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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 differential evolution ： ウィキペディア英語版 differential evolution In evolutionary computation, differential evolution (DE) is a method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. Such methods are commonly known as metaheuristics as they make few or no assumptions about the problem being optimized and can search very large spaces of candidate solutions. However, metaheuristics such as DE do not guarantee an optimal solution is ever found. DE is used for multidimensional real-valued functions but does not use the gradient of the problem being optimized, which means DE does not require for the optimization problem to be differentiable as is required by classic optimization methods such as gradient descent and quasi-newton methods. DE can therefore also be used on optimization problems that are not even continuous, are noisy, change over time, etc.〔 DE optimizes a problem by maintaining a population of candidate solutions and creating new candidate solutions by combining existing ones according to its simple formulae, and then keeping whichever candidate solution has the best score or fitness on the optimization problem at hand. In this way the optimization problem is treated as a black box that merely provides a measure of quality given a candidate solution and the gradient is therefore not needed. DE is originally due to Storn and Price.〔〔 Books have been published on theoretical and practical aspects of using DE in parallel computing, multiobjective optimization, constrained optimization, and the books also contain surveys of application areas.〔〔〔 == Algorithm == A basic variant of the DE algorithm works by having a population of candidate solutions (called agents). These agents are moved around in the search-space by using simple mathematical formulae to combine the positions of existing agents from the population. If the new position of an agent is an improvement it is accepted and forms part of the population, otherwise the new position is simply discarded. The process is repeated and by doing so it is hoped, but not guaranteed, that a satisfactory solution will eventually be discovered. Formally, let $f:\; \backslash Bbb^n\; \backslash to\; \backslash Bbb$ be the cost function which must be minimized or fitness function which must be maximized. The function takes a candidate solution as argument in the form of a vector of real numbers and produces a real number as output which indicates the fitness of the given candidate solution. The gradient of $f$ is not known. The goal is to find a solution $m$ for which $f(m)\; \backslash leq\; f(p)$ for all $p$ in the search-space, which would mean $m$ is the global minimum. Maximization can be performed by considering the function $h\; :=\; -f$ instead. Let $\backslash mathbf\; \backslash in\; \backslash Bbb^n$ designate a candidate solution (agent) in the population. The basic DE algorithm can then be described as follows: * Initialize all agents $\backslash mathbf$ with random positions in the search-space. * Until a termination criterion is met (e.g. number of iterations performed, or adequate fitness reached), repeat the following: * * For each agent $\backslash mathbf$ in the population do: * * * Pick three agents $\backslash mathbf,\backslash mathbf$, and $\backslash mathbf$ from the population at random, they must be distinct from each other as well as from agent $\backslash mathbf$ * * * Pick a random index $R\; \backslash in\; \backslash$ ($n$ being the dimensionality of the problem to be optimized). * * * Compute the agent's potentially new position $\backslash mathbf\; =\; (\backslash ldots,\; y\_n)$ as follows: * * * * For each $i$, pick a uniformly distributed number $r\_i\; \backslash equiv\; U(0,1)$ * * * * If or $i\; =\; R$ then set $y\_i\; =\; a\_i\; +\; F\; \backslash times\; (b\_i-c\_i)$ otherwise set $y\_i\; =\; x\_i$ * * * * (In essence, the new position is outcome of binary crossover of agent $\backslash mathbf$ with intermediate agent $\backslash mathbf\; =\; \backslash mathbf\; +\; F\; \backslash times\; (\backslash mathbf-\backslash mathbf)$.) * * * If then replace the agent in the population with the improved candidate solution, that is, replace $\backslash mathbf$ with $\backslash mathbf$ in the population. * Pick the agent from the population that has the highest fitness or lowest cost and return it as the best found candidate solution. Note that $F\; \backslash in\; ()$ is called the ''differential weight'' and $\backslash text\; \backslash in\; ()$ is called the ''crossover probability'', both these parameters are selectable by the practitioner along with the population size $\backslash text\; \backslash geq\; 4$ see below. 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「differential evolution」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.