# 双相演化

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Dual phase evolution (DPE) is a process that drives self-organization within complex adaptive systems.[1] It arises in response to phase changes within the network of connections formed by a system's components. DPE occurs in a wide range of physical, biological and social systems. Its applications to technology include methods for manufacturing novel materials and algorithms to solve complex problems in computation. 双相演化（DPE）是复杂适应系统中驱动自组织的过程。[1]它的产生是对系统组成部分所形成的连接网络中的相位变化的响应。DPE发生在广泛的物理、生物和社会系统中。它在技术上的应用包括制造新材料的方法和解决复杂计算问题的算法。

## Introduction介绍

DPE is capable of producing social networks with known topologies, notably small-world networks and scale-free networks. In the absence of social interaction, the uptake of an opinion promoted by media is a Markov process. The effect of social interaction under DPE is to retard the initial uptake until the number converted reaches a critical point, after which uptake accelerates rapidly.

DPE能够产生具有已知拓扑结构的社交网络，特别是小世界网络和无标度网络。在缺乏社会互动的情况下，媒体对某一观点的接受是一个 Markov process马尔可夫过程。DPE下的社会互动效应是延迟最初的吸收，直到转化的数量达到临界点，之后的吸收将迅速加速。

Dual phase evolution (DPE) is a process that promotes the emergence of large-scale order in complex systems. It occurs when a system repeatedly switches between various kinds of phases, and in each phase different processes act on the components or connections in the system. DPE arises because of a property of graphs and networks: the connectivity avalanche that occurs in graphs as the number of edges increases.[2] 双相演化（DPE）是一个促进复杂系统中大规模有序涌现的过程。当一个系统在不同的阶段之间反复切换，并且在每个阶段中，不同的过程作用于系统中的组件或连接时，就会发生这种情况。DPE的产生是由于网络的一个性质：当边的数目增加时，图中的连接性雪崩将会发生。

Social networks provide a familiar example. In a social network the nodes of the network are people and the network connections (edges) are relationships or interactions between people. For any individual, social activity alternates between a local phase, in which they interact only with people they already know, and a global phase in which they can interact with a wide pool of people not previously known to them. Historically, these phases have been forced on people by constraints of time and space. People spend most of their time in a local phase and interact only with those immediately around them (family, neighbors, colleagues). However, intermittent activities such as parties, holidays, and conferences involve a shift into a global phase where they can interact with different people they do not know. Different processes dominate each phase. Essentially, people make new social links when in the global phase, and refine or break them (by ceasing contact) while in the local phase. 社交网络提供了一个熟悉的例子。在社交网络中，网络的节点是人，网络连接（边缘）是人与人之间的关系或互动。对于任何个人来说，社会活动都是在“局部阶段”和“全局阶段”之间交替进行的，在前者中个体只与他们已经认识的人进行互动，在后者中可以与他们以前不认识的大量人进行互动。历史上，这些阶段是由于时间和空间的限制而强加给人们的。人们把大部分时间花在局部阶段，只与周围的人（家人、邻居、同事）交流。然而，诸如聚会、假日和会议之类的间歇式活动涉及到一个全局阶段的转变，在这个阶段，他们可以与不认识的不同的人进行互动。不同的过程控制着每个阶段。从本质上讲，人们在全局阶段建立新的社会联系，在局部阶段则通过停止联系来改善或打破这种联系。 DPE models of socio-economics interpret the economy as networks of economic agents. Several studies have examined the way socioeconomics evolve when DPE acts on different parts of the network. One model interpreted society as a network of occupations with inhabitants matched to those occupations. In this model social dynamics become a process of DPE within the network, with regular transitions between a development phase, during which the network settles into an equilibrium state, and a mutating phase, during which the network is transformed in random ways by the creation of new occupations.

## The DPE mechanism DPE机制

Another model interpreted growth and decline in socioeconomic activity as a conflict between cooperators and defectors. The cooperators form networks that lead to prosperity. However, the network is unstable and invasions by defectors intermittently fragment the network, reducing prosperity, until invasions of new cooperators rebuild networks again. Thus prosperity is seen as a dual phase process of alternating highly prosperous, connected phases and unprosperous, fragmented phases.

