多目标0-1规划问题的元胞狼群优化算法研究

针对多目标0-1规划问题,首先基于元胞自动机原理和人工狼群智能算法,提出一种元胞狼群优化算法,该算法将元胞机的演化规则与嚎叫信息素更新规则、人工狼群更新规则进行组合,采用元胞及其邻居来增强搜索过程的多样性和分布性,使人工头狼在元胞空间搜索的过程中,增强了人工狼群算法的全局搜索能力,并获得更多的全局非劣解;其次结合多目标0-1规划模型对元胞狼群算法进行了详细的数学描述,定义了人工狼群搜索空间、移动算子、元胞演化规则和非劣解集更新规则,并给出了元胞狼群算法的具体实现步骤;最后通过MATLAB软件对3个典型的多目标0-1规划问题算例进行解算,并将解算结果与其它人工智能算法的结果进行比较,结果表明:元胞狼群算法在多目标0-1规划问题求解方面可获得更多的非劣解集和更优的非劣解,并具有较快的收敛速度和较好的全局寻优能力。     

Crashworthiness optimization of VRB thin-walled structures under manufacturing constraints by the eHCA-VRB algorithm

Variable-thickness rolled blanks (VRBs) represent an important approach for constructing lightweight structures. However, the optimization of the crashworthiness and thickness distribution of VRB thin-walled structures under manufacturing constraints is a nonlinear dynamic-response structural-optimization problem that has a large number of design variables. To tackle this problem, this paper has extended and improved the hybrid cellular automaton for thin-walled structures (HCATWS) algorithm, and has proposed an extended hybrid cellular automaton for VRB thin-walled structures (eHCA-VRB) algorithm. This algorithm consists of an outer loop and an inner loop. The outer loop performs crash simulation analysis to define an appropriate target mass for the inner loop, whereas the inner loop adjusts cell thicknesses according to the internal energy density (IED) of the current cell and its neighboring cells so that the IED in the design domain becomes evenly distributed. A one-dimensional CA model is defined along with the rolling direction based on the thickness distribution of VRB thin-walled structures. Furthermore, the eHCA-VRB algorithm also generates a mapping relationship between the one-dimensional CA model and the FE model. To optimize the thickness distribution of VRB thin-walled structures under manufacturing constraints, our method uses cell thickness as a design variable and incorporates the constraints of the VRB rolling process in the cell thickness update rules. To verify the convergence and efficiency of the eHCA-VRB algorithm, VRB top-hat thin-walled structures are optimized for crashworthiness with/or without manufacturing constraints (M.C.), respectively. The results show that the eHCA-VRB algorithm can be used to efficiently solve the optimization problems of crashworthiness and the thickness distribution of VRB thin-walled structures under manufacturing constraints.     

Hybrid one-dimensional reversible cellular automata are regular

It is shown that the set of hybrid one-dimensional reversible cellular automata (CA) with the periodic boundary condition is a regular set. This has several important consequences. For example, it allows checking whether a given CA is reversible and the random generation of a reversible CA from the uniform distribution, both using time polynomial in the size of the CA. Unfortunately, the constant term in the resulting random generation algorithm is much too large to be of practical use. We show that for the less general case of null boundary (NB) CA, this constant can be reduced drastically, hence facilitating a practical algorithm for uniform random generation. Our techniques are further applied asymptotically to count the number of reversible NBCA.     

Influence of the topology of a cellular automaton on its dynamical properties

Notwithstanding the numerous scientific efforts that have been spent to unravel the dynamics of cellular automata (CA), there is still only fragmented and incomplete knowledge of the interference that possibly exists between a CA’s dynamical properties in general and its stability in particular, on the one hand, and the whole of its spatial entities and their interconnection, referred to as a CA’s topology, on the other hand. Since a clear understanding of this interference is unbearable to fully comprehend the dynamics of CA, this paper is devoted to a quantitative assessment of this interference. More precisely, after pinning down the so-called representative tessellation size (RTS), it is verified to what extent the input sensitivity of 2-state CA and their stability depends on the characteristics of their topology. Therefore, 12 random graphs having six different vertex degree distributions (VDDs) are used to embody the CA’s topology and to verify how their dynamics is affected by the specificities of these graphs. It is found that the RTS is 400. Further, the interference is strongest with regard to the CA’s stability to the extent that the classification of CA into behavioral classes can be seriously affected by the choice of the VDD.     

