We establish new lower bounds on the distance between two points of a minimum energy configuration of $N$ points in $\mathbb{R}^3$ interacting according to a pairwise potential function. For the Lennard-Jones case, this bound is 0.67985 (and 0.7633 in the planar case). A similar argument yields an estimate for the minimal distance in Morse clusters, … Read more
The evolutionary history of species may be described by a phylogenetic tree whose topology captures ancestral relationships among the species, and whose branch lengths denote evolution times. For a fixed topology and an assumed probabilistic model of nucleotide substitution, we show that the likelihood of a given tree is a d.c. (difference of convex) function … Read more
We describe scheduling algorithms for monitoring an information source whose contents change at times modeled by a nonhomogeneous Poisson process. In a given time period of length T, we enforce a politeness constraint that we may only probe the source at most n times. This constraint, along with an optional constraint that no two probes … Read more
The problem of finding the optimal placement of $N$ identical, non overlapping, circles with maximum radius in the unit square is a well known challenge both in classical geometry and in optimization. A database of putative optima is currently maintained at \url{www.packomania.com}. Recently, through clever use of an extremely simple global optimization method, we succeeded … Read more
One recently proposed criterion to separate two datasets in discriminant analysis, is to use a hyperplane which minimises the sum of distances to it from all the misclassified data points. Here all distances are supposed to be measured by way of some fixed norm,while misclassification means lying on the wrong side of the hyperplane, or … Read more
One recently proposed criterion to separate two datasets in discriminant analysis, is to use a hyperplane which minimises the sum of distances to it from all the misclassified data points. Here all distances are supposed to be measured by way of some fixed norm, while misclassification means lying on the wrong side of the hyperplane, … Read more
Managing shelf space is critical for retailers to attract customers and to optimize profit. This paper develops a shelf space allocation optimization model that explicitly incorporates essential in-store costs and considers space- and cross-elasticities. The resultant model maximizes a signomial objective function over linear and bilinear constraints in mixed-integer variables. We propose a piecewise linearization … Read more
A new method for data-based fuzzy system modeling is presented. The approach uses Takagi-Sugeno models and Adaptive Simulated Annealing (ASA) to achieve its goal . The problem to solve is well defined – given a training set containing a finite number of input-output pairs, construct a fuzzy system that approximates the behavior of the real … Read more
We deal with the problem of scheduling preventive maintenance (PM) by minimizing a performance function which reflects repair and replacement costs as well as the costs of the PM itself. It is assumed that there is a known model which predicts the frequency of system failure as a function of its age; and it is … Read more
This paper deals with the issue of buy-in thresholds in portfolio optimization using the Markowitz approach. Optimal values of invested fractions calculated using, for instance, the classical minimum-risk problem can be unsatisfactory in practice because they imply that very small amounts of certain assets are purchased. Realistically, we want to impose a disjoint restriction so … Read more