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Hi, Welcome aboard of EoM on behalf of the editorial board. Please find [[MediaWiki:Welcomecreation|here our working conditions]].--[[User:Ulf Rehmann|Ulf Rehmann]] 11:37, 25 May 2012 (CEST): I wonder, what for did you upload [[File:Encyclopedia EAs v10 alt versionEdit ac edit2a.docx]]? --[[User:Boris Tsirelson|Boris Tsirelson]] 18:25, 13 August 2012 (CEST)== Upload ==The upload was an error.  I am surprised the upload occured as there was an error message on my side saying it had failed.:I see. You can ask Ulf to delete it, [[User talk:Ulf Rehmann#Obsolete pages|here]]. --[[User:Boris Tsirelson|Boris Tsirelson]] 22:25, 13 August 2012 (CEST):Also it could be more convenient to create [[User:Tgawa63/sandbox|your personal sandbox]] and use it for drafts (rather than your user page). --[[User:Boris Tsirelson|Boris Tsirelson]] 22:28, 13 August 2012 (CEST)== Sandbox and a thank you ==Txs for the heads-up about the sandbox.  I have found it very useful this morning.  And I will contact Ulf about the misposted items.:Nice, but I see that you did not use my redlink, but instead typed in a different name. I just moved it. Now it is called [[User:Tgawa63/sandbox]], thus it belongs to your userspace. The old name [[Tgawa63/sandbox]] belongs formally to the mainspace, and means formally "a supplement to the article on Tgawa63", which was not intended. --[[User:Boris Tsirelson|Boris Tsirelson]] 18:30, 14 August 2012 (CEST)== MathJax ==I have the genetic algorithm paper in the sandbox and it is complete but for 2 very important things: 1)I cannot make certain symbols appear as bold or italics for example, how to do so is my question 2)all of the formulas are coming over in TEX format with some appearing ok but others getting broken into multiple pieces so one part of the formula is on 1 line while the continuation is on the next, how to fix this.  Pls excuse my inexperience and naviete in asking these questions.: Unfortunately, in many cases I really do not guess which effect do you try to produce. Anyway, I did some changes on my copy of your text [[User:Boris Tsirelson/sandbox1|here]]. Please look ''(to this end, click the blue word "here")'' and, if you like, copy it back into your sandbox. I did not finish this work, but probably you can continue it yourself. Do not hesitate to ask. It seems, you did not use TeX before; really? --[[User:Boris Tsirelson|Boris Tsirelson]] 22:49, 20 August 2012 (CEST): And please sign your messages (on talk pages) by four tildas: <nowiki>~~~~</nowiki>. --[[User:Boris Tsirelson|Boris Tsirelson]] 22:53, 20 August 2012 (CEST): There are several problems here -- you are putting displayed math in the middle of a line, but Wiki syntax interprets 4 space indentation as being a quote.  I have fixed the first to cases of this in your sandbox, please look at the source --[[User:Jjg|Jjg]] 19:33, 24 August 2012 (CEST)== GA entry ==Hello,My apologies for needing all the help you have given so far.  As to Boris' question about TeX, no I have never used it.  At to the other question about Wiki use, I have not done that either.  Pls know I will be contacting a pro in web building who will make the necessary entries and will hopefully not need as much help as I have so far.  Again my apologies for my deficiences.  [[User:Andrew Clark]] ([[User talk:Tgawa63|talk]]) 16:45, 18 September 2012 (CEST)Andrew Clark: Probably you need someone that knows TeX and Wiki (rather than web building). [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 21:44, 18 September 2012 (CEST): Anyway, it would help, first to look closely at existing texts and try to do as similarly as possible. Also, below I put my version of your text. Feel free to delete it if you do not need it here. At bottom, some portion is left intact; maybe try to correct it yourself similarly to the corrected top portion. [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 22:31, 18 September 2012 (CEST):Hi Boris - I have in the sandbox Tgawa63 a completed version of the article.  