Reversible cellular automata with memory of delay type

The effect of delay type memory of past states on reversible elementary cellular automata (CA) is examined in this study. It is assessed in simple scenarios, such as elementary CA, but the feasibility of enriching the dynamics with memory in a general reversible CA context is also outlined. © 2014 Wiley Periodicals, Inc. Complexity 20: 49–56, 2014     

Classifying cellular automata automatically: Finding gliders,filtering, and relating space‐time patterns,attractor basins,and the Z parameter

Cellular automata (CA) rules can be classified automatically for a spectrum of ordered, complex, and chaotic dynamics by a measure of the variance of input‐entropy over time. Rules that support interacting gliders and related complex dynamics can be identified, giving an unlimited source for further study. The distribution of rule classes in rule‐space can be shown. A byproduct of the method allows the automatic “filtering” of CA space‐time patterns to show up gliders and related emergent configurations more clearly. The classification seems to correspond to our subjective judgment of space‐time dynamics. There are also approximate correlations with global measures on convergence in attractor basins, characterized by the distribution of in‐degree sizes in their branching structure, and to the rule parameter, Z. Based on computer experiments using the software Discrete Dynamics Lab (DDLab), this article explains the methods and presents results for 1D CA. © 1999 John Wiley & Sons, Inc.     

Dynamics groups of asynchronous cellular automata

We say that a finite asynchronous cellular automaton (or more generally, any sequential dynamical system) is π-independent if its set of periodic points are independent of the order that the local functions are applied. In this case, the local functions permute the periodic points, and these permutations generate the dynamics group. We have previously shown that exactly 104 of the possible 2²³=2562^{2^{3}}=256 cellular automaton rules are π-independent. In the article, we classify the periodic states of these systems and describe their dynamics groups, which are quotients of Coxeter groups. The dynamics groups provide information about permissible dynamics as a function of update sequence and, as such, connect discrete dynamical systems, group theory, and algebraic combinatorics in a new and interesting way. We conclude with a discussion of numerous open problems and directions for future research.     

Hybrid vector transformations

We present in this paper hybrid and semi-hybrid vector extrapolation methods. For a vector sequence transformation, we will define the generalized residual which allows us to introduce a new hybrid vector transformation. When solving linear systems, this new transformation reduces to the hybrid procedure defined by Brezinski and Redivo Zaglia (1994) which is a generalization of the smoothing technique. In the second part of this paper, we define a new composite transformation called semi-hybrid. When applied to linearly generated sequences, we will show that the residual polynomial of the semi-hybrid transformation is the product of two residual polynomials.     

Hybrid cross approximation of integral operators

The efficient treatment of dense matrices arising, e.g., from the finite element discretisation of integral operators requires special compression techniques. In this article we use the -matrix representation that approximates the dense stiffness matrix in admissible blocks (corresponding to subdomains where the underlying kernel function is smooth) by low-rank matrices. The low-rank matrices are assembled by a new hybrid algorithm (HCA) that has the same proven convergence as standard interpolation but also the same efficiency as the (heuristic) adaptive cross approximation (ACA).     

Complex genetic evolution of artificial self‐replicators in cellular automata

It is widely believed that evolutionary dynamics of artificial self‐replicators realized in cellular automata (CA) are limited in diversity and adaptation. Contrary to this view, we show that complex genetic evolution may occur within simple CA. The evolving self‐replicating loops (“evoloops”) we investigate exhibit significant diversity in macro‐scale morphologies and mutational biases, undergoing nontrivial genetic adaptation by maximizing colony density and enhancing sustainability against other species. Nonmutable subsequences enable genetic operations that alter fitness differentials and promote long‐term evolutionary exploration. These results demonstrate a unique example of genetic evolution hierarchically emerging from local interactions between elements much smaller than individual replicators. © 2004 Wiley Periodicals, Inc. Complexity 10: 33–39, 2004     

基于可拓变换的产品适应性设计研究

适应性设计是一种在面向产品全生命周期设计中解决矛盾问题的有效途径.然而,现有设计方法很难客观地反映定性定量相结合求解设计矛盾问题.为此,提出一种基于可拓变换的产品适应性设计方法.首先建立可拓适应性设计一般流程,定义可拓设计基元,建立适应性设计矛盾问题,然后进行可拓分析,建立起传导矛盾环系统,以及满足产品功能-结构的变换规则、适应度函数,再通过可拓变换实现产品设计基元之间冲突的消解,输出适应性设计方案.最后将该方法应用于某全自动LED分拣机振动盘的适应性设计.应用实例表明:该设计方法不仅能快速满足不同需求下的个性化要求,而且能为计算机参与解决产品设计矛盾问题提供一种可行的途径.     

Advances in the study of elementary cellular automata regular language complexity

Cellular automata (CA) are discrete dynamical systems that, out of the fully local action of its state transition rule, are capable of generating a multitude of global patterns, from the trivial to the arbitrarily complex ones. The set of global configurations that can be obtained by iterating a one‐dimensional cellular automaton for a finite number of times can always be described by a regular language. The size of the minimum finite automaton corresponding to such a language at a given time step provides a complexity measure of the underlying rule. Here, we study the time evolution of elementary CA, in terms of such a regular language complexity. We review and expand the original results on the topic, describe an alternative method for generating the subsequent finite automata in time, and provide a method to analyze and detect patterns in the complexity growth of the rules. © 2015 Wiley Periodicals, Inc. Complexity 21: 267–279, 2016     

