Unconventional modelling of complex system via cellular automata and differential evolution

This introductory paper gives a short survey of cellular automata (CAs), from different points of view. It starts with the main definitions and theoretical results about CAs as an abstract model of computation or as discrete dynamical systems. Then, the main applications of CAs in different fields (biology, physics, etc.) as a model of complex systems are illustrated. Finally, implementations of the CA model on parallel computing platforms are surveyed.

The Differential Evolution (DE) algorithm, under the family of Evolutionary Algorithms (EAs), is one of the powerful algorithms used for solving continuous parameter optimization challenges. The simplistic nature and robustness of the classical DE algorithm have drawn researchers' attention towards its progressive enhancement. This work reports on an investigation of the behavioral changes of the classical DE algorithm, evoked when its mutation and crossover components are fine tuned for enhancement of DE's performance. The scope of this study covers the implementation of a mutation level enhancement and a crossover level enhancement, followed by their integration. The mutation and the crossover components are augmented by incorporation of Centroid DE and Superior-Superior & Superior-Inferior DE logics, respectively. The algorithms appraised in this inquiry were classical DE, Centroid based DE(cDE), Superior-Superior based DE (ssDE), Superior-Inferior DE (siDE), Centroid Superior-Superior DE (cssDE) and Centroid Superior-Inferior DE (csiDE). These algorithms were evaluated by comparison of the values of their mean objective function (MOV), and their speed, at solving the global optimization problems in a simple benchmarking function suite with 4 functions of different categories. The study concludes that the DE algorithm shows enhancement performance with modified mutation and crossover components. However, with a trend for inconsistency for varying values of its control parameters and benchmarking problems.

Data mining with a multitude of methodologies is a good basis for the integration of intelligent systems. Small, specialised systems have a large number of feasible solutions, but developing truly adaptive, and still understandable, systems for highly complex systems require domain expertise and more compact approaches at the basic level. This paper focuses on the integration of methodologies in the smart adaptive applications. Statistical methods and arti cial neural networks form a good basis for the data-driven analysis of interactions and fuzzy logic introduces solutions for knowledge-based understanding the system behaviour and the meaning of variable levels. Efficient normalisation, scaling and decomposition approaches are the key methodologies in developing large-scale applications. Linguistic equation (LE) approach originating from fuzzy logic is an efficient technique for these problems. The nonlinear scaling methodology based on advanced statistical analysis is the corner stone in representing the variable meanings in a compact way to introduce intelligent indices for control and diagnostics. The new constraint handling together with generalised norms and moments facilitates recursive parameter estimation approaches for the adaptive scaling. Well-known linear methodologies are used for the steady state, dynamic and case-based modelling in connection with the cascade and interactive structures in building complex large scale applications. To achieve insight and robustness the parameters are de ned separately for the scaling and the interactions. Introduction EK Juuso Intelligent Methods in Modelling and Simulation of Complex Systems 2 SNE 24(1) – 4/2014 ON 1 Steady-State Modelling multiple input, multiple output MIMO response surface methodology RSM multiple input, single output MISO Fuzzy set theory Extension principle Type-2 fuzzy Figure 1: Methodologies for modelling of complex system. EK Juuso Intelligent Method of Modelling and Simulation in Complex Systems SNE 24(1) – 4/2014 3 O N Linguistic fuzzy models Takagi-Sugeno (TS) fuzzy models Singleton models Fuzzy relational models Figure 2: Combined fuzzy modelling. Artificial neural networks ANN Linear networks multilayer perceptron MLP backpropagation learning Neurofuzzy systems Figure 3: A fuzzy neuron. function expansion Approximate reasoning 2 Decomposition Methodologies EK Juuso Intelligent Methods in Modelling and Simulation of Complex Systems 4 SNE 24(1) – 4/2014 ON Decomposition Figure 4: Decomposition for modelling. Hierarchical clustering Partitioning-based clustering algorithms fuzzy clustering Fuzzy c-means (FCM) Subtractive clustering Neural clustering Robust clustering number of clusters Composite local model Linear parameter varying (LPV) models Piecewise affine (PWA) systems Fuzzy models Multiple neural network systems mixed approach EK Juuso Intelligent Method of Modelling and Simulation in Complex Systems SNE 24(1) – 4/2014 5 O N 3 Adaptive Nonlinear Scaling Membership 3.1 Working point and feasible ranges Figure 5: Nonlinear scaling [28] EK Juuso Intelligent Methods in Modelling and Simulation of Complex Systems 6 SNE 24(1) – 4/2014 ON 3.2 Membership definitions linguistic range linguistic values • the corner points (Figure 5) are good for visualisation; • the parameters suit for tuning; • the coefficients are used in the calculations. 3.3 Adaptation of nonlinear scaling EK Juuso Intelligent Method of Modelling and Simulation in Complex Systems SNE 24(1) – 4/2014 7 O N 4 Intelligent Systems 4.1 LE models 4.2 Hybrid LE systems EK Juuso Intelligent Methods in Modelling and Simulation of Complex Systems 8 SNE 24(1) – 4/2014 ON extension principle linguistification

