grasshopper-galapagos遗传算法

Evolutionary Principles applied to

Problem Solving

遗传算法

There is nothing particularly new about Evolutionary Solvers or Genetic Algorithms. The first references to this field of computation stem from the early 60's when Lawrence J. Fogel published the landmark paper "On the Organization of Intellect" which sparked the first endeavours into evolutionary computing. The early 70's witnessed further forays with seminal work produced by -among others- Ingo Rechenberg and John Henry Holland. Evolutionary Computation didn't gain popularity beyond the programmer world until Richard Dawkins' book "The Blind Watchmaker" in 1986, which came with a small program that generated a seemingly endless stream of body-plans called "Bio-morphs" based on human selection. Since the 80's the advent of the personal computer has made it possible for individuals without government funding to apply evolutionary principles to personal projects and they have since made it into the common parlance.

其实在遗传算法和基因算法里并什么特别新的理论出现，该领域的第一篇文献出现在六十年代由Lawrence J. Fogel 出版的具有里程碑意义的论文“智能组织”，这篇论文使人们开始致力于研究遗传算法。七十年代又由ngo Rechenberg and John Henry Holland的工作进一步带动了基因算法的发展，遗传算法直到1986年才因为Richard Dawkins的“The Blind Watchmake”而让人广

为人知，里面有个小的例子，基于人类的选择仍然会产生无尽的被称为“生态形变”的动作计划。80年代由于个人电脑的出现使得每个人都可以将进化算法用于个人项目而不用政府提供资金支持，从此，进化算法开始像日常话题一样进入公众视野。

The term "Evolutionary Computing" may very well be widely known at this point in time, but they are still very much a programmers tool. 'By programmers for programmers' if you will. The applications out there that apply evolutionary logic are either aimed at solving specific problems, or they are generic libraries that allow other programmers to

piggyback along. It is my hope that Galapagos will provide a generic platform for the application of Evolutionary Algorithms to be used on a wide variety of problems by non-programmers.

虽然现在进化算法在现在已经广为人知，但他大部分还作为编程工具使用，只是程序员和程序员之间交流，遗传算法即使应用也是处理一些特别的问题，大部分时间还是呆在通用库里等着程序员来用它，我希望galapagos可以提供一个遗传算法的广泛平台来让那些非编程人员来处理一些问题。

Pros and Cons

赞成和反对

Before we dive into the subject matter too deeply though I feel it is important to highlight some of the (dis)advantages of this particular type of solver, just so you know what to expect. Since we are not living in the best of all possible worlds there is often no such thing as the perfect solution. Every approach has drawbacks and limitations. In the case of Evolutionary Algorithms these are luckily well known and easily understood drawbacks, even though they are not trivial. Indeed, they may well be prohibitive for many a particular problem.

在我们深入探讨这个问题之前，我认为有必要向大家介绍这类特殊算法处理方式的优缺点，这样可能更利于你了解你到底想通过这个获得什么。事实上我们生活在一个不完美的世界，没有什么事情会有一个完美地解决方案，每个解决方案都会有他的缺陷和限制。而在遗传算法领域可喜的是我们明确地知道他的一些缺陷，而且这些缺陷也不小，而且确实在一些具体问题的处理上明确禁止用遗传算法来解决。

Firstly; Evolutionary Algorithms are slow. Dead slow. It is not unheard of that a single process may run for days or even weeks. Especially complicated set-ups that require a long time in order to solve a single iteration will quickly run out of hand. A light/shadow or acoustic computation for example may easily take a minute per iteration. If we assume we'll need at least 50 generations of 50 individuals each (which is almost certainly an underestimate unless the problem has a very obvious solution.) we're already looking at a two-day runtime.

首先，遗传算法在运行起来的时候很慢，奇慢，非常慢，慢的要死。一个小程序运行几天甚至几个星期一点也不见怪，尤其是需要长时间简单迭代的复杂数据结构，运行起来会马上超出你的掌控，就算简单的光影分析或者是声学分析每次迭代就要几分钟，假设我们设置50代，每代50个个体（这都是按照最少最理想的状态来设定的），那这个程序需要两天才能做完。

Secondly, Evolutionary Algorithms do not guarantee a solution. Unless a predefined

'good-enough' value is specified, the process will tend to run on indefinitely, never reaching The Answer, or, having reached it, not recognizing it for what it is.