Chaotic annealing with hypothesis test for function optimization in noisy environments

As a special mechanism to avoid being trapped in local minimum, the ergodicity property of chaos has been used as a novel searching technique for optimization problems, but there is no research work on chaos for optimization in noisy environments. In this paper, the performance of chaotic annealing (CA) for uncertain function optimization is investigated, and a new hybrid approach (namely CAHT) that combines CA and hypothesis test (HT) is proposed. In CAHT, the merits of CA are applied for well exploration and exploitation in searching space, and solution quality can be identified reliably by hypothesis test to reduce the repeated search to some extent and to reasonably estimate performance for solution. Simulation results and comparisons show that, chaos is helpful to improve the performance of SA for uncertain function optimization, and CAHT can further improve the searching efficiency, quality and robustness.     

Stochastic dominance in an ordinal world

Existing stochastic dominance rules apply to variables such as income, wealth and rates of return, all of which are measured on cardinal scales. This study develops and applies stochastic dominance rules for ordinal data. It is shown that the new rules are consistent with the traditional von Neumann-Morgenstern expected utility approach, and that they are applicable and relevant in a wide variety of managerial decision making situations, where existing stochastic dominance rules fail to apply. We apply ordinal SD rules to the transformation of random variables.     

Finite-time stability of hybrid systems with continuous and Boolean dynamics

The hybrid systems with continuous and discrete variables can be used to describe many real-world phenomena. In this paper, by generalizing the mathematical form of gene regulatory networks, a novel class of hybrid systems consisting of continuous and Boolean dynamics is investigated. Firstly, the new hybrid system is introduced in detail, and a concept of finite-time stability (FTS) for it is proposed. Next, the existence and uniqueness of solutions are proved by fixed point theory. Furthermore, based on Lyapunov functions and the semi-tensor product (STP), i.e., Cheng product, some sufficient conditions of FTS for the hybrid systems are presented. The main results are illustrated by two numerical examples.     

考虑多元关联关系和语义变换的直觉不确定语言多属性决策方法

针对属性值为直觉不确定语言变量的多属性决策问题,提出一种不仅可以捕获属性间的多元关联关系并且能够满足决策者不同语义转换需求的多属性决策方法。首先,考虑已有运算法则缺少封闭性和灵活性,结合语言刻度函数,提出一种新的直觉不确定语言变量运算法则和排序方法。其次,根据新的运算法则,提出可以捕获属性间多元关联关系的直觉不确定语言Hamy平均及其加权形式,并对新算子的优良性质和特例进行了探讨和分析。进而,提出一种新的多属性决策方法。最后,通过算例和对比分析验证了该方法的有效性和优越性。     

Comparative analysis of asynchronous cellular automata in stochastic pharmaceutical modelling

In pharmaceutical modelling, cellular automata have been used as an established tool to represent molecular changes through discrete structural interactions. The data quality provided by such modelling is found suitable for the early drug design phase where flexibility is paramount. While both synchronous (CA) and asynchronous (ACA) types of automata have been used, analysis of their nature and comparative influence on model outputs is lacking. In this paper, we outline a representative probabilistic CA for modelling complex controlled drug formulations and investigate its transition from synchronous to asynchronous update algorithms. The key investigation points include quantification of model dynamics through three distinct scenarios, parallelisation performance and the ability to describe different release phenomena, namely erosion, diffusion and swelling. The choice of the appropriate update mechanism impacts the perceived realism of the simulation as well as the applicability of large-scale simulations.     

Input-to-state stability of impulsive systems with hybrid delayed impulse effects

The goal of this paper is to study properties of input-to-state stability (ISS) and integral input-to-state stability (iISS) of impulsive systems with hybrid delayed impulses, and a set of Lyapunov-based sufficient conditions ensuring ISS/iISS properties are obtained. Those conditions reveal the effects of hybrid delayed impulses on ISS/iISS and establish the relationship between impulsive frequency and the time delay existing in hybrid impulses. When the continuous dynamics of the system are stabilizing, the ISS property can be retained under the impulse scheme even if there exist destabilizing impulses. Conversely, when the impulse dynamics are stabilizing, but the continuous dynamics are not, the ISS property can be obtained if the interval between impulses are not overly long. Two illustrative examples are presented, with their numerical simulations, to demonstrate the effectiveness of the main results.     

Theoretical analysis of high speed spindle air bearings by a hybrid numerical method

To study the behavior of the high speed spindle air bearing (HSSAB) system, we conduct the research by means of a hybrid numerical method which combines the differential transformation method and the finite difference method in this paper. According to the results of the research, the flexible rotor center is found to include a complex dynamic behavior that comprises periodic, sub-harmonic and quasi-periodic responses. In addition, as the rotor mass and the bearing number are increased, there will be some changes taking place in the dynamic behavior of the bearing system. The results are proven to have no conflict with those of the other numerical methods, which enables an effective means in gaining insights into the nonlinear dynamics of HSSAB systems.