Eduardo Conde

Multi-criteria analysis with partial information about the weighting coefficients

Abstract In this paper we address the problem of ranking a set of alternatives with partial information about the weighting coefficients. We introduce a family of quasiorders that are easily interpretable and manageable, which includes among others, the natural quasiorder in R n and other well known preference structures in the literature. The enrichment of the preference structure with respect to the natural quasiorder is measured by means of an absolute measure we introduce.

An improved algorithm for selecting p items with uncertain returns according to the minmax-regret criterion

Abstract.We consider the problem of selecting a subset of p investments of maximum total return out of a set of n available investments with uncertain returns, where uncertainty is represented by interval estimates for the returns, and the minmax regret objective is used. We develop an algorithm that solves this problem in O(min{p,n−p}n) time. This improves the previously known complexity O(min{p,n−p}2n).

Semi-obnoxious location models: A global optimization approach

In the last decades there has been an increasing interest in environmental topics. This interest has been reflected in modeling the location of obnoxious facilities, as shown by the number of important papers published in this field. However, a very common drawback of the existing literature is that, as soon as environmental aspects are taken into account, economical considerations (e.g. transportation costs) are ignored, leading to models with dubious practical interest. In this paper we take into account both the environmental impact and the transportation costs caused by the location of an obnoxious facility, and propose a solution method the well-known BSSS, with a new bounding scheme which exploits the structure of the problem.

A note on the minmax regret centdian location on trees

The minmax regret optimization model of the doubly weighted centdian location on trees is considered. Assuming that both types of weights, demands and relative importance of the customers, are partially known through interval estimates, an exact algorithm of complexity O(n^3logn) is derived. This bound is improved in some special cases.

An HMM for detecting spam mail

Hidden Markov Models, or HMMs for short, have been recently used in Bioinformatics for the classification of DNA or protein chains, giving rise to what is known as Profile Hidden Markov Models. In this paper, we show that these models can also be adapted to the problem of classifying misspelled words by identifying its primary structure through statistical tools. This process leads to a new learning algorithm which is based in the parametrization of the set of recognizable words in order to detect any misspelled form of these words. As an application, a method to classify spam mails by means of the detection of the adulterated words, from a blacklist of words frequently used by spammers, is described.

A minmax regret approach to the critical path method with task interval times

The execution of a given project, with a number of interrelated tasks due to precedence constraints, represents a challenge when one must to control the available resources and the compromised due dates. In this paper, we analyse this problem under uncertain individual task completing times, specifically, we will assume that a given range, for the admissible values of each individual completing time, is available. Taking into account that the precedence relations between tasks must be preserved, each realization of the admissible execution times for the set of tasks will define a new scenario determining the ending time for the project and the subset of critical tasks. The minmax regret criterion will be used in order to obtain a robust approximation to the critical set of tasks determining the overall execution time for the project.

Efficiency in Euclidean constrained location problems

In this note we present geometrical characterizations for the set of efficient, weakly efficient and properly efficient solutions to the multiobjective Euclidean Location problem with convex locational constraints, extending the known results for the unconstrained problem. It is shown that the set of the (weakly) efficient points coincides with the closest-point projection of the convex hull of the demand points onto the feasible set S. It is also shown that the set of properly efficient solutions is the union of two sets: the set of feasible demand points and the closest-point projection of the relative interior of the convex hull of the demand points onto S.

Inferring Efficient Weights from Pairwise Comparison Matrices

Several multi-criteria-decision-making methodologies assume the existence of weights associated with the different criteria, reflecting their relative importance.One of the most popular ways to infer such weights is the analytic hierarchy process, which constructs first a matrix of pairwise comparisons, from which weights are derived following one out of many existing procedures, such as the eigenvector method or the least (logarithmic) squares. Since different procedures yield different results (weights) we pose the problem of describing the set of weights obtained by “sensible” methods: those which are efficient for the (vector-) optimization problem of simultaneous minimization of discrepancies. A characterization of the set of efficient solutions is given, which enables us to assert that the least-logarithmic-squares solution is always efficient, whereas the (widely used) eigenvector solution is not, in some cases, efficient, thus its use in practice may be questionable.

On a constant factor approximation for minmax regret problems using a symmetry point scenario

In order to find a robust solution under an unknown linear cost function it will be considered the minmax regret criterion. It is assumed the vector of costs can take on values from a given uncertainty set. The resulting optimization model has been extensively analyzed in the literature when the uncertain costs are modeled by closed intervals. Unfortunately, except for rare applications, this problem has NP-hard complexity which has led to the appearance of approximated methods seeking for good solutions in a short computational time.

Simpson points in planar problems with locational constraints: the polyhedral-gauge case

In this paper we address the problem of finding Simpson points in planar models with locational constraints when distances are measured by polyhedral gauges. Making use of the results we have stated in a previous paper, we show here the existence of a finite set of points in the plane, independent of the weights associated with the users, that contains at least a Simpson point. Connection between Simpson points as a result of a voting process and Weber points as the outcome of a planning process are explored. It is shown by means of an example that the existing relations for the unconstrained case are no longer true when locational constraints are imposed. In order to reconcile both voting and planning processes, a biobjective problem is described, for which we construct a finite dominating set.