其次，遗传算法并不能百分之百的保证求出正确的解，除非一个预先你已经想好的差不多的解已经确定下来，遗传算法会尽量的朝着你想要的那个解努力，但是他永远不会找到“真理”，当然，也可能找到了只不过他是电脑，根本意识不到那个是最优解，即“真理”。

All is not bleak and dismal however, Evolutionary Algorithms have strong benefits as well, some of them rather unique amongst the plethora of computational methods. They are remarkably flexible for example, able to tackle a wide variety of problems. There are classes of problems which are by definition beyond the reach of even the best solver implementation and other classes that are very difficult to solve, but these are typically rare in the province of the human meso-world. By and large the problems we encounter on a daily basis fall into the 'evolutionary solvable' category.

当然，遗传算法也并不是上面我说的那么单调无力，一直被吐槽。进化算法在一些方面也有着强大的性能体现，在茫茫多的计算算法里他确实一枝独秀，进化算法有很强的灵活性，能同时处理各种各样的问题，有些问题最好的解算器也解不出来，而且很多的我们日常遇到的问题都可以放到进化算法的范畴内进行解决。

Evolutionary Algorithms are also quite forgiving. They will happily chew on problems that have been under- or over-constrained or otherwise poorly formulated. Furthermore, because the run-time process is progressive, intermediate answers can be harvested at practically any time. Unlike many dedicated algorithms, Evolutionary Solvers spew forth a never ending stream of answers, where newer answers are generally of a higher quality than older answers. So even a pre-maturely aborted run will yield something which could be called a result. It might not be a very good result, but it will be a result of sorts.

进化算法的容忍性也很好，他很有能力去处理一些你低估或者高估或者很傻X的操作，进一步讲，因为它运行的时候是动态的，所以你在任何时候都可以收获一大堆的解而不像其他解算法（解完了才能得到答案），进化算法射出来一大堆永远没有尽头的解，而且这一代的解总体上来说会比上一代的质量更高，所以，尽管一些早产的结果产生我们也可以姑且把他认为是结果，虽然他不是最优秀的结果，但是他确是得到最优结果必不可少的一部分。

Finally, Evolutionary Solvers allow -in principle- for a high degree of interaction with the user. This too is a fairly unique feature, especially given the broad range of possible applications. The run-time process is highly transparent and browsable, and there exists a lot of opportunity for a dialogue between algorithm and human. The solver can be coached across barriers with the aid of human intelligence, or it can be goaded into exploring sub-optimal branches and superficially dead-ends.

最后讲一点，进化算法和用户有很强的交互性，这是非常特别独特的属性，特别是当你给了他一大堆可能的条件是。当他在运行起来的时候，求解过程非常透明也便于浏览，因此存在很多机会创建人机交互的对话窗口，引导解算跨过障碍，或者探索一些并不是很理想的答案，甚至一条死胡同。

The Process

运行特点

In this section I shall briefly outline the process of an Evolutionary Solver run. It is a highly simplified version of the remainder of the blog post, and I'll skip over many interesting and even important details. I'll show the process as a series of image frames, where each frame shows the state of the 'population' at a given moment in time. Before I can start however, I need to explain what the image below means.

在这段里我将简单的介绍一下进化算法是如何运行的，这些内容都是以前一些博客简化了的，所以忽略了一些有趣甚至重要的细节。下面我会用一系列的图片来展示他是如何运行的，每一张图都记录了在特定时刻的“代”的关系，在开始之前，我先解释一下下图是啥意思。

What you see here is the Fitness Landscape of a particular model. The model contains two variables, meaning two values which are allowed to change. In Evolutionary Computing we refer to variables as genes. As we change Gene A, the state of the model changes and it either becomes better or worse (depending on what we're looking for). So as Gene A changes, the fitness of the entire model goes up or down. But for every value of A, we can also vary Gene B, resulting in better or worse combinations of A and B. Every combination of A and B results in a particular fitness, and this fitness is expressed as the height of the Fitness Landscape. It is the job of the solver to find the highest peak in this landscape.

