Accelerated execution of P systems with active membranes to solve the N-queens problem

The N-queens problem has attracted increasing attention because of its potential applications in different areas, such as parallel memory storage approaches, image processing, and physical and chemical studies. Local search is a powerful method for solving real problems, such as the N-queens problem. Recently, models of P systems with active membranes have been used for local search to solve the N-queens problem. However, there have been insufficient studies of the parallelism of the P-system models with active membranes. In addition, the active membrane systems defined for N queens have several individual membranes that contain one object and no internal rules in each membrane, as well as several communication rules among membranes, which reduce the execution speed. In this study, a new P system model with active membranes is defined for solving the N-queens problem, and multi-core simulation of the proposed membrane system allows the execution of alternative computations in parallel, thus reducing the average time for finding a successful computation. The speed of the proposed model was compared with previous models that used P systems with active membranes for local search. The model contains two membranes, but the inclusion of several objects and rules within each membrane increases the parallelism and performance. This model reduces the number of communication rules required among membranes, and increases the execution speed. This model also increases the parallelism of previous P systems with active membranes when several rules evolve concurrently and more than one queen is exchanged during each step to reach a solution. Multi-core processing has been used to decrease the probability of restarting the P systems and to decrease processing time by distributing the processing of the active membrane on the multi-core. The speed of the proposed model when solving N = 200 queens was almost 1000 times faster than previous methods.

[1]  Mario J. Pérez-Jiménez,et al.  A Model of the Quorum Sensing System in Vibrio fischeri Using P Systems , 2008, Artificial Life.

[2]  Marian Gheorghe,et al.  Quorum sensing P systems , 2007, Theor. Comput. Sci..

[3]  G. Paun,et al.  Tracing Some Open Problems in Membrane Computing , 2007 .

[4]  Mario J. Pérez-Jiménez,et al.  A uniform solution to SAT using membrane creation , 2007, Theor. Comput. Sci..

[5]  Artiom Alhazov,et al.  Solving HPP and SAT by P Systems with Active Membranes and Separation Rules , 2006, Acta Informatica.

[6]  Gheorghe Paun,et al.  Membrane Computing , 2002, Natural Computing Series.

[7]  Xiangxiang Zeng,et al.  Deterministic solutions to QSAT and Q3SAT by spiking neural P systems with pre-computed resources , 2010, Theor. Comput. Sci..

[8]  Mario J. Pérez-Jiménez,et al.  Depth-First Search with P Systems , 2010, Int. Conf. on Membrane Computing.

[9]  Enrique Alba,et al.  A Methodology for Comparing the Execution Time of Metaheuristics Running on Different Hardware , 2012, EvoCOP.

[10]  Mario J. Pérez-Jiménez,et al.  A Linear-Time Solution to the Knapsack Problem Using P Systems with Active Membranes , 2003, Workshop on Membrane Computing.

[11]  Mario J. Pérez-Jiménez,et al.  Modeling Ecosystems Using P Systems: The Bearded Vulture, a Case Study , 2009, Workshop on Membrane Computing.

[12]  Ying Ju,et al.  Solving Multidimensional 0-1 Knapsack Problem with Time-Free Tissue P Systems , 2014, J. Appl. Math..

[13]  Mario J. Pérez-Jiménez,et al.  Local Search with P Systems: A Case Study , 2011, Int. J. Nat. Comput. Res..

[14]  Vincenzo Manca,et al.  Predator-prey dynamics in P systems ruled by metabolic algorithm , 2008, Biosyst..

[15]  Marian Gheorghe,et al.  An Appealing Computational Mechanism Drawn from Bacterial Quorum Sensing , 2005, Bull. EATCS.

[16]  Mario J. Pérez-Jiménez,et al.  An Overview of P-Lingua 2.0 , 2009, Workshop on Membrane Computing.

[17]  Mario J. Pérez-Jiménez,et al.  Available Membrane Computing Software , 2006, Applications of Membrane Computing.

[18]  Charles Gouin-Vallerand,et al.  A Macro and Micro Context Awareness Model for the Provision of Services in Smart Spaces , 2012, ICOST.

[19]  Xiangxiang Zeng,et al.  Spiking Neural P Systems with Weighted Synapses , 2011, Neural Processing Letters.

[20]  Mario de Jesús Pérez Jiménez,et al.  Solving the N-Queens Puzzle with P Systems , 2009 .

[21]  Artiom Alhazov,et al.  Uniform Solution of , 2007, MCU.

[22]  Mario J. Pérez-Jiménez,et al.  A Linear-time Tissue P System Based Solution for the 3-coloring Problem , 2007, Electron. Notes Theor. Comput. Sci..

[23]  Gheorghe Paun,et al.  Membrane Computing , 2002, Natural Computing Series.

[24]  Brett Stevens,et al.  A survey of known results and research areas for n-queens , 2009, Discret. Math..

[25]  Gheorghe Paun,et al.  A quick introduction to membrane computing , 2010, J. Log. Algebraic Methods Program..

[26]  Mario J. Pérez-Jiménez,et al.  A uniform family of tissue P systems with cell division solving 3-COL in a linear time , 2008, Theor. Comput. Sci..

[27]  Abdullah Mohd Zin,et al.  Converting differential-equation models of biological systems to membrane computing , 2013, Biosyst..

[28]  Abdullah Mohd Zin,et al.  Modeling hormone-induced calcium oscillations in liver cell with membrane computing , 2012 .

[29]  Gheorghe Paun,et al.  The Oxford Handbook of Membrane Computing , 2010 .

[30]  Abdullah Mohd Zin,et al.  Modeling framework for membrane computing in biological systems: Evaluation with a case study , 2014, J. Comput. Sci..

[31]  Marian Gheorghe,et al.  3-Col problem modelling using simple kernel P systems , 2013, Int. J. Comput. Math..