I receivd some good help w/posting it so I would like to submit it for review.  If you can tell me how to start the review process, I'll be happy to take those steps. [[User:Andrew Clark]] =Genetic Algorithms===Genetic algorithms (GAs): basic form==A generic GA (also known as an evolutionary algorithm [EA]) assumes a discrete search space $H$ and a function\[f:H\to\R,\]where $H$ is a subset of the Euclidean space $\R$.The general problem is to find\[\arg\underset{X\in H}{\mathop{\min }}\,f\]where $X$ is a vector of the decision variables and $f$ is the objective function.With  GAs it is customary to distinguish genotype–the encoded representation  of the variables–from phenotype–the set of variables themselves. The  vector $X$ is represented by a string (or chromosome) $s$ of length $l$  made up of symbols drawn  from an alphabet $A$ using the mapping\[c:A^l\to H\]The  mapping $c$ is not necessarily surjective. The range of $c$ determine  the subset of $A^l$ available for exploration by a GA.  The range of  $c$, $\Xi$\[\Xi\subseteq {{A}^{l}}\]is  needed to account  for the fact that some strings in the image $A^l$ under $c$  may  represent invalid solutions to the original problem.The  string length $l$ depends on the dimensions of both $H$ and $A^l$,  with the elements of the string corresponding to  genes and the values  to alleles. This statement of genes and alleles is  often referred to as  genotype-phenotype mapping.Given the statements above, the optimization becomes:\[\arg\underset{S\in L}{\mathop{\min g}}\,,\]given the function \[g(s)=f(c(s)).\]Finally,  with GAs it is helpful if $c$ is a bijection. The  important property  of bijections as they apply to GAs is that bijections have an inverse,  i.e., there is a unique vector $x$ for every string and a unique string  for each $x$.==Genetic algorithms and their Operators==Let $H$ be a nonempty set (the individual or search  space)\[{{\left\{{{u}^{i}} \right\}}_{i\ in \mathbb{N}}}\]a sequence in\[{{\mathbb{Z}}^{+}}\](the parent populations).\[{{\left\{  {{u}^{'(i)}} \right\}}_{i\in \mathbb{N}}}\]a sequence in\[{{\mathbb{Z}}^{+}}\](the offspring population sizes),\[\phi:H\to  \mathbb{R}\]a fitness function,\[\iota :\cup_{i=1}^{\infty}{{({{H}^{u}})}^{(i)}}\to\{\text{true},\text{false}\}\](the termination  criteria),\[\chi\in\{\text{true},\text{false}\},\]$r$ a sequence\[\left\{{{r}^{(i)}}  \right\}\]Define the collection $\mu$ (the  number of individuals) via $H_\mu$. The population transforms are denoted by\[T:{{H}^{\mu }}\to {{H}^{\mu }}\]where\[\mu \in \mathbb{N}\]of recombination operators $\tau(i)$: \[X_{r}^{(i)}\to T(\Omega_{r}^{(i)},T\left( {{H}^{{{u}^{(i)}}}},{{H}^{u{{'}^{(i)}}}} \right)),\]$m$ a sequence of {m(i)} of mutation operators in mi,\[X_{m}^{(i)}\to T(\Omega  _{m}^{(i)},T\left({{H}^{{{u}^{(i)}}}},{{H}^{u{{'}^{(i)}}}} \right)),\]$s$ a sequence of {si} selection operators s(i):\[X_{s}^{(i)}\times  T(H,\mathbb{R})\to T(\Omega_{s}^{(i)},T(({{H}^{u{{'}^{(i)+\chi  {{\mu}^{(i)}}}}}}),{{H}^{{{\mu  }^{(i+1)}}}})),\]\[\Theta_{r}^{(i)}\in X_{r}^{(i)}\](the  recombination parameters),\[\Theta_{m}^{(i)}\in X_{m}^{(i)}\](the  mutation parameters), and\[\Theta_{s}^{(i)}\in X_{s}^{(i)}\](the  selection parameters).To account for the cases where populations whose size not equal to their predecessors’, the following expression \[T:{{H}^{\mu}}\to {{H}^{{{\mu }'}}}\]accommodates  populations that contain the same or different individuals. This  mapping has the ability to represent all population sizes, genetic  operators, and parameters as sequences.The  execution  of a GA typically begins by random sampling with replacement  from  $A^l$.  