The following features are necessary for DPE to occur.[1] 发生DPE需要以下特性

### Underlying network底层网络

In a forest, the landscape can be regarded as a network of sites where trees might grow. Some sites are occupied by living trees; others sites are empty. In the local phase, sites free of trees are few and they are surrounded by forest, so the network of free sites is fragmented. In competition for these free sites, local seed sources have a massive advantage, and seeds from distant trees are virtually excluded. Even if a few isolated trees do find free ground, their population is prevented from expanding by established populations, even if the invaders are better adapted to the local environment. A fire in such conditions leads to an explosion of the invading population, and possibly to a sudden change in the character of the entire forest.

DPE occurs where a system has an underlying network. That is, the system's components form a set of nodes and there are connections (edges) that join them. For example, a family tree is a network in which the nodes are people (with names) and the edges are relationships such as "mother of" or "married to". The nodes in the network can take physical form, such as atoms held together by atomic forces, or they may be dynamic states or conditions, such as positions on a chess board with moves by the players defining the edges. DPE发生在系统有底层网络的地方。也就是说，系统的组件形成一组节点，并且有连接（边）将它们连接起来。例如，家谱是一个网络，其中节点是人（有名字），边是关系，如“母亲”或“已婚”。网络中的节点可以采取物理形式，例如原子力将原子结合在一起，或者它们可以是动态状态或条件，例如棋盘上的位置，棋手的移动定义了边缘。 This dual phase process in the landscape explains the consist appearance of pollen zones in the postglacial forest history of North America, Europe, as well as the suppression of widespread taxa, such as beech and hemlock, followed by huge population explosions. Similar patterns, pollen zones truncated by fire-induced boundaries, have been recorded in most parts of the world

In mathematical terms (graph theory), a graph $\displaystyle{ \textstyle G = \langle N,E\rangle }$ is a set of nodes $\displaystyle{ \textstyle N }$ and a set of edges $\displaystyle{ \textstyle E \subset \{ (x,y) \mid x,y \in N \} }$. Each edge $\displaystyle{ \textstyle (x,y ) }$ provides a link between a pair of nodes $\displaystyle{ \textstyle x }$ and $\displaystyle{ \textstyle y }$. A network is a graph in which values are assigned to the nodes and/or edges.

### Phase shifts相变

Dual phase evolution is a family of search algorithms that exploit phase changes in the search space to mediate between local and global search. In this way they control the way algorithms explore a search space, so they can be regarded as a family of metaheuristic methods.

Graphs and networks have two phases: disconnected (fragmented) and connected. In the connected phase every node is connected by an edge to at least one other node and for any pair of nodes, there is at least one path (sequence of edges) joining them. 图和网络有两个阶段：断开（碎片化）和连接。在连接阶段，每个节点通过一条边连接到至少一个其他节点，对于任何一对节点，至少有一条路径（边序列）连接它们 Problems such as optimization can typically be interpreted as finding the tallest peak (optimum) within a search space of possibilities. The task can be approached in two ways: local search (e.g. hill climbing) involves tracing a path from point to point, and always moving "uphill". Global search involves sampling at wide-ranging points in the search space to find high points.

The Erdős–Rényi model shows that random graphs undergo a connectivity avalanche as the density of edges in a graph increases.<ref name="Erdos1960"> Erdős–Rényi模型表明，随着图中边密度的增加，随机图会经历连接性雪崩。 Many search algorithms involve a transition between phases of global search and local search. A simple example is the Great Deluge algorithm in which the searcher can move at random across the landscape, but cannot enter low-lying areas that are flooded. At first the searcher can wander freely, but rising water levels eventually confine the search to a local area. Many other nature-inspired algorithms adopt similar approaches. Simulated annealing achieves a transition between phases via its cooling schedule. The cellular genetic algorithm places solutions in a pseudo landscape in which they breed only with local neighbours. Intermittent disasters clear patches, flipping the system into a global phase until gaps are filled again.

