Improving genetic search for one-dimensional cellular automata, using heuristics related to their dynamic behavior forecast

Acceleration of cellular automata algorithms using genetic algorithms

Various investigations have been carried out on the computational power of cellular automata (CA), with concentrated efforts in the study of one-dimensional CA. One of the approaches is the use of genetic algorithms (GA) to look for CA with a predefined computational behavior. We have previously shown a set of parameters that can be effective in helping forecast CA dynamic behavior; here, they are used as an heuristic to guide the GA search, by biasing selection, mutation and crossover, in the context of the Grouping Task (GT) for one-dimensional CA. Since GT is a new task, no a priori knowledge about its solutions is presently available; even then, the incorporation of the parameter-based heuristic entails a significant improvement over the results achieved by the plain genetic search.KeywordsGenetic AlgorithmCellular AutomatonCellular AutomatonGroup TaskTransition RuleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Evolving cellular automata to perform computations: mechanisms and impediments

Although deep learning has recently increased in popularity, it suffers from various problems including high computational complexity, energy greedy computation, and lack of scalability, to mention a few. In this paper, we investigate an alternative brain-inspired method for data analysis that circumvents the deep learning drawbacks by taking the actual dynamical behavior of biological neural networks into account. For this purpose, we develop a general framework for dynamical systems that can evolve and model a variety of substrates that possess computational capacity. Therefore, dynamical systems can be exploited in the reservoir computing paradigm, i.e., an untrained recurrent nonlinear network with a trained linear readout layer. Moreover, our general framework, called EvoDynamic, is based on an optimized deep neural network library. Hence, generalization and performance can be balanced. The EvoDynamic framework contains three kinds of dynamical systems already implemented, namely cellular automata, random Boolean networks, and echo state networks. The evolution of such systems towards a dynamical behavior, called criticality, is investigated because systems with such behavior may be better suited to do useful computation. The implemented dynamical systems are stochastic and their evolution with genetic algorithm mutates their update rules or network initialization. The obtained results are promising and demonstrate that criticality is achieved. In addition to the presented results, our framework can also be utilized to evolve the dynamical systems connectivity, update and learning rules to improve the quality of the reservoir used for solving computational tasks and physical substrate modeling.

A cellular automaton (CA) is reversible if it repeats its configuration in a cycle. Reversible one-dimensional CA are studied as automorphisms of the shift dynamical system, and analyses using graph-theoretical approaches and with block permutations. Reversible CA are dynamical systems which conserve their initial information. This is why they pose a particular interest in mathematics, coding and cryptography.

An approach based on an application of cellular automata (CA) to the problem of two-dimensional (2D) patterns or images reconstruction from ones with only partial information available is presented in the paper. 2D CA are used to process patterns/images, and genetic algorithm (GA) is applied to discover CA rules, which will be able to reconstruct original patterns/images from, e.g. destroyed or modified ones. A number of experiments have been conducted to reconstruct patterns and human face images with use of the proposed approach. Results of experiments show that CA rules discovered by GA in the learning process allow to reconstruct images with large number of damaged pixels.

Wolfram's Cellular Automata and Complexity, an anthology of some of his best work in the area, was published in 1994, and it seems fitting to attempt to explain how his seminal work can be put to good use in laboratory‐based computer science education. This article documents the advantages of using cellular automata (CA) to model complexity theory, chaos, and some aspects of the theory of computation. It explains how CA are constructed, it details the fourfold classification scheme advocated by Wolfram, and it explores in some depth issues associated with induction and Class 2 CA. Several CA are examined with an eye to determining what kinds of empirical evidence count for and against such classifications. The argument is that such lab explorations are pedagogically effective and engaging as an introduction to computer modeling, complexity theory, and related issues in the theory of computation. Software to run the CA simulations has been written by the author and can be downloaded from America Online and...

