双相演化

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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.

Introduction

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 能够生成具有已知拓扑结构的社会网络，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，媒体宣传的观点的理解是一个马尔可夫过程。DPE 下的社会相互作用的效果是延缓初始吸收，直到转化数量达到临界点，之后吸收迅速加速。

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.

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.

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.

社会经济学的 DPE 模型将经济解释为经济主体的网络。一些研究已经检查了当 DPE 作用于网络的不同部分时，社会经济学的发展方式。一种模式将社会解释为一个有居民从事与这些职业相匹配的职业网络。在这个模型中，社会动力学成为网络内部的 DPE 过程，在发展阶段和变异阶段之间有规律地转换，在这个阶段中，网络进入一个平衡状态，在这个阶段中，网络通过创造新的职业以随机的方式进行转换。

The DPE mechanism

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.

另一个模型将社会经济活动的增长和减少解释为合作者和背叛者之间的冲突。合作者形成了通向繁荣的网络。然而，网络是不稳定的，叛逃者的入侵断断续续地破坏了网络，减少了繁荣，直到新的合作者再次入侵重建网络。因此，繁荣被视为一个高度繁荣、相互关联的阶段与不繁荣、分裂的阶段相互交替的双重阶段过程。

The following features are necessary for DPE to occur.

Underlying network

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.

在森林中，景观可以被看作是树木可能生长的地点网络。有些地方被活树占据，有些地方则是空的。在局部阶段，没有树木的地点很少，而且被森林包围，所以免费地点的网络是支离破碎的。在争夺这些免费种植地的竞争中，当地的种子资源有着巨大的优势，而来自远方树木的种子几乎被排除在外。即使一些孤立的树木找到了自由的土地，它们的种群数量也会被已有的种群所阻止，即使这些入侵者更好地适应了当地的环境。在这种情况下，一场火灾会导致入侵种群的爆发，并可能导致整个森林特征的突然改变。

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.

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

这种景观中的双重阶段过程解释了北美、欧洲冰后森林历史中花粉带的出现，以及广泛分布类群的抑制，如山毛榉和铁杉，随之而来的大规模种群爆发。世界上大部分地区都有类似的花粉带被火灾引起的边界所截断的记录

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

Phase shifts

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.

双相进化算法是利用搜索空间中的相位变化，在局部搜索和全局搜索之间进行调节的一类搜索算法。通过这种方式，它们控制算法探索搜索空间的方式，因此它们可以被看作是一族元启发式方法。

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.

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.

诸如优化之类的问题通常可以解释为在可能的搜索空间中找到最高的峰(最优)。这个任务可以通过两种方式来完成: 本地搜索(例如:。爬山)包括沿着一条小路从一个点到另一个点，并且总是“上山”。全局搜索包括在搜索空间中的广泛点上进行抽样，以找到高点。

The Erdős–Rényi model shows that random graphs undergo a connectivity avalanche as the density of edges in a graph increases.<ref name="Erdos1960">

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.

许多搜索算法涉及到全局搜索和局部搜索阶段之间的过渡。一个简单的例子是大洪水算法，其中搜索者可以随机移动的景观，但不能进入低洼地区是洪水。起初，搜寻者可以自由漫步，但是不断上升的水位最终将搜寻限制在局部地区。许多其他受自然启发的算法也采用了类似的方法。模拟退火通过其冷却时间表实现了两阶段之间的转换。细胞遗传算法将解决方案置于一个伪景观中，在这个伪景观中，解决方案只与当地邻居交配繁殖。断断续续的灾难清除了一小块一小块，将整个系统翻转到一个全球阶段，直到空隙再次被填满。

{{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).

模因算法的一些变化涉及在不同层次的选择之间的交替。这些都与鲍德温效应有关，这种效应在表型作用过程中出现(例如:。学习)影响基因型水平的选择。在这个意义上，Baldwin 效应在全局搜索(基因型)和局部搜索(表型)之间交替。

| 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.

双相进化与众所周知的自组织临界性现象有关。两者都涉及关键阶段变化促进系统内部适应和组织的过程。然而，SOC 与 DPE 在几个基本方面有所不同。在 SOC 下，系统的自然状态是临界状态，在 DPE 中，系统的自然状态是非临界状态。在 SOC 中，扰动的大小遵循幂律，而在 DPE 中，扰动不一定按相同的方式分布。在 SOC 中，一个系统不一定受制于其他过程; 在 DPE 中，不同的过程(例如:。选择和变异)分两个阶段进行。

| 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

类别: 自然启发的启发式元推理

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