Solving Travelling Salesman Problem in a Simulation of Genetic Algorithms with DNA

In this paper it is explained how to solve a fully connected N-City travelling salesman problem (TSP) using a genetic algorithm. A crossover operator to use in the simulation of a genetic algorithm (GA) with DNA is presented. The aim of the paper is to follow the path of creating a new computational model based on DNA molecules and genetic operations. This paper solves the problem of exponentially size algorithms in DNA computing by using biological methods and techniques. After individual encoding and fitness evaluation, a protocol of the next step in a GA, crossover, is needed. This paper also shows how to make the GA faster via different populations of possible solutions.

Static Analysis of Usefulness States in Transition P Systems

Transition P Systems are a parallel and distributed computational model based on the notion of the cellular membrane structure. Each membrane determines a region that encloses a multiset of objects and evolution rules. Transition P Systems evolve through transitions between two consecutive configurations that are determined by the membrane structure and multisets present inside membranes. Moreover, transitions between two consecutive configurations are provided by an exhaustive non-deterministic and parallel application of evolution rules. But, to establish the rules to be applied, it is required the previous calculation of useful, applicable and active rules. Hence, computation of useful evolution rules is critical for the whole evolution process efficiency, because it is performed in parallel inside each membrane in every evolution step. This work defines usefulness states through an exhaustive analysis of the P system for every membrane and for every possible configuration of the membrane structure during the computation. Moreover, this analysis can be done in a static way; therefore membranes only have to check their usefulness states to obtain their set of useful rules during execution.

A Hierarchical Architecture with Parallel Comunication for Implementing P Systems

Membrane systems are computational equivalent to Turing machines. However, its distributed and massively parallel nature obtain polynomial solutions opposite to traditional non-polynomial ones. Nowadays, developed investigation for implementing membrane systems has not yet reached the massively parallel character of this computational model. Better published approaches have achieved a distributed architecture denominated “partially parallel evolution with partially parallel communication” where several membranes are allocated at each processor, proxys are used to communicate with membranes allocated at different processors and a policy of access control to the communications is mandatory. With these approaches, it is obtained processors parallelism in the application of evolution rules and in the internal communication among membranes allocated inside each processor. Even though, external communications share a common communication line, needed for the communication among membranes arranged in different processors, are sequential. In this work, we present a new hierarchical architecture that reaches external communication parallelism among processors and substantially increases parallelization in the application of evolution rules and internal communications. Consequently, necessary time for each evolution step is reduced. With all of that, this new distributed hierarchical architecture is near to the massively parallel character required by the model.

Decision Trees for Applicability of Evolution Rules in Transition P Systems

Transition P Systems are a parallel and distributed computational model based on the notion of the cellular membrane structure. Each membrane determines a region that encloses a multiset of objects and evolution rules. Transition P Systems evolve through transitions between two consecutive configurations that are determined by the membrane structure and multisets present inside membranes. Moreover, transitions between two consecutive configurations are provided by an exhaustive non-deterministic and parallel application of active evolution rules subset inside each membrane of the P system. But, to establish the active evolution rules subset, it is required the previous calculation of useful and applicable rules. Hence, computation of applicable evolution rules subset is critical for the whole evolution process efficiency, because it is performed in parallel inside each membrane in every evolution step. The work presented here shows advantages of incorporating decision trees in the evolution rules applicability algorithm. In order to it, necessary formalizations will be presented to consider this as a classification problem, the method to obtain the necessary decision tree automatically generated and the new algorithm for applicability based on it.

Extended Networks of Evolutionary Processors

This paper presents an extended behavior of networks of evolutionary processors. Usually, such nets are able to solve NP-complete problems working with symbolic information. Information can evolve applying rules and can be communicated though the net provided some constraints are verified. These nets are based on biological behavior of membrane systems, but transformed into a suitable computational model. Only symbolic information is communicated. This paper proposes to communicate evolution rules as well as symbolic information. This idea arises from the DNA structure in living cells, such DNA codes information and operations and it can be sent to other cells. Extended nets could be considered as a superset of networks of evolutionary processors since permitting and forbidden constraints can be written in order to deny rules communication.

A DNA Codification for Genetic Algorithms Simulation

In this paper we propose a model of encoding data into DNA strands so that this data can be used in the simulation of a genetic algorithm based on molecular operations. DNA computing is an impressive computational model that needs algorithms to work properly and efficiently. The first problem when trying to apply an algorithm in DNA computing must be how to codify the data that the algorithm will use. In a genetic algorithm the first objective must be to codify the genes, which are the main data. A concrete encoding of the genes in a single DNA strand is presented and we discuss what this codification is suitable for. Previous work on DNA coding defined bond-free languages which several properties assuring the stability of any DNA word of such a language. We prove that a bond-free language is necessary but not sufficient to codify a gene giving the correct codification.

Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem

We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads to an explicit form for the approximation error in terms of the mesh parameter, which confirms the theoretical error estimates, obtained in [2].

Data Flow Analysis and the Linear Programming Model

* The research is supported partly by INTAS: 04-77-7173 project, http://www.intas.be

Model Construction and Research using System Compositional Approach on Natural Hierarchical Neural Networks. Development of Computer Toolbox

System compositional approach to model construction and research of informational processes, which take place in biological hierarchical neural networks, is being discussed. A computer toolbox has been successfully developed for solution of tasks from this scientific sphere. A series of computational experiments investigating the work of this toolbox on olfactory bulb model has been carried out. The well-known psychophysical phenomena have been reproduced in experiments.

Increasing the Calculation Speed of an Acceleration Scheme for an Age-Structured Diffusion Model

Дойчин Бояджиев, Галена Пеловска - В статията се предлага оптимизиран алгоритъм, който е по-бърз в сравнение с по- рано описаната ускорена (модифицирана STS) диференчна схема за възрастово структуриран популационен модел с дифузия. Запазвайки апроксимацията на модифицирания STS алгоритъм, изчислителното времето се намаля почти два пъти. Това прави оптимизирания метод по-предпочитан за задачи с нелинейност или с по-висока размерност.