你可以把上面这张图当成一个特别的景观模型（类似于山脉），这个模型包涵了两个变量，他们可以同时变化。在进化算法中我们习惯把变量称为基因。当我们改变基因A的时候结果会变好或者变坏（取决于我们希望他变好还是变坏）来匹配适合模型的状态。所以，当基因A改变时，整个模型都在变化。同理，在基因A发生变化时，基因B也可以同时参与变化，这时候出来的结果就是A和B同时起的作用。每一个A和B所产生出来的结果都被反映在这个模型的Z轴高度上，因为我们的任务就是找

出来这个山峰的最高点。

Of course a lot of problems are defined by not just two but many genes, in which case we can no longer speak of a 'landscape' in the strict sense. A model with 12 genes would be a 12-dimensional fitness volume deformed in 13 dimensions instead of a

two-dimensional fitness plane deformed in 3 dimensions. As this is impossible to visualize I shall only use one and two-dimensional models, but note that when we speak of a "landscape", it might mean something terribly more complex than the above image shows.

诚然，大量的问题并非简单的通过两个基因就能确定，而是需要很多基因，所以严格意义上来讲的话也就不能用景观（山脉）这个概念来解释，你想想看，一个用12个变量确定的将会是一个12维体扭曲在13维空间里，而不再是2维平面扭曲在三维空间里。所以我用一个2维的模型是不可能展示出来12维物体的，不过我提到这个只是想说有时候我们研究的要比上面这个2维世界的图复杂得多。

As the solver starts it has no idea about the actual shape of the fitness landscape. Indeed, if we knew the shape we wouldn't need to bother with all this messy evolutionary stuff in the first place. So the initial step of the solver is to populate the landscape (or "model-space") with a random collection of individuals (or "genomes"). A genome is nothing more than a specific value for each and every gene. In the above case, a genome could for example be {A=0.2 B=0.5}. The solver will then evaluate the fitness for each and every one of these random genomes, giving us the following distribution:

当这个进化算法开始的时候，其实电脑是不知道这个山脉景观的，如果电脑会像我们一样一眼看出来这个山脉的高低一开始就不用这么麻烦的去弄一大堆的数据。所以，在一开始，电脑就要用一大堆随机的点（基因组）来给他塑形。基因组就是一组数据，没别的，在这个例子里，一个基因组就相当于A=0.2 B=0.5的一个坐标。电脑计算过每一个随机的基因组，并且适应化之后，我们就可以看到下图这样的分布。

Once we know how fit every genome is (i.e., the elevation of the red dots), we can make a hierarchy from fittest to lamest. We are looking for high-ground in the landscape and it is a reasonable assumption that the higher genomes are closer to potential

high-ground than the low ones. Therefore we can kill off the worst performing ones and focus on the remainder:

一旦我们知道了这些基因组（下图这些抬高的红点点）匹配这个山脉的程度，我们就可以通过匹配的程度，非常匹配或者差一些的，来给他们分级。我们是在寻找这个山脉上位置较高的点，所以有充足的理由来假设这些位置较高的基因组要比位置靠下的基因组更加接近顶端，所以，我们可以把那些表现的差一些的拖出去斩了而只关注那些剩下来的优秀的。

It is not good enough to simply pick the best performing genome from the initial population and call it quits. Since all the genomes in Generation 0 were picked at random, it is actually quite unlikely that any of them will have hit the jack-pot. What we need to do is breed the best performing genomes in Generation 0 to create Generation 1. When we breed two genomes, their offspring will end up somewhere in the intermediate model-space, thus exploring fresh ground:

如果我们只是把位置较好的基因从第一代提取出来并且停止工作这样并不是很好，因为0代基因是随机生成的点，不一定这些随机的点就有一个恰好在这个山脉的顶端。所以我们要做的是把第一代表现优良的基因组取出来并且让他们培育第二代，他们的后代会在这个原来父代模型空间的中间区域，所以也相当于扩展到了新的空间。

We now have a new population, which is no longer completely random and which is already starting to cluster around the three fitness 'peaks'. All we have to do is repeat the above steps (kill off the worst performing genomes, breed the best-performing genomes) until we have reached the highest peak.

现在我们有了新的一代人，并且这一代人并不是完全的随机了，而是更加的成组团的靠近三个山峰。后面我们要做的就是重复上一步（干掉那些掉链子的，养育那些表现好的，PS题外话：这就是赤裸裸的落后就要挨打啊，还不光挨打，直接干掉。。。。）直到我们找到到达最顶峰的点。

In order to perform this process, an Evolutionary Solver requires five interlocking parts, which I'll discuss in something resembling detail. We could call this the anatomy of the Solver.