In the paper we propose using cellular automata (CAs) to solve a problem of scheduling tasks of a parallel program in the two processor system. We examine a hypothesis that a nonlinear structure of a program graph can be approximated by a linear CA structure. Corresponding CAs solving the scheduling problem act according to some rules which must be found. Searching effective rules is conducted with the use of a genetic algorithm (GA). We show that for any initial allocation of tasks, a CA with discovered rules is able to find optimal or near-optimal solutions. Corresponding architecture of a CA is simpler than the ones known in the literature.

Numerous studies can be found in literature concerning the idea of learning cellular automata (CA) rules that perform a given task by means of machine learning methods. Among these methods, genetic algorithms (GAs) have often been used with excellent results. Nevertheless, few attention has been dedicated so far to the generality and robustness of the learned rules. In this paper, we show that when GAs are used to evolve asynchronous one-dimensional CA rules, they are able to find more general and robust solutions compared to the more usual case of evolving synchronous CA rules.

Land management is a complex activity associated with the determination of land uses, the placement of activities and facilities and the distribution of resources over extensive territories with a view to satisfying one or more criteria of economical and/or ecological character. It follows from this descriptive definition that in land management it is not sufficient to distribute goods or commodities to a number of beneficiaries, but, mainly, to carry out planning with respect to space and location, thus intervening and shaping the local geography of economical and environmental characteristics. An important part of land management is land use planning, in which a given area is divided into land blocks with each one of them being assigned a specific land use, taken from a set of possible land uses. The search for suitable combinations of land uses, so as to attain given objectives, constitutes a computationally intensive optimization problem. A related problem concerns spatial resource allocation, in which one or several resources have to be allocated to each one of the described land blocks, again in order to attain preset objectives and possibly satisfy constraints. The sought for distribution and nature of these resources bears a strong relation to the land uses of the respective blocks. This fact gives rise to even more difficult, but also more realistic optimization problems. A basic resource to be managed is water. Allocating water may not simply involve its unit price, but also the estimation of transportation and extraction costs. In the latter case physical modeling of groundwater movement and pumping is needed and this contributes to the complexity and nonlinearity of the problem. This fact makes the present problem different from the typical allocation problems. Problems of land use planning and water allocation combined with water extraction have been presented by Sidiropoulos & Fotakis (2009) and Fotakis (2009) and are reviewed in this chapter, along with new results concerning a cellular – genetic approach. Genetic algorithms and cellular automata will be the basic tools to be implemented in the present approach. Genetic algorithms are well-known biologically-inspired meta-heuristics. Their properties and characteristics are described in textbooks such as Michalewicz (1992) and Goldberg (1989). Applications abound in the literature. Cellular automata date back to von Neumann. Their fundamental importance was demonstrated by Wolfram (2002). They have been used as a background for modeling a great diversity of natural, as well as social and economic systems. Cellular automata have been used for simulating natural phenomena. Also, numerous applications have been

PurposeDiagenetic modelling, the mathematical simulation of the breakdown of sedimentary organic matter and subsequent fate of associated nutrients, has progressed to a point where complex, non-steady state environments can be accurately modelled. A genetic algorithm has never been used in conjunction with an early diagenetic model, and so we aim to discover whether this method is viable to determining a set of realistic model parameters, which itself is often a difficult task.Materials and methodsA range of sensitivity analyses were conducted to establish the parameters for which the model was most sensitive before a micro-genetic algorithm (μGA) was used to fit an output from a previously published diagenetic model (OMEXDIA) to observational data, taken at the North Dogger site from a series of cruises in the North Sea. Profiles of carbon, oxygen, nitrate and ammonia were considered. The method allows a set of parameters to be determined in a manner analogous to natural selection. Each iteration of the genetic algorithm within each experiment decreases the variance between the observed profiles and those calculated by OMEXDIA.Results and discussionDespite some of the observed profiles, particularly for carbon, showing unusual patterns, the genetic algorithm was able to generate a set of parameters which was able to fit the observations. The genetic algorithm can therefore help to determine the values of other parameters used in the model, for which observational values are difficult to measure (e.g. the flux of organic matter to the sediment from the overlying water column and the rates of degradation of organic matter). We also show that the values of the parameters determined by the μGA technique are able to be used in a potentially temporally predictive manner.ConclusionsThe μGA used is a viable method to fit carbon and nutrient sedimentary profiles observed in complex, dynamic shelf sea systems, despite OMEXDIA originally being designed for a different sedimentary environment. The results therefore show that this novel use of a genetic algorithm is a suitable method for both model calibration and validation and that the technique may help in explaining processes which are poorly understood.

