Joaquín Pérez-Ortega

Algorithm Selection: From Meta-Learning to Hyper-Heuristics

In order for a company to be competitive, an indispensable requirement is the efficient management of its resources. As a result derives a lot of complex optimization problems that need to be solved with high-performance computing tools. In addition, due to the complexity of these problems, it is considered that the most promising approach is the solution with approximate algorithms; highlighting the heuristic optimizers. Within this category are the basic heuristics that are experience-based techniques and the metaheuristic algorithms that are inspired by natural or artificial optimization processes.

Mathematical Model for Optimizing the Composition of an Investment Portfolio for the Mexican Stock Market

A linear programming mathematical model is presented, which permits to compose an investment portfolio that achieves the maximal return at minimal risk from public information published on the web page of the Mexican stock exchange (BMV). Each of the linear programming problems (return maximization and risk minimization) is solved individually, and their optimal values are compared against those of a portfolio obtained using a statistical method. The results show that it is possible to compose a portfolio at minimal risk at time zero, and that the portfolio obtained by the statistical method is different from the one obtained by solving the optimization mathematical model.

Minimizing roundtrip response time in distributed databases with vertical fragmentation

The main purpose of this paper is to show the advantage of using a model proposed by us, which minimizes roundtrip response time versus traditional models that minimize query transmission and processing costs for the design of a distributed database with vertical fragmentation. To this end, an experiment was conducted to compare the roundtrip response time of the optimal solution obtained using our model versus the roundtrip response time of the optimal solution obtained using a traditional model. The experimental results show that for most cases the optimal solution from a traditional model yields a response time which is larger than the response time of the optimal solution obtained from our model, and sometimes it can be thrice as large.

An Efficient Heuristic Applied to the K-means Algorithm for the Clustering of Large Highly-Grouped Instances

Con la presencia cada vez mayor de Big Data surge la necesidad de agrupar grandes instancias. Estas instancias presentan un numero de objetos de naturaleza multidimensional, los cuales requieren agruparse en cientos o miles de grupos. En este articulo se presenta una mejora al algoritmo K-means, la cual esta orientada a la solucion eficiente de instancias con un gran numero de grupos y de dimensiones. A dicha mejor heuristica se le denomina Honeycomb (HC) y esta basada en la relacion entre el numero de dimensiones y el numero de centroides que conforman una vecindad, permitiendo reducir el numero de calculos de distancias objeto-centroide para cada objeto. La heuristica se valido resolviendo un conjunto de instancias sinteticas obteniendo reducciones del tiempo de ejecucion de hasta un 90% y con disminucion de la calidad menor al 1%, respecto a K-means estandar. Para instancias reales de baja y alta dimensionalidad, HC obtuvo una reduccion del tiempo de ejecucion entre 84.74% y 95.44% y con una reduccion de la calidad entre el 1.07% y 1.62%, respectivamente. Los resultados experimentales son alentadores porque esta heuristica beneficiaria a aquellos dominios que requieren instancias con valores cada vez mayores de objetos, dimensiones y grupos.

Application of formal languages in polynomial transformations of instances between NP-complete problems

We propose the usage of formal languages for expressing instances of NP-complete problems for their application in polynomial transformations. The proposed approach, which consists of using formal language theory for polynomial transformations, is more robust, more practical, and faster to apply to real problems than the theory of polynomial transformations. In this paper we propose a methodology for transforming instances between NP-complete problems, which differs from Garey and Johnson’s. Unlike most transformations which are used for proving that a problem is NP-complete based on the NP-completeness of another problem, the proposed approach is intended for extrapolating some known characteristics, phenomena, or behaviors from a problem A to another problem B. This extrapolation could be useful for predicting the performance of an algorithm for solving B based on its known performance for problem A, or for taking an algorithm that solves A and adapting it to solve B.

Selection of an investment portfolio by means of multi-objective mathematical model applied to mexican stock market in period of debacle

The selection of a portfolio of investment through a multi-objective mathematical model indicates that it possible have several available portfolios. In our model, the selection of one of them is performed with the same principle used by the Capital Assets Pricing Model, a single point touches the border of optimal portfolios. The model is tested with selection of an investment portfolio during period debacle of the Mexican Stock Market. This is possible because our model can be applied when there is no positive return. The results show that it is possible to obtain profit positive investment portfolios in periods of debacle.