这种算法需要五个具有连锁反应的部分，稍后我们会讨论下类似的细节，下面我们开始解剖他吧。

1Fitness Function 适应度函数

2Selection Mechanism 选择机制

3Coupling Algorithm 耦合算法

4Coalescence Algorithm 合并算法

5Mutation Factory 突变因素

Fitness Functions

适应度函数

In biological evolution, the quality known as "Fitness" is actually something of a stumbling block. Usually it is very difficult to say exactly what it means to be fit. It certainly has little or nothing to do with being the strongest, or the fastest, or the most vicious. The reason there are no flying dogs isn't that evolution hasn't gotten around to making any yet, it is that the dog lifestyle is supremely incompatible with flying and the sacrifices required to equip a dog with flight would certainly detract more from the overall fitness than flight would add to it. Fitness is the result of a million conflicting forces. Evolutionary Fitness is the ultimate compromise.

在生物进化论里，适应度这种概念在一定程度上就相当于阻碍。有时候我们很难准确定义什么是适应。适应这种概念这个年代看起来和更强壮的，更快的，或者是更邪恶的没有什么关系。没有进化出来飞狗并不是进化还没到一个很高的程度，而是狗的生活习惯不适于飞行，如果非要让一个狗进化出来能飞的翅膀，这个翅膀反而会大大削减其他方面的机能，所以他没有进化出来。适应的进化是百万年外界压力的磨合，进化的形态是最终向大自然妥协的结果。

A fit individual is on average able to produce more offspring than an unfit one, so we could say that fitness equals the number of genetic children. A better measure yet would be to count the number of grand-children. And a better measure yet would be to count the allele frequency in the gene-pool of the genes that made up the individual in question. But these are all rather ad-hoc definitions that cannot be measured on the spot.

一个适应性更强的父代平均来说要比适应性差的父代子孙更多，所以我们可以简单地说适应性就相当于后代数量。一个很好的测算方法就是看他的后代数量，或者更好的方法就是看后代基因组频率和父代的相似度。但是这些专门定义方法在一些情况下不适用。

At least in Evolutionary Computation, fitness is a very easy concept. Fitness is whatever we want it to be. We are trying to solve a specific problem, and therefore we know what it means to be fit. If for example we are seeking to position a shape so that it may be milled with minimum material waste, there is a very strict fitness function that leaves no room for argument.

在进化算法里，适应性是个很简单的概念，适应性就是我们想要的结果，当我们尝试解决一些特别的我们已经知道以何种方式匹配的问题。举个例子，我们试图寻找一个图形的位置他可以尽量的减少材料的浪费，这就是一个非常严格的没有什么讨论余地的问题。

Let's have a look at the fitness landscape again and let's imagine it represents a model that seeks to encase an object in a minimum volume bounding-box. A minimum bounding-box is the smallest orthogonal box that completely contains any given shape. In the image below, the green shape is encased by two bounding boxes. B has a smaller area than A and is therefore fitter.

我们再看一个地形，让我们把它想象成一个包在最小长方形体里的模型，最小包裹体就是包含任何形状最小的正交方体，在下面的图例，绿色的形状被两个盒子包含，B就比A的面积更小，更合适。

When we need to mill or 3D-print a shape, it is often a good idea to rotate it until it requires the least amount of material to be used during manufacturing. For a real minimum bounding-box we need at least three rotation axes, but since that will not allow me to display the real fitness landscape, we will restrict ourselves to rotation around the world X and Y axes. So, Gene A will represent the rotation around the X axis and Gene B will represent rotation around the Y axis. There is no need to allow for rotation higher than 360 degrees, so both genes have a limited working domain. (In fact, since we are talking about orthogonal boxes, even a 0-90 degree domain would suffice). Behold rotation around a single axis:

当我们需要做一个三维的模型时，如果能在加工制造时最大化的减少材料的浪费是个很好的想法，一个三维的最小的包涵盒子最少要3个旋转轴，但是因为也显示不了真正的结果，我们在这里就只围绕X，Y轴旋转。所以基因A就代表X轴旋转，基因B就代表Y轴旋转。没必要旋转360度因为每个基因都有一个限制工作的范围（事实上，因为我们讨论的是正交的盒子，所以90度就已经足够了）看他围绕单轴旋转：