The main thesis of this chapter is that a dynamical viewpoint allows us to better understand some important foundational issues of computation theory. Effective procedures are traditionally studied from two different but complementary points of view. The first approach is concerned with individuating those numeric functions that are effectively calculable. This approach reached its systematization with the theory of the recursive functions (Gödel, Church Kleene).This theory is not directly concerned with computing devices or computations. Rather, the effective calculability of a recursive function is guaranteed by the algorithmic nature of its definition. In contrast, the second approach focuses on a family of abstract mechanisms, which are then typically used to compute or recognize numeric functions, sets of numbers, or numbers. These devices can be divided into two broad categories: automata or machines (Turing and Post), and systems of rules for symbol manipulation (Post). The mechanisms that have been studied include: a. Automata or Machines 1. gate-nets and McCulloch-Pitts nets 2. finite automata (Mealy and Moore machines) 3. push-down automata 4. stack automata 5. Turing machines 6. register machines 7. wang machines 8. cellular automata b. Systems of Rules 9. monogenic production systems in general 10. monogenic Post canonical systems 11. monogenic Post normal systems 12. tag systems. I call any device studied by computation theory a computational system. Computation theory is traditionally interested in studying the relations between each type of computational system and the others, and in establishing what class of numeric functions each type can compute. Accordingly one proves two kinds of theorem: (1) that systems of a given type emulate systems of another type (examples: Turing machines emulate register machines and cellular automata; cellular automata emulate Turing machines, etc.), and (2) that a certain type of system is complete relative to the class of the (partial) recursive functions or, in other words, that this type of system can compute all and only the (partial) recursive functions (examples of complete systems: Turing machines, register machines, cellular automata, tag systems, etc.). All different types of computational systems have much in common. Nevertheless, it is not at all clear exactly which properties these mechanisms share.

Although cellular automata (CAs) have been invented only about three quarter of a century ago, much has been written about the fascinating space-time patterns these utter discrete dynamical systems can bring forth, which can be largely attributed to the fact that it is striking to notice that the dynamics of these overly simple dynamical systems can be so intriguing. Driven by the advances in the theory of dynamical systems of continuous dynamical systems, several quantitative measures have been proposed to grasp the stability of CAs, among which the Lyapunov exponent (LE) has received particular attention. Originally, the latter was understood as the Hamming distance between configurations evolved by the same CA from different initially close configurations, but it suffers from the important drawback that it can grow only linearly over time. In this paper, it will be shown how one should determine the LE of a two-state CA, in such a way that its meaning is in line with the framework of continuous dynamical systems. Besides, the proposed methodology will be exemplified for two CA families.KeywordsLyapunov ExponentCellular AutomatonInitial PerturbationPositive Lyapunov ExponentDefective CellThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In this paper, cellular automata (CA) are viewed as an abstract model for distributed computing. The author argues that the classical CA model must be modified in several important respects to become a relevant model for large-scale MAS. The paper first proposes sequential cellular automata (SCA) and formalizes deterministic and nondeterministic versions of SCA. The author then analyzes differences in possible dynamics between classical parallel CA and various SCA models. The analysis in this paper focuses on one-dimensional parallel and sequential CA with node update rules restricted to simple threshold functions, as arguably the simplest totalistic, yet non-linear (and non-affine) update rules. The author identifies properties of asymptotic dynamics that can be proven to be entirely due to the assumption of perfect synchrony in classical, parallel CA. Finally, the paper discusses what an appropriate CA-based abstraction would be for large-scale distributed computing, insofar as the inter-agent communication models. In that context, the author proposes genuinely asynchronous CA and discusses main differences between genuinely asynchronous CA and various weakly asynchronous sequential CA models found in the literature.