Researchers can solve Simple optimization problems using various methods. But differential Evolution (DE) is a method(population based) to solve complex optimization problems in some easy steps that is not possible to handle by mathematical optimization methods. For global optimization problems DE is a probabilistic approach. DE when tested over some bench mark functions and real world problems it performed better than some evolutionary algorithms and swarm - intelligence based algorithms. Balancing between Exploration and Exploitation using DE mutation and crossover with control parameters F and CR (fine tunned) is to be done. DE does not complete demand of good convergence and stagnation. DE Explore better but this exploration capability sometimes may skip the true solution and exhibit premature convergence. To improve this we can decrease the step size but this exhibit stagnation. So for Better exploitation, another approach called Memetic algorithm based on levy flight based local search strategy is used with DE. Further to balance exploration and exploitation in local search area in this paper a population or generation based exploitation of local search area in LFDE is proposed that is called PGLFDE. To show better result proposed strategy is tested on some bench mark functions and compare with recent variants of DE.

Parameters setting is an important problem of evolution algorithms, include differential evolution algorithm. It has an effect on the performance of evolution algorithms. Although there is only three control parameters in differential evolution (DE) algorithm, the parameters setting is also a difficult problem. Self-adaptation is highly beneficial for adjusting the control parameters, especially when done without any user interaction. This paper presents differential evolution algorithm, called (AdaptDE), which use self-adaptive mechanisms applied to the control parameters. It can get the optimal control parameters for different optimization problem without user interaction. Experimental results indicate that AdaptDE algorithm is efficient and feasible. It is superior to jDE algorithm and FADE algorithm on the quality of solution.

Cellular automata (CA) are fully parallel computational models and are widely applied to numerical modelling for many complex systems or nonlinear systems, such as fluid dynamics. Those systems are often governed by nonlinear partial differential equations which are hard to solve by using traditional numerical methods. In this paper, based on CA, a general model for a kind of evolutionary physics systems is proposed. As an example, a CA-like model for nonlinear parabolic equation is built by using multi-scalar analysis. The model is applied to several typical problems and satisfactory results are achieved.

This research deals with the hybridization of several approaches for evolutionary algorithms, which are the adaptive control parameter adjusting strategy and multi-chaotic dynamics driving the selection of indices in Differential Evolution (DE). The novelty of the paper is given by the experiments with the multi-chaos-driven adaptive DE concept inside adaptive parameter adjusting DE strategies. These experiments are representing the investigations on the mutual influences of several different randomizations types together with adaptive DE strategies. The multi-chaotic concept is representing the adaptive switching between two different chaotic systems based on the progress of individuals within population. This paper is aimed at the embedding of discrete dissipative chaotic systems in the form of multi-chaotic pseudo random number generators for the jDE, which is the state of the art representative of simple adaptive control parameter adjusting strategy for DE. Repeated simulations for two different combinations of driving chaotic systems were performed on the IEEE CEC 13 benchmark set. Finally, the obtained results are compared with the canonical not-chaotic jDE.