When we pick two rotational angles at random, we end up somewhere on the fitness landscape. If we allow for 4 decimal places in the rotation angles it means we can actually generate almost 810,000,000,000 (or 810 billion) unique rotations. It is therefore exceptionally unlikely that we manage to pick a random rotation that yields the best possible answer. But let's say we don't even manage to get close. Let's say we manage to pick a random genome that is at the bad end of the fitness scale, i.e. at the bottom of the fitness landscape. What can we say about the blood-line of this genome? When we track the descendants of a particular genome there is always a large amount of randomness involved due to the workings of the Solver, but there is a strong general tendency that can be distinguished. Just like water will always flow downhill along the steepest slope, so genetic descendants will generally climb uphill along the steepest slope:

当我们选择两个旋转轴的时候，随机停在一个时候，如果我们的旋转轴设定4位小数，那就意味着我们会产生810,000,000,000 个角度的解，看来我们随机选一个角度来产生优秀的解这个方法是行不通了，甚至根本无法接近那个最优解，我们随机选的这些基因最后都不是最优解，像是在刚才那个

山丘的最底层的那些点。我们怎么来定义这些基因的血缘呢？当我们去追溯一个基因的后代，通常因为计算会产生出大量的后代，但是他们都有一个很强的易区别的某种倾向性。就像水流只顺着斜率最大的陡坡流下，这些后代会朝着最小阻力的顶部攀登。

Every individual tries to maximize its own fitness, as high fitness is rewarded by the solver. And the steepest uphill climb is the fastest way towards high fitness. So if the black sphere represents the location of the ancestral genome, the orange track represents the pathway of its most successful offspring. We can repeat this exercise for a large amount of sample points which will tell us something about how the Solver and the Fitness Landscape interact:

每一个个体都尽力最大化自己的适应性，因为适应性高才能存活，而且斜率最高的攀爬路径是最快的，所以大家看上面那张图，黑色的球体代表最初的基因，而橘黄色的路径就是那些表现最优良的基因所攀爬的方式，我们可以通过大量的点来测试一下，看看基因算法和适应性机制是如何相互作用的。

Since every genome is pulled uphill, every peak in the fitness landscape has a basin of attraction around it. This basin represents all the points in model-space that will converge upon that specific peak. It is important to notice that the area of the basin is in no way representative of the quality of the peak. Indeed, a very poor solution may have a large basin of attraction while a good peak might have a small catchment area. Problems like this are typically very difficult to solve, as the solution tends to get stuck in local optima. But we'll have a look at problematic fitness functions later on.

因为每个基因都会被拉到山顶，所以开始之前就有点池在山顶的周围环绕，这个池子里面就是将会聚集到山顶的点，我们要特别注意一点就是点池并不意味着山顶的质量，因为存在一个问题，有可能一个比较矮的山顶周围围绕了大量的点，而较高的山顶只围绕了少量的，像出现这样的问题一般很难处理，这个解算在局部最优以后就会停止，所以随后我们会看见一个有些问题的解。

First, let's have a closer look at the actual fitness landscape for our minimum bounding-box model. I'm afraid it's not quite as simple as the image we've been using so far. I was actually quite surprised how organic and un-box-like the actual fitness landscape for this problem is. Remember, the x-axis rotation is mapped along the Gene A direction and the y-axis rotation along the Gene B direction. So every point on the AB plane represents a unique rotation composed of two angles. The elevation of this point is a direct mapping of the volume of the bounding-box at those two rotation angles:

首先，看一下上图那个平面景观的最小的包含体，实际上远没有那么简单。如果是有机形态或者是非长方体那复杂程度真的吓我一跳。记住，基因A代表X轴旋转角度，基因B代表Y轴旋转角度，，所以以AB为平面的每一个点都代表了相应的XY轴旋转的角度，而那些提高的点（z轴坐标）意味着xy旋转轴所对应的最小的包含体的体积。

The first thing to notice is that the landscape is periodic. I.e., it repeats itself every 90 degrees in both directions. Also, this landscape is in fact inverted as we're looking for a minimum volume, not a maximum one. Thus, the orange peaks in fact represent the worst solutions to this problem. Note that there are 16 of these peaks in the entire range and that they are rounded. When we look at the bottom of this fitness landscape, we get a rather different view:

首先我们观察到的是由那些数据绘制出来的图是这样的周期曲面，说明每90度他们就会重复一次，这张图展示的和我们预想的正好相反（因为最顶端代表体积越大），你看图中橘黄色的就代表最差的结果，而且在我们搜寻的范围内，他们能够出现16次，当我们看看这个图的底部的时候，我们会发现一个有趣的现象：

It would appear that the lowest points in this landscape (the minimum bounding-boxes) are both fewer in number and of a different kind. We only get 8 optimal solutions and they are all very sharp, indicating a somewhat more fragile state.