The  resulting collection is the initial population, denoted by  $P(0)$. In general, a population is a collection \[P=({{a}_{1}},{{a}_{2}},...,{{a}_{\mu }})\]of  individuals, where\[{{a}_{i}}\in {{A}^{l}},\]and populations are treated as $n$-tuples of individuals. The number of individuals ($\mu$) is defined as the population size.Following  upon the  work of Lamont and Merkle (Lamont, 1997) and others, the  termination  criteria and the other genetic operators(GOs)will be  defined in more  detail.Since $H$ is a nonempty  set,\[c:{{A}^{l}}\to H,\]and\[f:H\to \mathbb{R},\]the fitness scaling  function can be defined as\[{{T}_{s}}:\mathbb{R}\to \mathbb{R}\]and a  related fitness function as\[\Phi \triangleq {{T}_{s}}\circ f\circ c.\]In  this definition it is understood that the objective function $f$ is  determined by the application, while the specification of  the decoding  function $c[1]$ and the fitness scaling  function $T_s$ are  design  issues.After initialization, the  execution  proceeds iteratively.  Each iteration consists of an  application of  one or more GOs. The combined effect of the GOs applied  in a particular  generation $t\in N$ is a transformation of the current  population  ''Italic text''P(t) into a new population ''Italic  text''P(t+1).In  the population transformation $\mu  ,{\mu}'\ in {{\mathbb{Z}}^{+}}$(the  parent and offspring population  sizes, respectively). A mapping  $T:{{H}^{\mu }}\ to {{H}^{{{\mu }'}}}$  is called a population  transformation (''Italic text''PT). If  $T(P)={P}'$, then ''Italic  text''P is the parent population and  <sup>Superscript  text</sup>''Italic text''P/ the offspring  population. If $\mu  ={\mu }'$,then it is called the population size.The  ''Italic text''PT resulting from a GO often depends on the outcome of a  random experiment. This result is referred to as a random population  transformation (''Italic text''RPT or random PT). To define ''Italic  text''RPT, let $\mu \in {{\mathbb{Z}}^{+}}$and $\Omega $ be a set (the  sample space). A random function $R:\Omega \to T({{H}{\mu  }},\bigcup\limits_{{\mu }'\ in {{\mathbb{Z}}^{+}}}^{{}}{{{H}^{{{\mu  }'}}}})$ is called a ''Italic text''RPT. The distribution of ''Italic  text''PTs resulting from the application of a GO depends on the operator  parameters; in other words, a GO maps its parameters to a ''Italic  text''RPT.Now that both the fitness function and  ''Italic text''RPT have been defined, let$\mu \in {{\mathbb{Z}}^{+}}$,  ''Italic text''X be a set (the parameter space) and $\Omega $ a set. The  mapping $\Zeta :X\to T\left( \Omega ,T\left[ {{H}^{\mu  }},\bigcup\limits_{{\mu }'\in {{\mathbb{Z}}^{+}}}^{{}}{{{H}^{{{\mu}'}}}}  \right] \right)$ is a GO. The set of GOs is denoted as $GAOP\left(  H,\mu ,X,\Omega  \right)$.There are three  common GOs: recombination,mutation, and selection. These three operators  are roughly analogous to their similarly named counterparts in  genetics. The application of them in GAs is strictly Darwin-like in  nature, i.e., “survival of the fittest.”For the  recombination operator let $r\in GAOP\left( H,\mu ,X,\Omega  \right)$.  If there exists $P\in {{H}^{\mu }},\Theta \in X$, and $\omega \in \Omega  $, such that one individual in the offspring population ${{r}_{\Theta  }}\left( P \right)$ depends on more than one individual of P,then r is  referred to as a recombination operator. For the  mutation operator let $m\in GAOP\left( H,\mu ,X,\Omega\right)$. If for  every $P\in {{H}^{\mu }}$, for every $\Theta \in X$, for every  $\omega\in \Omega $, and if each individual in the offspring population  ${{m}_{\Theta}}\left( P \right)$ depends on at most one individual of  P,  then m is called a mutation operator.Finally, for  the selection operator let $s\in EVOP\left( H,\mu ,X\times  T\left(H,\mathbb{R}),\Omega  \right) \right)$. If $P\in {{H}^{\mu  }}$,$\Theta \in X$,$\Phi :H\to\mathbb{R}$in all cases, and satisfies  $a\in {{s}_{\left( \Theta ,\Phi \right)}}(P)\Rightarrow a\in P$, then s  is a selection operator.'''Bold text'''Endnotes[1]  If the domain of c is total, i.e., the domain of c is all of A I, c is  called a decoding function. The mapping of c is not necessarily  surjective. The range of c determines the subset of Al available for  exploration by the evolutionary algorithm.
