Differential evolution for solving the mobile location management

In this work we present two new approaches to solve the location management problem, respectively, based on the location areas and the reporting cells strategies. The location management problem corresponds to the management of the network configuration with the objective of minimizing the costs involved. We use the differential evolution algorithm to find the best configuration for the location areas and the reporting cells strategies, which principally considers the location update and paging costs. With this work we want to define the best values to the differential evolution configuration, using test networks and also realistic networks, as well as compare our results with the ones obtained by other authors. These two new approaches applied to this problem have given us very good results, when compared with those obtained by other authors.     

A flux-free a posteriori error estimator for the incompressible Stokes problem using a mixed FE formulation

In this contribution, we present an a posteriori error estimator for the incompressible Stokes problem valid for a conventional mixed FE formulation. Due to the saddle-point property of the problem, conventional error estimators developed for pure minimization problems cannot be utilized straight-forwardly. The new estimator is built up by two key ingredients. At first, a computed error approximation, exactly fulfilling the continuity equation for the error, is obtained via local Dirichlet problems. Secondly, we adopt the approach of solving local equilibrated flux-free problems in order to bound the remaining, incompressible, error. In this manner, guaranteed upper and lower bounds, of the velocity “energy norm” of the error as well as goal-oriented (linear) output functionals, with respect to a reference (overkill) mesh are obtained. In particular, it should be noted that this approach requires no computation of hybrid fluxes. Furthermore, the estimator is applicable to mixed FE formulations using continuous pressure approximations, such as the Mini and Taylor–Hood class of elements. In conclusion, a few simple numerical examples are presented, illustrating the accuracy of the error bounds.     

Slicing for architectural analysis

Current software development often relies on non-trivial coordination logic for combining autonomous services, eventually running on different platforms. As a rule, however, such a coordination layer is strongly woven within the application at source code level. Therefore, its precise identification becomes a major methodological (and technical) problem and a challenge to any program understanding or refactoring process.The approach introduced in this paper resorts to slicing techniques to extract coordination data from source code. Such data are captured in a specific dependency graph structure from which a coordination model can be recovered either in the form of an Orc specification or as a collection of code fragments corresponding to the identification of typical coordination patterns in the system. Tool support is also discussed.     

Deciding k-Colorability of P 5-Free Graphs in Polynomial Time

The problem of computing the chromatic number of a P ₅-free graph (a graph which contains no path on 5 vertices as an induced subgraph) is known to be NP-hard. However, we show that for every fixed integer k, there exists a polynomial-time algorithm determining whether or not a P ₅-free graph admits a k-coloring, and finding one, if it does.     

A parallel evolutionary algorithm to optimize dynamic memory managers in embedded systems

For the last 30 years, several dynamic memory managers (DMMs) have been proposed. Such DMMs include first fit, best fit, segregated fit and buddy systems. Since the performance, memory usage and energy consumption of each DMM differs, software engineers often face difficult choices in selecting the most suitable approach for their applications. This issue has special impact in the field of portable consumer embedded systems, that must execute a limited amount of multimedia applications (e.g., 3D games, video players, signal processing software, etc.), demanding high performance and extensive memory usage at a low energy consumption. Recently, we have developed a novel methodology based on genetic programming to automatically design custom DMMs, optimizing performance, memory usage and energy consumption. However, although this process is automatic and faster than state-of-the-art optimizations, it demands intensive computation, resulting in a time-consuming process. Thus, parallel processing can be very useful to enable to explore more solutions spending the same time, as well as to implement new algorithms. In this paper we present a novel parallel evolutionary algorithm for DMMs optimization in embedded systems, based on the Discrete Event Specification (DEVS) formalism over a Service Oriented Architecture (SOA) framework. Parallelism significantly improves the performance of the sequential exploration algorithm. On the one hand, when the number of generations are the same in both approaches, our parallel optimization framework is able to reach a speed-up of 86.40× when compared with other state-of-the-art approaches. On the other, it improves the global quality (i.e., level of performance, low memory usage and low energy consumption) of the final DMM obtained in a 36.36% with respect to two well-known general-purpose DMMs and two state-of-the-art optimization methodologies.     

On the Planar Piecewise Quadratic 1-Center Problem

In this paper we introduce a minimax model unifying several classes of single facility planar center location problems. We assume that the transportation costs of the demand points to the serving facility are convex functions {Q _i }, i=1,…,n, of the planar distance used. Moreover, these functions, when properly transformed, give rise to piecewise quadratic functions of the coordinates of the facility location. In the continuous case, using results on LP-type models by Clarkson (J. ACM 42:488–499, 1995), Matoušek et al. (Algorithmica 16:498–516, 1996), and the derandomization technique in Chazelle and Matoušek (J. Algorithms 21:579–597, 1996), we claim that the model is solvable deterministically in linear time. We also show that in the separable case, one can get a direct O(nlog n) deterministic algorithm, based on Dyer (Proceedings of the 8th ACM Symposium on Computational Geometry, 1992), to find an optimal solution. In the discrete case, where the location of the center (server) is restricted to some prespecified finite set, we introduce deterministic subquadratic algorithms based on the general parametric approach of Megiddo (J. ACM 30:852–865, 1983), and on properties of upper envelopes of collections of quadratic arcs. We apply our methods to solve and improve the complexity of a number of other location problems in the literature, and solve some new models in linear or subquadratic time complexity.     

DEMORS: A hybrid multi-objective optimization algorithm using differential evolution and rough set theory for constrained problems

The aim of this paper is to show how the hybridization of a multi-objective evolutionary algorithm (MOEA) and a local search method based on the use of rough set theory is a viable alternative to obtain a robust algorithm able to solve difficult constrained multi-objective optimization problems at a moderate computational cost. This paper extends a previously published MOEA [Hernández-Díaz AG, Santana-Quintero LV, Coello Coello C, Caballero R, Molina J. A new proposal for multi-objective optimization using differential evolution and rough set theory. In: 2006 genetic and evolutionary computation conference (GECCO’2006). Seattle, Washington, USA: ACM Press; July 2006], which was limited to unconstrained multi-objective optimization problems. Here, the main idea is to use this sort of hybrid approach to approximate the Pareto front of a constrained multi-objective optimization problem while performing a relatively low number of fitness function evaluations. Since in real-world problems the cost of evaluating the objective functions is the most significant, our underlying assumption is that, by aiming to minimize the number of such evaluations, our MOEA can be considered efficient. As in its previous version, our hybrid approach operates in two stages: in the first one, a multi-objective version of differential evolution is used to generate an initial approximation of the Pareto front. Then, in the second stage, rough set theory is used to improve the spread and quality of this initial approximation. To assess the performance of our proposed approach, we adopt, on the one hand, a set of standard bi-objective constrained test problems and, on the other hand, a large real-world problem with eight objective functions and 160 decision variables. The first set of problems are solved performing 10,000 fitness function evaluations, which is a competitive value compared to the number of evaluations previously reported in the specialized literature for such problems. The real-world problem is solved performing 250,000 fitness function evaluations, mainly because of its high dimensionality. Our results are compared with respect to those generated by NSGA-II, which is a MOEA representative of the state-of-the-art in the area.