图中展示的最低点（也就是我们要找的最小盒子）在数量上和差异性上都要少一些，我们只得到8个最优解，而且他们所处的地方都很陡峭，说明他们所处的状态很脆弱（也就是他们的相似值范围很小，我们搜寻是很容易错过）。

Still, on the whole we have nothing to complain about. All the solutions are of equal quality and there are no local optima at all. We can generalize this landscape to a

2-dimensional graph:

直到现在，我们对这些结果也没什么抱怨的，所有的解品质都一样而且也没有局部最优的现象，我们可以把那张图做成这样的二维图表：

No matter where you end up as an ancestral genome, your blood-line will always find its way to a minimum bounding box. There's nowhere for it to get 'stuck'. So it's really just a question about who gets there first. If we look at a slightly more complex fitness graph, it becomes apparent that this need not be the case:

无论你在什么时候暂停，并把当前状态作为最初的父代，根据原来的血缘我们还是能够找到那个最小的盒子，而且运行时不会被卡主。唯一的问题就是谁更快的到达那个地方。但是如果我们做个稍微复杂一点的图形，你就可以很明显的看出来问题所在。

This fitness landscape has two kinds of solutions. The high quality sharp ones near the bottom of the graph and the low quality flat ones near the top. The basin of attraction is given for both solutions (yellow for high quality, pink for low quality) and you can see that about half of the model space is attracted to the low quality solutions.

根据上面这张图这时候有两类解，高质量的解在这张图表的最下面锋利的地方，二低质量的解在靠近顶部的地方，开始的那些父代给了我们两种解（黄色代表高质量解，粉色代表低质量解）你可以看出将近有一半的父代导致我们求出了低质量的解。

An even worse example (flipped upright again this time, so high values indicate good solutions) would be the following fitness landscape:

现在我们把刚才那个最优和次优的图标简化一下翻转过来，现在高的代表高质量解，低的代表低质量解：

The basins for these peaks are very small indeed and therefore easy to miss by a random sampling of the landscape. As soon as a lucky genome finds the peak on the left, its offspring will rapidly populate the low peak causing the rest of the population to go extinct. It is now even less likely that the better peak on the right will be found. The smaller the basins for solution, the harder it is to solve a problem with an evolutionary algorithm.

如果点池很少那么很可能错过一些最优解。一旦一个基因幸运的找到左侧的那个山峰，他就会跑过去并进行大量的繁衍，而下面的就会渐渐消失，这样右侧那个更高的山峰可能就找不到了，所以说刚开始的点池越少（父代越少），进化算法越难算出来你想要的结果。

Another example of a cumbersome problem to solve would be a discontinuous fitness landscape:

另一类更难处理的就是这种不连续适应性的问题：

Even though there are strictly speaking no local optima, there is also no 'improvement' on the plateaus. A genome which finds itself in the middle of one of these horizontal patches doesn't know where to go. If it takes a step to the left, nothing changes. If it takes a step to the right, nothing changes. There's no 'pressure' in this fitness landscape, so all the genomes will wander about aimlessly, until one of them has the good fortune to suddenly step onto a higher plateau. At this point it will quickly dominate the

gene-pool and the wandering starts again until the next plateau is accidentally found.

尽管在严格意义上说这里不存在什么局部最优解，但是他们在不同的层级之间却没有提高，当一个基因发现自己在一个水平的平面时，他就不知道去哪儿了，往左一步没什么变化，往右一步也没什么变化，因为在这个系统里没有压力，所以每一个基因也是这样漫无目的的游牧，直到有一个幸运的基因突然找到了那个最高的平面，这时候这个店会迅速占领整个基因池，并开始漫无目的的游牧直到下一个新大陆被发现。

Even worse than this though is a landscape that has a high degree of noise or chaos. A landscape may be continuous and yet feature so much detail that it becomes impossible to make any intelligible pronunciations regarding the fitness of a local patch:

更糟糕的情况就是下图这种类似多级噪音或混沌状态的图。这个图虽然是连续的，但是大量的细节让他们很难的展示出来甚至是局部最优：

In a landscape like this, mommy and daddy may both be very similar and both be very fit, but when they mate the offspring might end up in one of the fissures. A landscape like this defies navigation.

