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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Holland's schema theorem ： ウィキペディア英語版 Holland's schema theorem Holland's schema theorem, also called the fundamental theorem of genetic algorithms, is widely taken to be the foundation for explanations of the power of genetic algorithms. It says that short, low-order schemata with above-average fitness increase exponentially in successive generations. The theorem was proposed by John Holland in the 1970s. A schema is a template that identifies a subset of strings with similarities at certain string positions. Schemata are a special case of cylinder sets, and hence form a topological space. == Description == For example, consider binary strings of length 6. The schema 1 *10 *1 describes the set of all strings of length 6 with 1's at positions 1, 3 and 6 and a 0 at position 4. The * is a wildcard symbol, which means that positions 2 and 5 can have a value of either 1 or 0. The ''order of a schema'' $o(H)$ is defined as the number of fixed positions in the template, while the ''defining length'' $\backslash delta(H)$ is the distance between the first and last specific positions. The order of 1 *10 *1 is 4 and its defining length is 5. The ''fitness of a schema'' is the average fitness of all strings matching the schema. The fitness of a string is a measure of the value of the encoded problem solution, as computed by a problem-specific evaluation function. Using the established methods and genetic operators of genetic algorithms, the schema theorem states that short, low-order schemata with above-average fitness increase exponentially in successive generations. Expressed as an equation: :$\backslash operatorname(m(H,t+1))\; \backslash geq\; ().$ Here $m(H,t)$ is the number of strings belonging to schema $H$ at generation $t$, $f(H)$ is the ''observed'' average fitness of schema $H$ and $a\_t$ is the ''observed'' average fitness at generation $t$. The probability of disruption $p$ is the probability that crossover or mutation will destroy the schema $H$. It can be expressed as: :$p\; =\; p\_c\; +\; o(H)\; p\_m$ where $o(H)$ is the order of the schema, $l$ is the length of the code, $p\_m$ is the probability of mutation and $p\_c$ is the probability of crossover. So a schema with a shorter defining length $\backslash delta(H)$ is less likely to be disrupted. An often misunderstood point is why the Schema Theorem is an ''inequality'' rather than an equality. The answer is in fact simple: the Theorem neglects the small, yet non-zero, probability that a string belonging to the schema $H$ will be created "from scratch" by mutation of a single string (or recombination of two strings) that did ''not'' belong to $H$ in the previous generation. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Holland's schema theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.