+
Hi, Welcome aboard of EoM on behalf of the editorial board. Please find [[MediaWiki:Welcomecreation|here our working conditions]].--[[User:Ulf Rehmann|Ulf Rehmann]] 11:37, 25 May 2012 (CEST): I wonder, what for did you upload [[File:Encyclopedia EAs v10 alt versionEdit ac edit2a.docx]]? --[[User:Boris Tsirelson|Boris Tsirelson]] 18:25, 13 August 2012 (CEST)== Upload ==The upload was an error.  I am surprised the upload occured as there was an error message on my side saying it had failed.:I see. You can ask Ulf to delete it, [[User talk:Ulf Rehmann#Obsolete pages|here]]. --[[User:Boris Tsirelson|Boris Tsirelson]] 22:25, 13 August 2012 (CEST):Also it could be more convenient to create [[User:Tgawa63/sandbox|your personal sandbox]] and use it for drafts (rather than your user page). --[[User:Boris Tsirelson|Boris Tsirelson]] 22:28, 13 August 2012 (CEST)== Sandbox and a thank you ==Txs for the heads-up about the sandbox.  I have found it very useful this morning.  And I will contact Ulf about the misposted items.:Nice, but I see that you did not use my redlink, but instead typed in a different name. I just moved it. Now it is called [[User:Tgawa63/sandbox]], thus it belongs to your userspace. The old name [[Tgawa63/sandbox]] belongs formally to the mainspace, and means formally "a supplement to the article on Tgawa63", which was not intended. --[[User:Boris Tsirelson|Boris Tsirelson]] 18:30, 14 August 2012 (CEST)== MathJax ==I have the genetic algorithm paper in the sandbox and it is complete but for 2 very important things: 1)I cannot make certain symbols appear as bold or italics for example, how to do so is my question 2)all of the formulas are coming over in TEX format with some appearing ok but others getting broken into multiple pieces so one part of the formula is on 1 line while the continuation is on the next, how to fix this.  Pls excuse my inexperience and naviete in asking these questions.: Unfortunately, in many cases I really do not guess which effect do you try to produce. Anyway, I did some changes on my copy of your text [[User:Boris Tsirelson/sandbox1|here]]. Please look ''(to this end, click the blue word "here")'' and, if you like, copy it back into your sandbox. I did not finish this work, but probably you can continue it yourself. Do not hesitate to ask. It seems, you did not use TeX before; really? --[[User:Boris Tsirelson|Boris Tsirelson]] 22:49, 20 August 2012 (CEST): And please sign your messages (on talk pages) by four tildas: <nowiki>~~~~</nowiki>. --[[User:Boris Tsirelson|Boris Tsirelson]] 22:53, 20 August 2012 (CEST): There are several problems here -- you are putting displayed math in the middle of a line, but Wiki syntax interprets 4 space indentation as being a quote.  I have fixed the first to cases of this in your sandbox, please look at the source --[[User:Jjg|Jjg]] 19:33, 24 August 2012 (CEST)== GA entry ==Hello,My apologies for needing all the help you have given so far.  As to Boris' question about TeX, no I have never used it.  At to the other question about Wiki use, I have not done that either.  Pls know I will be contacting a pro in web building who will make the necessary entries and will hopefully not need as much help as I have so far.  Again my apologies for my deficiences.  [[User:Andrew Clark]] ([[User talk:Tgawa63|talk]]) 16:45, 18 September 2012 (CEST)Andrew Clark: Probably you need someone that knows TeX and Wiki (rather than web building). [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 21:44, 18 September 2012 (CEST): Anyway, it would help, first to look closely at existing texts and try to do as similarly as possible. Also, below I put my version of your text. Feel free to delete it if you do not need it here. At bottom, some portion is left intact; maybe try to correct it yourself similarly to the corrected top portion. [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 22:31, 18 September 2012 (CEST):Hi Boris - I have in the sandbox Tgawa63 a completed version of the article.  I receivd some good help w/posting it so I would like to submit it for review.  If you can tell me how to start the review process, I'll be happy to take those steps. [[User:Andrew Clark]]