在这样的图表中，父代和母代都非常相似适应性也都非常高，然而当他们孕育出下一代的时候，那一代很可能在另一个图中的裂缝里，像这样的图表，你很难给他做一个方向性的引导。

Selection Mechanisms

选择机制

Biological Evolution proceeds by Natural Selection. The ruthless force identified by Darwin as the arbiter of progress. Put simply, Natural Selection affects the direction of the gene-pool over time by regulating who gets to mate. In extreme cases mating is prevented because a specific genome is so unfit that the bearer cannot survive until reproductive age. Another rather extreme case would be sterility. However, there's a

myriad ways in which Natural Selection can make it difficult or impossible for certain individuals to pass on their genetic footprint.

生物进化的进程取决于自然选择，这种无情的定义源于达尔文。简单地讲，自然选择通过调整交配来影响基因池发展的方向。在一些极端的例子里，那些适应性差的基因很难活到繁殖期。在另一些极端情况下甚至是不孕不育。然而，并非只有上述的哪两种，自然选择有无数的方法来让那些适应性差的物种很难，基本不可能来传递他们的精子或卵子。

However, Natural Selection isn't the only game in town. For a long time now humans have been using Artificial Selection in order to breed specific characteristics into a (sub)species. When we try to solve problems using an Evolutionary Solver, we always use some form of artificial selection. There's no such thing as sex or gender in the computer. The process of selection is also much simpler than in nature, as there is basically only one question that needs to be answered: Who gets to mate?

其实自然选择并不是自然界中唯一的游戏规则，其实人类很早就开始利用人工选择来培育亚物种成为我们想要的。当我们用进化算法来解决问题的时候，其实我们也是利用了人工选择，因为电脑里可没有性或者是性器官一类的东西，所以这种进程要比在自然界简单得多，所以我们唯一要关心的基本的问题就是：我们给谁权利去交配？

Allow me to enumerate the mechanisms for parent selection that are available in Galapagos. This is only a small subset of the selection algorithms that are possible, but they seem to cover the basics rather well.

下面我介绍一下galapagos里面应用的选择机制，其实他只是选择算法里的一小部分，不过他基本上涵盖了大部分应用的机制。

First off, we have Isotropic Selection, which is the simplest kind of algorithm you can imagine. In fact, it is the absence of a selection algorithm. In Isotropic Selection everyone gets to mate:

首先，我们有等方性选择机制，这个算法很好理解，事实上，他在选择算法里是不存在的，在等方性选择机制里，每个个体都有权利去交配：

No matter where you find yourself on this fitness graph, your chances of ending up in a mating couple are constant. You might think that this is a particularly pointless selection strategy as it does nothing to further the evolution of the gene-pool. But it is not without precedent in nature. Take for example wind-pollination or coral spawning. If you're a sexually functioning member of such a species, you get to play ball come mating season. Another example would be females in a walrus colony. Every female in a colony gets to breed with the dominant male, no matter how fit or unfit she is. Isotropic Selection is

certainly not without function either. For one, it dampens the speed with which a population runs uphill. It therefore acts as a safe-guard against a premature colonization of a local -and possibly inferior- optimum.

无论你在这个图标里找什么位置，这种交配的机会都是均等的，你可能会向这种无意义的选择策略对基因池根本没什么影响。但是，其实自然界并不是没有这种先例，例如风媒传播和珊瑚繁殖。如果你是这样的一类性功能物种，在交配的季节你就只能玩个球了。另一个例子就是海象殖民地的雌性，每一个雌性海象都会和占领这个地方的雄性海象一一发生性关系（听起来好happy），而不管这个雌海象是不是适应性很高的。等方性选择也并不是没有一定的作用。其中有一条就是他会抑制往上进化的速度，这种选择策略其实起到了一种安全保护的作用，他可以在一个不成熟的繁殖环境进行局部次级优化。

Another mechanism available in Galapagos is Exclusive Selection, where only the top N% of the population get to mate:

另一种galapagos里的选择机制是独有选择机制，也就是只有顶端的N%才有权利进行交配，

If you're lucky enough to be in the top N%, you'll likely have multiple offspring. A good analogy in nature for Exclusive Selection would be Walrus males. There's only a few harems to go around and far too many males to assign them all (a harem of one female after all is not really a harem). The flunkies get to sit on the side-line without a single chance to father a walrus baby, doing whatever it is walruses do when they can't get any action.