Global change study is an interdisciplinary and comprehensive research activity with international cooperation, arising in 1980s, with the largest scopes. The interaction between land use and cover change, as a research field with the crossing of natural science and social science, has become one of core subjects of global change study as well as the front edge and hot point of it. It is necessary to develop research on land use and cover change in urbanization process and build an analog model of urbanization to carry out description, simulation and analysis on dynamic behaviors in urban development change as well as to understand basic characteristics and rules of urbanization process. This has positive practical and theoretical significance for formulating urban and regional sustainable development strategy. The effect of urbanization on land use and cover change is mainly embodied in the change of quantity structure and space structure of urban space, and LUCC model in urbanization process has been an important research subject of urban geography and urban planning. In this paper, based upon previous research achievements, the writer systematically analyzes the research on land use/cover change in urbanization process with the theories of complexity science research and intelligent computation; builds a model for simulating and forecasting dynamic evolution of urban land use and cover change, on the basis of cellular automation model of complexity science research method and multi-agent theory; expands Markov model, traditional CA model and Agent model, introduces complexity science research theory and intelligent computation theory into LUCC research model to build intelligent computation-based LUCC model for analog research on land use and cover change in urbanization research, and performs case research. The concrete contents are as follows: 1. Complexity of LUCC research in urbanization process. Analyze urbanization process in combination with the contents of complexity science research and the conception of complexity feature to reveal the complexity features of LUCC research in urbanization process. Urban space system is a complex economic and cultural phenomenon as well as a social process, is the comprehensive characterization of urban society, economy and culture, and is a complex space system formed by society, economy and nature. It has dissipative structure characteristics, such as opening, dynamics, self-organization, non-balance etc. Traditional model cannot simulate these social, economic and natural driving forces of LUCC including main feedback relation from LUCC to driving force. 2. Establishment of Markov extended model of LUCC analog research in urbanization process. Firstly, use traditional LUCC research model to compute change speed of regional land use through calculating dynamic degree, exploitation degree and consumption degree of land use; use the theory of fuzzy set to rewrite the traditional Markov model, establish structure transfer matrix of land use, forecast and analyze dynamic change and development trend of land use, and present noticeable problems and corresponding measures in urbanization process according to research results. 3. Application of intelligent computation research and complexity science research method in LUCC analog model in urbanization process. On the basis of detailed elaboration of the theory and the model of LUCC research in urbanization process, analyze the problems of existing model used in LUCC research (namely, difficult to resolve many complexity phenomena in complex urban space system), discuss possible structure realization forms of LUCC analog research in combination with the theories of intelligent computation and complexity science research. Perform application analysis on BP artificial neural network and genetic algorithms of intelligent computation and CA model and MAS technology of complexity science research, discuss their theoretical origins and their own characteristics in detail, elaborate the feasibility of them in LUCC analog research, and bring forward improvement methods and measures on existing problems of this kind of model. 4. Establishment of LUCC analog model in urbanization process based on theories of intelligent computation and complexity science. Based on the research on abovementioned BP artificial neural network, genetic algorithms, CA model and multi-agent technology, put forward improvement methods and application assumption towards their expansion on geography, build LUCC analog model in urbanization process based on CA model and Agent model, realize the combination of learning mechanism of BP artificial neural network and fuzzy logic reasoning, express the regulation with explicit formula, and amend the initial regulation through self study; optimize network structure of LUCC analog model and methods and procedures of model parameters with genetic algorithms. In this paper, I introduce research theory and methods of complexity science into LUCC analog research and presents LUCC analog model based upon CA model and MAS theory. Meanwhile, I carry out corresponding expansion on traditional Markov model and introduce the theory of fuzzy set into data screening and parameter amendment of improved model to improve the accuracy and feasibility of Markov model in the research on land use/cover change.