{{cite journal

| author = Erdős, P.


Some variations on the memetic algorithm involve alternating between selection at different levels. These are related to the Baldwin effect, which arises when processes acting on phenotypes (e.g. learning) influence selection at the level of genotypes. In this sense, the Baldwin effect alternates between global search (genotypes) and local search (phenotypes).

| author2 = Rényi, A.

| name-list-style = amp

| year = 1960

| title = On the evolution of random graphs


Dual phase evolution is related to the well-known phenomenon of self-organized criticality (SOC). Both concern processes in which critical phase changes promote adaptation and organization within a system. However, SOC differs from DPE in several fundamental ways. Under SOC, a system's natural condition is to be in a critical state; in DPE a system's natural condition is a non-critical state. In SOC the size of disturbances follows a power law; in DPE disturbances are not necessarily distributed the same way. In SOC a system is not necessarily subject to other processes; in DPE different processes (e.g. selection and variation) operate in the two phases.

| journal = Publications of the Mathematical Institute of the Hungarian Academy of Sciences

| volume =5

| pages = 17–61

| url = http://www.renyi.hu/~p_erdos/1960-10.pdf

 | author2-link = Alfréd Rényi


Category:Nature-inspired metaheuristics

This page was moved from wikipedia:en:Dual-phase evolution. Its edit history can be viewed at 双相演化/edithistory

1. Dual phase evolution (DPE) is a process that drives self-organization within complex adaptive systems. It arises in response to phase changes within the network of connections formed by a system's components. DPE occurs in a wide range of physical, biological and social systems. Its applications to technology include methods for manufacturing novel materials and algorithms to solve complex problems in computation. Dual phase evolution 双相演化（DPE）是一个在复杂自适应系统中驱动自组织的过程。它的产生是对系统组成部分所形成的连接网络中的相位变化的响应。DPE发生在广泛的物理、生物和社会系统中。它在技术上的应用包括制造新材料的方法和解决复杂计算问题的算法。 Green, D.G.; [[Liu Jing (programmer) In each of the two phases, the network is dominated by different processes. 在双阶段中的任一个阶段，网络都由不同的进程控制。 |Liu, J.]]; [[Hussein Abbass Dual phase evolution (DPE) is a process that promotes the emergence of large-scale order in complex systems. It occurs when a system repeatedly switches between various kinds of phases, and in each phase different processes act on the components or connections in the system. DPE arises because of a property of graphs and networks: the connectivity avalanche that occurs in graphs as the number of edges increases. This avalanche amounts to a sudden phase change in the size of the largest connected subgraph. In effect, a graph has two phases: connected (most nodes are linked by pathways of interaction) and fragmented (nodes are either isolated or form small subgraphs). These are often referred to as global and local phases, respectively. 双相演化（DPE）是一个促进复杂系统中大规模有序出现的过程。当一个系统在不同的阶段之间反复切换，并且在每个阶段中，不同的过程作用于系统中的组件或连接时，就会发生这种情况。DPE的产生是因为图和网络的一个特性：当边的数目增加时，图中发生连接性雪崩。这种雪崩相当于最大连通子图大小的突然相位变化。实际上，一个图有两个阶段：连接（大多数节点通过相互作用的路径连接）和分段（节点要么是孤立的，要么形成小的子图）。这些阶段通常分别称为全局阶段和局部阶段。 |Abbass, H. Fragmented graph. 零碎的图表。]] (2014). Dual Phase Evolution: from Theory to Practice An essential feature of DPE is that the system undergoes repeated shifts between the two phases. In many cases, one phase is the system's normal state and it remains in that phase until shocked into the alternate phase by a disturbance, which may be external in origin. DPE 的一个基本特征是系统在两个阶段之间进行不断重复的转换。在许多情况下，一个阶段是系统的正常状态，它保持在该阶段，直到受到一种可能来自外部的扰动而进入交替阶段。. Berlin: Springer. ISBN 978-1441984227.
2. 引用错误：无效<ref>标签；未给name属性为Erdos1960的引用提供文字