Differential Evolution (DE) is a very simple but powerful Evolutionary Algorithm (EA) for real-world applications. There are two aspects affecting the overall optimization performance significantly, one is parameter control scheme and the other is trial vector generation strategy. As all the control parameters are employed in generating trial vectors, from this perspective of view, the trial vector generation strategy dominates the overall optimization performance. Therefore, trial vector generation strategies are often designed first, and then the corresponding parameter control schemes are well-tuned thereafter. Both of them constitute the main body of a new DE variant. Here in the paper, a novel DE variant with a new designed trial vector generation strategy as well as novel parameter control scheme is proposed to tackle freight trains scheduling problem. By incorporating both a time-stamp mechanism of the external archive and a novel parameter control scheme, the new algorithm can secure better optimization performance not only on man-made benchmarks but also on real-world applications. Both the man-made benchmarks from Congress on Evolutionary Computation (CEC) test suite and the real-world freight train scheduling problem are employed in the validation of the new DE variant. The experiment results show that it is competitive with other state-of-the-art DE techniques for these optimization problems.

In this paper, we propose a new method to obtain the transition rules of two-dimensional cellular automata (CA) that performs grayscale image processing. CA has the advantages of producing complex systems from the local interaction of simple elements, and has attracted increased research interest. The difficulty of designing CA's transition rules to perform a particular task has severely limited their applications. So, the evolutionary design of CA rules has been studied. In this method, an evolutionary algorithm was used to evolve CA. In recent years, this method has been applied to image processing. Rosin has studied the evolutionary design of two-dimensional CA to perform noise reduction, thinning and convex hulls. Batouche et al. and Slatnia et al. employed genetic algorithm to investigate the possibility of CA to perform edge detection. In the previous methods, 2-state CA was used for binary image processing. Unlike the previous methods, the present method uses 256-state CA rules to perform grayscale image processing. Gene Expression Programming (GEP) proposed by Ferreira is employed as a learning algorithm in which the chromosomes encode the transition rules as expression trees. Experimental results for the reduction of impulse noise, salt-and-pepper noise and gaussian noise show that the proposed method is equivalent to previous methods in performance and more than 100 times faster than the method proposed by Rosin. We show that the rule obtained by the proposed method employs symmetry-based strategy in the noise reduction process and this property can reduce complexity of CA.

To celebrate Hans Frauenfelder’s achievements, we examine energy(-like) “landscapes” for complex living systems. Energy landscapes summarize all possible dynamics of some physical systems. Energy(-like) landscapes can explain some biomolecular processes, including gene expression and, as Frauenfelder showed, protein folding. But energy-like landscapes and existing frameworks like statistical mechanics seem impractical for describing many living systems. Difficulties stem from living systems being high dimensional, nonlinear, and governed by many, tightly coupled constituents that are noisy. The predominant modeling approach is devising differential equations that are tailored to each living system. This ad hoc approach faces the notorious “parameter problem”: models have numerous nonlinear, mathematical functions with unknown parameter values, even for describing just a few intracellular processes. One cannot measure many intracellular parameters or can only measure them as snapshots in time. Another modeling approach uses cellular automata to represent living systems as discrete dynamical systems with binary variables. Quantitative (Hamiltonian-based) rules can dictate cellular automata (e.g., Cellular Potts Model). But numerous biological features, in current practice, are qualitatively described rather than quantitatively (e.g., gene is (highly) expressed or not (highly) expressed). Cellular automata governed by verbal rules are useful representations for living systems and can mitigate the parameter problem. However, they can yield complex dynamics that are difficult to understand because the automata-governing rules are not quantitative and much of the existing mathematical tools and theorems apply to continuous but not discrete dynamical systems. Recent studies found ways to overcome this challenge. These studies either discovered or suggest an existence of predictive “landscapes” whose shapes are described by Lyapunov functions and yield “equations of motion” for a “pseudo-particle.” The pseudo-particle represents the entire cellular lattice and moves on the landscape, thereby giving a low-dimensional representation of the cellular automata dynamics. We outline this promising modeling strategy.

