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第7行： − Simulated annealing can be used to approximate the global minimum for a function with many variables. In 1983, this approach was used by Kirkpatrick, Gelatt Jr.,Vecchi, <ref name=":2" /> for a solution of the traveling salesman problem. They also proposed its current name, simulated annealing. − Simulated annealing can be used to approximate the global minimum for a function with many variables. In 1983, this approach was used by Kirkpatrick, Gelatt Jr.,Vecchi, for a solution of the traveling salesman problem. They also proposed its current name, simulated annealing.+ − 模拟退火可以用来逼近具有多个变量的函数的全局最小值。1983年，这种方法被Kirkpatrick, Gelatt Jr.,Vecchi用来解决旅行商问题。他们还提出了它现在的名字---- 模拟退火。 − − − − This notion of slow cooling implemented in the simulated annealing algorithm is interpreted as a slow decrease in the probability of accepting worse solutions as the solution space is explored. Accepting worse solutions is a fundamental property of metaheuristics because it allows for a more extensive search for the global optimal solution. In general, simulated annealing algorithms work as follows. The temperature progressively decreases from an initial positive value to zero. At each time step, the algorithm randomly selects a solution close to the current one, measures its quality, and moves to it according to the temperature-dependent probabilities of selecting better or worse solutions, which during the search respectively remain at 1 (or positive) and decrease towards zero. − − This notion of slow cooling implemented in the simulated annealing algorithm is interpreted as a slow decrease in the probability of accepting worse solutions as the solution space is explored. Accepting worse solutions is a fundamental property of metaheuristics because it allows for a more extensive search for the global optimal solution. In general, simulated annealing algorithms work as follows. The temperature progressively decreases from an initial positive value to zero. At each time step, the algorithm randomly selects a solution close to the current one, measures its quality, and moves to it according to the temperature-dependent probabilities of selecting better or worse solutions, which during the search respectively remain at 1 (or positive) and decrease towards zero. − + − The simulation can be performed either by a solution of kinetic equations for density functions<ref name=":0">{{cite journal |pages=519–524 |last1=Khachaturyan |first1=A. |last2=Semenovskaya |first2=S. |last3=Vainshtein |first3=B. |title=Statistical-Thermodynamic Approach to Determination of Structure Amplitude Phases |journal=Sov.Phys. Crystallography |year=1979 |volume=24 |issue=5 }}</ref><ref name=":1">{{cite journal |pages=742–754 |last1=Khachaturyan |first1=A. |last2=Semenovskaya |first2=S. |last3=Vainshtein |first3=B. |title=The Thermodynamic Approach to the Structure Analysis of Crystals |issue=A37 |journal=Acta Crystallographica |volume=37 |year=1981 |doi=10.1107/S0567739481001630|bibcode=1981AcCrA..37..742K }}</ref> or by using the stochastic sampling method.<ref name=":2">{{cite journal |jstor=1690046 |pages=671–680 |last1=Kirkpatrick |first1=S. |last2=Gelatt Jr |first2=C. D. |last3=Vecchi |first3=M. P. |title=Optimization by Simulated Annealing |volume=220 |issue=4598 |journal=Science |year=1983 |pmid=17813860 |doi=10.1126/science.220.4598.671|bibcode=1983Sci...220..671K |citeseerx=10.1.1.123.7607 }}</ref><ref>{{cite journal |doi=10.1007/BF00940812 |title=Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm |year=1985 |last1=Černý |first1=V. |journal=Journal of Optimization Theory and Applications |volume=45 |pages=41–51}}</ref> The method is an adaptation of the [[Metropolis–Hastings algorithm]], a [[Monte Carlo method]] to generate sample states of a thermodynamic system, published by [[Nicholas Metropolis|N. Metropolis]] et al. in 1953.