ON WEYL GROUPS IN MINIMAL SIMPLE GROUPS OF FINITE MORLEY RANK

We prove that generous non-nilpotent Borel subgroups of connected minimal simple groups of finite Morley rank are self-normalizing. We use this to introduce a uniform approach to the analysis of connected minimal simple groups of finite Morley rank through a case division incorporating four mutually exclusive classes of groups. We use these to analyze Carter subgroups and Weyl groups in connected minimal simple groups of finite Morley rank. Finally, the self-normalization theorem is applied to give a new proof of an important step in the classification of simple groups of finite Morley rank of odd type

A discrete competitive facility location model with variable attractiveness

We consider the discrete version of the competitive facility location problem in which new facilities have to be located by a new market entrant firm to compete against already existing facilities that may belong to one or more competitors. The demand is assumed to be aggregated at certain points in the plane and the new facilities can be located at predetermined candidate sites. We employ Huff’s gravity-based rule in modelling the behaviour of the customers where the probability that customers at a demand point patronize a certain facility is proportional to the facility attractiveness and inversely proportional to the distance between the facility site and demand point. The objective of the firm is to determine the locations of the new facilities and their attractiveness levels so as to maximize the profit, which is calculated as the revenue from the customers less the fixed cost of opening the facilities and variable cost of setting their attractiveness levels. We formulate a mixed-integer nonlinear programming model for this problem and propose three methods for its solution: a Lagrangean heuristic, a branch-and-bound method with Lagrangean relaxation, and another branch-and-bound method with nonlinear programming relaxation. Computational results obtained on a set of randomly generated instances show that the last method outperforms the others in terms of accuracy and efficiency and can provide an optimal solution in a reasonable amount of time

An evolutionary approach for tuning parametric Esau and Williams heuristics

Owing to its inherent difficulty, many heuristic solution methods have been proposed for the capacitated minimum spanning tree problem. On the basis of recent developments, it is clear that the best metaheuristic implementations outperform classical heuristics. Unfortunately, they require long computing times and may not be very easy to implement, which explains the popularity of the Esau and Williams heuristic in practice, and the motivation behind its enhancements. Some of these enhancements involve parameters and their accuracy becomes nearly competitive with the best metaheuristics when they are tuned properly, which is usually done using a grid search within given search intervals for the parameters. In this work, we propose a genetic algorithm parameter setting procedure. Computational results show that the new method is even more accurate than an enumerative approach, and much more efficien