Revision as of 16:15, 22 October 2012

Hi, Welcome aboard of EoM on behalf of the editorial board. Please find here our working conditions.--Ulf Rehmann 11:37, 25 May 2012 (CEST): I wonder, what for did you upload File:Encyclopedia EAs v10 alt versionEdit ac edit2a.docx? --Boris Tsirelson 18:25, 13 August 2012 (CEST)== Upload ==The upload was an error. I am surprised the upload occured as there was an error message on my side saying it had failed.:I see. You can ask Ulf to delete it, here. --Boris Tsirelson 22:25, 13 August 2012 (CEST):Also it could be more convenient to create your personal sandbox and use it for drafts (rather than your user page). --Boris Tsirelson 22:28, 13 August 2012 (CEST)== Sandbox and a thank you ==Txs for the heads-up about the sandbox. I have found it very useful this morning. And I will contact Ulf about the misposted items.:Nice, but I see that you did not use my redlink, but instead typed in a different name. I just moved it. Now it is called User:Tgawa63/sandbox, thus it belongs to your userspace. The old name Tgawa63/sandbox belongs formally to the mainspace, and means formally "a supplement to the article on Tgawa63", which was not intended. --Boris Tsirelson 18:30, 14 August 2012 (CEST)== MathJax ==I have the genetic algorithm paper in the sandbox and it is complete but for 2 very important things: 1)I cannot make certain symbols appear as bold or italics for example, how to do so is my question 2)all of the formulas are coming over in TEX format with some appearing ok but others getting broken into multiple pieces so one part of the formula is on 1 line while the continuation is on the next, how to fix this. Pls excuse my inexperience and naviete in asking these questions.: Unfortunately, in many cases I really do not guess which effect do you try to produce. Anyway, I did some changes on my copy of your text here. Please look (to this end, click the blue word "here") and, if you like, copy it back into your sandbox. I did not finish this work, but probably you can continue it yourself. Do not hesitate to ask. It seems, you did not use TeX before; really? --Boris Tsirelson 22:49, 20 August 2012 (CEST): And please sign your messages (on talk pages) by four tildas: ~~~~. --Boris Tsirelson 22:53, 20 August 2012 (CEST): There are several problems here -- you are putting displayed math in the middle of a line, but Wiki syntax interprets 4 space indentation as being a quote. I have fixed the first to cases of this in your sandbox, please look at the source --Jjg 19:33, 24 August 2012 (CEST)== GA entry ==Hello,My apologies for needing all the help you have given so far. As to Boris' question about TeX, no I have never used it. At to the other question about Wiki use, I have not done that either. Pls know I will be contacting a pro in web building who will make the necessary entries and will hopefully not need as much help as I have so far. Again my apologies for my deficiences. User:Andrew Clark (talk) 16:45, 18 September 2012 (CEST)Andrew Clark: Probably you need someone that knows TeX and Wiki (rather than web building). Boris Tsirelson (talk) 21:44, 18 September 2012 (CEST): Anyway, it would help, first to look closely at existing texts and try to do as similarly as possible. Also, below I put my version of your text. Feel free to delete it if you do not need it here. At bottom, some portion is left intact; maybe try to correct it yourself similarly to the corrected top portion. Boris Tsirelson (talk) 22:31, 18 September 2012 (CEST):Hi Boris - I have in the sandbox Tgawa63 a completed version of the article. I receivd some good help w/posting it so I would like to submit it for review. If you can tell me how to start the review process, I'll be happy to take those steps. User:Andrew Clark

How to Cite This Entry:
Tgawa63. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Tgawa63&oldid=28595
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