets, which are typical of large, medium and small data sets encountered in practice.

Comprehensive Analysis of Golf Performance on the Pga Tour: 1990–2004

Researchers have investigated the relationship between different shot-making measures and performance on the PGA Tour. Prior studies have typically focused on a short period of time or used a restricted sample so long-term trends were not discernible. To remedy this situation, the present study looked at the longitudinal performance of professional golfers from 1990–2004. The findings indicated a remarkable stability in terms of the relative importance of Greens In Regulation and Putting Average in explaining the variability in Scoring Average. The findings also indicated a declining importance of driving in recent years due, in part, to a strengthening of the negative relationship between Driving Distance and Driving Accuracy.

Quality confusion: Too many gurus, not enough disciples

These words, which seem especially valid today, belong to the great Mahatma Gandhi in a speech given to immigrant Indians in Johannesburg, South Africa in 1890. It underscores the message that quality and the importance of the customer are timeless. Such pioneers as W. Shewhart and J.M. Juran were writing about quality assurance in the 1920s and 1930s joined by W.E. Deming, E. Feigenbaum, and many others in the post-war era of the late 1940s. American management was only mildly interested in the ideas of these pioneers until the 197Os, when the erosion of American dominance in world markets became noticeable. The continuation of this erosion was the backdrop for Deming’s 1982 book, Out of the Crisis, which provided a timely bandwagon for everyone to board. The ensuing rush has been a chaotic and confusing experience; that experience is the subject of our discussion. Despite many decades of prodd&g by pioneers and relentless competitive pressure, progress in achieving high levels of quality in American manufacturing has been very slow compared to the accomplishments of foreign competitors. There are success stories, to be sure, and quality decline has been halted in many cases. Yet real questions remain about whether America can close the gap and regain markets in a number of industries that have fallen on hard times, or maintain lead1 ership in other industries now being threatened. Managers must learn ~ the principles of quality before they ’ can understand its practice. I i