Problemas de optimización combinatoria: una propuesta que combina algoritmos genéticos y metaheurísticas

Timetabling se refiere al conjunto de problemas de optimización combinatoria que intentan asignar recursos, sean aulas, docentes o intervalos de tiempo, para distintas necesidades de estudiantes, cursos y exámenes. El presente trabajo se ocupa de una de las variantes de este problema, que busca agendar exámenes a distintos intervalos de tiempo, cumpliendo con las restricciones de que ningún alumno debe asistir a más de un examen en el mismo momento y que, en la medida de lo posible, tenga el mayor tiempo libre entre las evaluaciones. Los intervalos de tiempo no tienen restricciones en cuanto a la cantidad de exámenes que puedan asignárseles. Como estrategia de resolución se utiliza un algoritmo genético, que combina diversas heurísticas para la construcción de soluciones factibles que conforman la población inicial con la que trabaja el algoritmo. Dichas heurísticas fueron seleccionadas priorizando la calidad de la solución construida. También se definieron operadores de cruzamiento y mutación particulares, con el objetivo de mejorar la calidad de la solución resultante del proceso genético o, al menos, evitar la generación de soluciones no factibles. Mediante el algoritmo propuesto se alcanzaron soluciones relativamente buenas con pocas evaluaciones de la función objetivo y en un tiempo de ejecución razonable

The GPU on the simulation of cellular computing models

Membrane Computing is a discipline aiming to abstract formal computing models, called membrane systems or P systems, from the structure and functioning of the living cells as well as from the cooperation of cells in tissues, organs, and other higher order structures. This framework provides polynomial time solutions to NP-complete problems by trading space for time, and whose efficient simulation poses challenges in three different aspects: an intrinsic massively parallelism of P systems, an exponential computational workspace, and a non-intensive floating point nature. In this paper, we analyze the simulation of a family of recognizer P systems with active membranes that solves the Satisfiability problem in linear time on different instances of Graphics Processing Units (GPUs). For an efficient handling of the exponential workspace created by the P systems computation, we enable different data policies to increase memory bandwidth and exploit data locality through tiling and dynamic queues. Parallelism inherent to the target P system is also managed to demonstrate that GPUs offer a valid alternative for high-performance computing at a considerably lower cost. Furthermore, scalability is demonstrated on the way to the largest problem size we were able to run, and considering the new hardware generation from Nvidia, Fermi, for a total speed-up exceeding four orders of magnitude when running our simulations on the Tesla S2050 server.Agencia Regional de Ciencia y Tecnología - Murcia 00001/CS/2007Ministerio de Ciencia e Innovación TIN2009–13192Ministerio de Ciencia e Innovación TIN2009-14475-C04European Commission Consolider Ingenio-2010 CSD2006-0004

P systems simulations on massively parallel architectures

Membrane Computing is an emergent research area studying the behaviour of living cells to de ne bio-inspired computing devices, also called P systems. Such devices provide polynomial time solutions to NP-complete problems by trading time for space. The e cient simulation of P systems poses challenges in three di erent aspects: an intrinsic massively parallelism of P systems, an exponential computational workspace, and a non-intensive oating point nature. In this paper, we analyze the simulation of a family of recognizer P systems with active membranes that solves the Satis ability (SAT) problem in linear time on three di erent architectures: a shared memory system, a distributed memory system, and a set of Graphics Processing Units (GPUs). For an e cient handling of the exponential workspace created by the P systems computation, we enable di erent data policies on those architectures to increase memory bandwidth and exploit data locality through tiling. Parallelism inherent to the target P system is also managed on each architecture to demonstrate that GPUs o er a valid alternative for high-performance computing at a considerably lower cost: Considering the largest problem size we were able to run on the three parallel platforms involving four processors, execution times were 20049.70 ms. using OpenMP on the shared memory multiprocessor, 4954.03 ms. using MPI on the distributed memory multiprocessor and 565.56 ms. using CUDA in our four GPUs, which results in speed factors of 35.44x and 8.75x, respectively.Fundación Séneca 00001/CS/2007Ministerio de Ciencia e Innovación TIN2009–13192European Community CSD2006- 00046Junta de Andalucía P06-TIC-02109Junta de Andalucía P08–TIC-0420