<ref>{{cite journal |doi=10.1063/1.1699114 |title=Equation of State Calculations by Fast Computing Machines |year=1953 |last1=Metropolis |first1=Nicholas |last2=Rosenbluth |first2=Arianna W. |last3=Rosenbluth |first3=Marshall N. |last4=Teller |first4=Augusta H. |last5=Teller |first5=Edward |journal=The Journal of Chemical Physics |volume=21 |issue=6 |pages=1087|bibcode=1953JChPh..21.1087M }}</ref> − − The simulation can be performed either by a solution of kinetic equations for density functions or by using the stochastic sampling method. The method is an adaptation of the Metropolis–Hastings algorithm, a Monte Carlo method to generate sample states of a thermodynamic system, published by N. Metropolis et al. in 1953. − − 可以通过求解密度函数的动力学方程或采用随机抽样方法进行模拟仿真。这种方法是对 Metropolis-Hastings 算法（一种用于生成热力学系统的样本状态的Monte Carlo方法）的一种改进，该算法在1953年由N. Metropolis等人提出。 − −
无编辑摘要
这个名字和灵感来自于冶金学中的退火，这种技术涉及对材料进行加热和控制冷却以增加其晶体的尺寸并减少其缺陷。两者都是材料的属性，取决于它的热力学自由能。加热和冷却材料都会影响温度和热力学自由能。
这个名字和灵感来自于冶金学中的退火，这种技术涉及对材料进行加热和控制冷却以增加其晶体的尺寸并减少其缺陷。两者都是材料的属性，取决于它的热力学自由能。加热和冷却材料都会影响温度和热力学自由能。
模拟退火可以用来逼近具有多个变量的函数的全局最小值。1983年，这种方法被Kirkpatrick, Gelatt Jr.,Vecchi<ref name=":2" />用来解决旅行商问题。他们还提出了它现在的名字----模拟退火。
模拟退火算法中实现缓慢冷却的概念可被理解为探索解决方案空间时接受较差解决方案的概率缓慢下降。由于元启发法允许对全局最优解进行更广泛的搜索，所以接受较差的解可以说是元启发法的一个基本属性。一般来说，模拟退火算法的工作原理如下：温度从最初的正值逐渐降低到零。该算法在每个时间步长上随机选择一个接近当前解的解，测量其质量并根据温度相关的概率选择更好或更坏的解，在搜索过程中分别保持在1(或正值)并向零递减。
模拟退火算法中实现缓慢冷却的概念可被理解为探索解决方案空间时接受较差解决方案的概率缓慢下降。由于元启发法允许对全局最优解进行更广泛的搜索，所以接受较差的解可以说是元启发法的一个基本属性。一般来说，模拟退火算法的工作原理如下：温度从最初的正值逐渐降低到零。该算法在每个时间步长上随机选择一个接近当前解的解，测量其质量并根据温度相关的概率选择更好或更坏的解，在搜索过程中分别保持在1(或正值)并向零递减。
可以通过求解密度函数的动力学方程<ref name=":0">{{cite journal |pages=519–524 |last1=Khachaturyan |first1=A. |last2=Semenovskaya |first2=S. |last3=Vainshtein |first3=B. |title=Statistical-Thermodynamic Approach to Determination of Structure Amplitude Phases |journal=Sov.Phys. Crystallography |year=1979 |volume=24 |issue=5 }}</ref><ref name=":1">{{cite journal |pages=742–754 |last1=Khachaturyan |first1=A. |last2=Semenovskaya |first2=S. |last3=Vainshtein |first3=B. |title=The Thermodynamic Approach to the Structure Analysis of Crystals |issue=A37 |journal=Acta Crystallographica |volume=37 |year=1981 |doi=10.1107/S0567739481001630|bibcode=1981AcCrA..37..742K }}</ref> 或采用随机抽样方法进行模拟仿真。<ref name=":2">{{cite journal |jstor=1690046 |pages=671–680 |last1=Kirkpatrick |first1=S. |last2=Gelatt Jr |first2=C. D. |last3=Vecchi |first3=M. P. |title=Optimization by Simulated Annealing |volume=220 |issue=4598 |journal=Science |year=1983 |pmid=17813860 |doi=10.1126/science.220.4598.671|bibcode=1983Sci...220..671K |citeseerx=10.1.1.123.7607 }}</ref><ref>{{cite journal |doi=10.1007/BF00940812 |title=Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm |year=1985 |last1=Černý |first1=V. |journal=Journal of Optimization Theory and Applications |volume=45 |pages=41–51}}</ref> 这种方法是对[[Metropolis-Hastings算法]]（一种用于生成热力学系统的样本状态的[[Monte Carlo方法]]）的一种改进，该算法在1953年由N. Metropolis等人提出。<ref>{{cite journal |doi=10.1063/1.1699114 |title=Equation of State Calculations by Fast Computing Machines |year=1953 |last1=Metropolis |first1=Nicholas |last2=Rosenbluth |first2=Arianna W. |last3=Rosenbluth |first3=Marshall N. |last4=Teller |first4=Augusta H. |last5=Teller |first5=Edward |journal=The Journal of Chemical Physics |volume=21 |issue=6 |pages=1087|bibcode=1953JChPh..21.1087M }}</ref>
==概述Overview==
==概述Overview==