如果你很幸运的就是那N%，那你会有很多的后代，一个好的独有选择机制就是海象里面的雄海象，很少的妻妾群要被很多雄海象分配（一个妻妾群里只有一个雌海象肯定不能算是一个妻妾群），那些除了雄海象王剩下的随从只能在在一边，根本没有交配的机会，除了交配他们倒是可以做一些自己想做的事。

Another common pattern in nature is Biased Selection, where the chance of mating increases as the fitness increases. This is something we typically see with species that form stable couples. Everyone is basically capable of finding a mate, but the really attractive individuals manage to get a lot of hanky-panky on the side, thus increasing their chances of becomes genetic founders for future generations. Biased Selection can be amplified by using power functions, which have the effect of flattening or exaggerating the curve.

另一类常用的类型就是偏向选择，交配的频率和适应程度是相一致的，这个图形我们在形态稳定的物种中经常见到，没一个个体都有能力去找一个伴侣，但是那些更有吸引力的个体会使用各种花招来增

加他们成为更多后代父亲的机会，偏向选择可以通过外力来扩大或者缩小幅度，在图里就意味着更陡峭的曲线或者更扁平的曲线。

Coupling Algorithms

耦合算法

Coupling is the process of finding mates. Once a genome has been elected to mate by the active Selection Algorithm, it has to pick a mate from the population to complete the act. There are of course many ways in which mate selection could occur, but Galapagos at the moment only allows one; selection by genomic distance. In order to explain this in detail, I should first tell you how a Genome Map works. This

耦合就是寻找配对对象的过程，一旦有基因通过选择算法被选择出来并赋予交配的权利，那么他就要在他这一代中找一个对象来完成耦合。在其他场合中虽然有很多的配对耦合的方法，但是在galapagos里只有一种方法，通过一进组的距离来选择，为了解释这个细节，我会先讲一下下面这个基因图是怎么工作的：

is a Genome Map. It displays all the genomes (individuals) in a certain population as dots on a grid. The distance between two genomes on the grid is roughly analogous with the distance between the genomes in gene-space. I say roughly because it is in fact impossible to draw a map with exact distances. A single genome is defined by a number of genes. We assume that all the genomes in a species have the same number of genes (this is not technically a limitation of Evolutionary Algorithms, even though it is currently a limitation of Galapagos). Therefore the distance between two genomes is an

N-Dimensional value, where N equals the number of genes. It is not possible to accurately display an N-Dimensional point cloud on a 2-Dimensional screen so the Genome Map is only a coarse approximation. It also follows that the axes of this graph have no meaning whatsoever, the only information a Genome Map conveys is which genomes are more or less similar (close together) and which genomes are more or less different (far apart).

这是一个基因地图，每一代的个体在这个网格中就是一个点。在基因地图上两个点之间的距离和真实的基因空间里两个基因的距离对比起来图中的明显很粗糙，我之所以说它粗糙是引文事实上不可能在这个网格上画出准确的距离。一个基因组是有许多基因组成的。我们假设所有的基因组都有相同的基因数（其实在进化算法里没这样的限制，只是在galapagos里才有这样的限制），因此，存在于两个基因组之间的距离就是N维域，这个N等同于组成基因组的基因数量，所以不可能在一个2维的平面上面来准确的展示N维空间的点云，所以基因地图只是一个很粗糙的接近值。所以随着轴的推移所对应的数据没有什么意义，基因地图唯一能够传达给我们的信息就是哪些基因组离得近一些差异小一些，哪些基因组离得远一些差异大一些。

Imagine you are an individual that has been selected for mating (yay). The population is well distributed and you are somewhere near the average (I'm sure you are a wildly original and delightful person in real life, but for the time being try to imagine you are in fact sort of average):

现在把你想象成被选中有交配权利的个体（我知道你在暗爽），这一代分布的很均匀，而你也恰好在平均值附近（我知道你在现实生活中非常有才而且受人喜爱，但是这个时候你就委屈一下把自己当成一个在平均水平的普通人）：