Simulating a P system based efficient solution to SAT by using GPUs

P systems are inherently parallel and non-deterministic theoretical computing devices defined inside the field of Membrane Computing. Many P system simulators have been presented in this area, but they are inefficient since they cannot handle the parallelism of these devices. Nowadays, we are witnessing the consolidation of the GPUs as a parallel framework to compute general purpose applications. In this paper, we analyse GPUs as an alternative parallel architecture to improve the performance in the simulation of P systems, and we illustrate it by using the case study of a family of P systems that provides an efficient and uniform solution to the SAT problem. Firstly, we develop a simulator that fully simulates the computation of the P system, demonstrating that GPUs are well suited to simulate them. Then, we adapt this simulator to the GPU architecture idiosyncrasies, improving the performance of the previous simulator.Ministerio de Ciencia e Innovación TIN2009–13192Junta de Andalucía P08–TIC-0420

Simulation of P systems with active membranes on CUDA

P systems or Membrane Systems provide a high-level computational modelling framework that combines the structure and dynamic aspects of biological systems in a relevant and understandable way. They are inherently parallel and non-deterministic computing devices. In this article, we discuss the motivation, design principles and key of the implementation of a simulator for the class of recognizer P systems with active membranes running on a (GPU). We compare our parallel simulator for GPUs to the simulator developed for a single central processing unit (CPU), showing that GPUs are better suited than CPUs to simulate P systems due to their highly parallel nature.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía P08–TIC-0420

Implementing P Systems Parallelism by Means of GPUs

Software development for Membrane Computing is growing up yielding new applications. Nowadays, the efficiency of P systems simulators have become a critical point when working with instances of large size. The newest generation of GPUs (Graphics Processing Units) provide a massively parallel framework to compute general purpose computations. We present GPUs as an alternative to obtain better performance in the simulation of P systems and we illustrate it by giving a solution to the N-Queens problem as an example.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía P08–TIC-0420

Simulation of Recognizer P Systems by Using Manycore GPUs

Software development for cellular computing is growing up yielding new applications. In this paper, we describe a simulator for the class of recognizer P systems with active membranes, which exploits the massively parallel nature of the P systems computations by using a massively parallel computer architecture, such as Compute Unified Device Architecture (CUDA) from Nvidia, to obtain better performance in the simulations. We illustrate it by giving a solution to the N-Queens problem as an example.Ministerio de Educación y Ciencia TIN2006–13425Junta de Andalucía P08–TIC0420

A massively parallel framework using P systems and GPUs

Since CUDA programing model appeared on the general purpose computations, the developers can extract all the power contained in GPUs (Graphics Processing Unit) across many computational domains. Among these domains, P systems or membrane systems provide a high level computational modeling framework that allows, in theory, to obtain polynomial time solutions to NP-complete problems by trading time for space, and also to model biological phenomena in the area of computational systems biology. P systems are massively parallel distributed devices and their computation can be divided in two levels of parallelism: membranes, that can be expressed as blocks in CUDA programming model; and objects, that can be expressed as threads in CUDA programming model. In this paper, we present our initial ideas of developing a simulator for the class of recognizer P systems with active membranes by using the CUDA programing model to exploit the massively parallel nature of those systems at maximum. Experimental results of a preliminary version of our simulator on a Tesla C1060 GPU show a 60X of speed-up compared to the sequential code.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía P08–TIC-0420

Analysis of P systems simulation on CUDA

GPUs (Graphics Processing Unit) have been con- solidated as a massively data-parallel coprocessor to develop many general purpose computations, and en- able developers to utilize several levels of parallelism to obtain better performance of their applications. The massively parallel nature of certain computa- tions leads to use GPUs as an underlying architec- ture, becoming a good alternative to other paral- lel approaches. P systems or membrane systems are theoretical devices inspired in the way that liv- ing cells work, providing computational models and a high level computational modeling framework for biological systems. They are massively parallel dis- tributed, and non-deterministic systems. In this pa- per, we evaluate the GPU as the underlying archi- tecture to simulate the class of recognizer P systems with active membranes. We analyze the performance of three simulators implemented on CPU, CPU-GPU and GPU respectively. We compare them using a pre- sented P system as a benchmark, showing that the GPU is better suited than the CPU to simulate those P systems due to its massively parallel nature.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía P08–TIC0420