This paper presents the results of the nonlinear system modelling approach based on the use of fuzzy rules optimized by different population based optimization algorithms. Fuzzy rule based models with different number of the rules are used to describe the some nonlinear systems in the literature. Firstly, parameters of the fuzzy models are determined by the artificial bee colony (ABC) algorithm. To demonstrate the efficiency of the ABC algorithm, its modelling ability is compared with the other two powerful population based algorithms, particle swarm optimization (PSO) and differential evolution algorithm (DEA). Simulation results show that a successful model performance with good description ability in the modelling of nonlinear or complex systems can be obtained by using one of the population based algorithms in design of the fuzzy rule based models. DOI: http://dx.doi.org/10.5755/j01.eie.22.5.16336

Differential evolution (DE) is an effective and efficient evolutionary algorithm in continuous space. The setting of control parameters is highly relevant with the convergence efficiency, and varies with different optimization problems even at different stages of evolution. Self-adapting control parameters for finding global optima is a long-term target in evolutionary field. This paper proposes a two-layered DE (TLDE) with self-adaptive control parameters combined with niching method based mutation strategy. The TLDE consists of two DE layers: a bottom DE layer for the basic evolution procedure, and a top DE layer for control parameter adaptation. Both layers follow the procedure of DE. Moreover, to mitigate the common phenomenon of premature convergence in DE, a clearing niching method is brought out in finding efficient mutation individuals to maintain diversity during the evolution and stabilize the evolution system. The performance is validated by a comprehensive set of twenty benchmark functions in parameter optimization and competitive results are presented.

The Cellular Automata paradigm is an efficient tool to model and study complex systems such as traffic simulation, lava flows and swarm based behaviour. In addition, cellular automata can be profitably used in many mathematical problems such as differential equations and chaos theory. Due to their inherent parallel nature, cellular automata can be efficiently parallelized among a set of computing nodes in order to scale and speed up their execution. This paper presents a preliminary study on different parallelizzation techniques for structured grid models such as cellular automata on distributed memory architectures. In particular, three strategies are presented and compared in order to evaluate their efficiency in terms of speedup. An experimental section shows the performance achieved by the three strategies when a real-life application, namely the SciddicaT cellular automata model for debris-flows simulation, is adopted.

The differential evolution (DE) algorithm is an efficient random search algorithm based on swarm intelligence for solving optimization problems. It has the advantages of easy implementation, fast convergence, strong optimization ability and good robustness. However, the performance of DE is very sensitive to the design of different operators and the setting of control parameters. To solve these key problems, this paper proposes an improved self-adaptive differential evolution algorithm with a shuffled frog-leaping strategy (SFSADE). It innovatively incorporates the idea of the shuffled frog-leaping algorithm into DE, and at the same time, it cleverly introduces a new strategy of classification mutation, and also designs a new adaptive adjustment mechanism for control parameters. In addition, we have carried out a large number of simulation experiments on the 25 benchmark functions of CEC 2005 and two nonparametric statistical tests to comprehensively evaluate the performance of SFSADE. Finally, the results of simulation experiments and nonparametric statistical tests show that SFSADE is very effective in improving DE, and significantly improves the overall diversity of the population in the process of dynamic evolution. Compared with other advanced DE variants, its global search speed and optimization performance also has strong competitiveness.

by Sara S Pallekonda Dr. Woflgang Bein, Examination Committee Chair Professor of Computer Science University of Nevada, Las Vegas The term ‘complex systems’ may sound terrifying whenever you come across it as it depicts an overall collective structure which indeed can live upto its name; but when you comprehend the system at its fundamental level by stripping to its simpler multipleinteracting individual parts, the insights it provides may be used to describe and understand different problems ranging from atomic particles to the economics of societies and evolution. The simple laws can be used to simulate the behaviors of disparate complex systems. In this thesis, a brief study is done emulating few such complex systems through programming techniques like cellular automata and neural networks. The patterns of complex behavior obtained are also classified respectively along with the help of Conway’s game of life; the working of an autonomous and self organizing organism is simulated in a program written to show the complex patterns formed by a virtual ant. Then an important aspect of competition and cooperation among these agents is shown through game theory and dilemmas which throws light on the essence of survival of complex systems. A formal study is also done on the uses of artificial neural networks as associative memories and pattern recognizers. iii