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软件简介: brief introduction
这是一个处理全局最优化问题的算法，叫模拟退火法 ( Simulated annealing)。它采用Monte-Carlo思想可以处理多维（譬如100个自由度）的全局最优化搜索问题。通常的最优化搜索算法，譬如牛顿下山法，在处理局域最优化问题时比较成功。但是要求初值在最小值附近，如果要研究的问题有多个极小值，（大多数情况都是这样），那么通常的下山法就可能找不到全局最小而是局部最小值。
该算法的缺点就是需要多次计算函数值以确保找到全局最小。如果用户的函数每计算一次的代价很小，譬如只是一个解析表达式，那么这个算法就非常合适。反之，如果用户的函数每计算一次需要的时间很长，譬如该函数本身就是一个多维积分，这个算法就非常耗时。
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ABSTRACT:
Simulated annealing is a global optimization method that distinguishes
between different local optima. Starting from an initial point, the
algorithm takes a step and the function is evaluated. When minimizing a
function, any downhill step is accepted and the process repeats from this
new point. An uphill step may be accepted. Thus, it can escape from local
optima. This uphill decision is made by the Metropolis criteria. As the
optimization process proceeds, the length of the steps decline and the
algorithm closes in on the global optimum. Since the algorithm makes very
few assumptions regarding the function to be optimized, it is quite
robust with respect to non-quadratic surfaces. The degree of robustness
can be adjusted by the user. In fact, simulated annealing can be used as
a local optimizer for difficult functions.
This implementation of simulated annealing was used in "Global Optimization
of Statistical Functions with Simulated Annealing," Goffe, Ferrier and
Rogers, Journal of Econometrics, vol. 60, no. 1/2, Jan./Feb. 1994, pp.
65-100. Briefly, we found it competitive, if not superior, to multiple
restarts of conventional optimization routines for difficult optimization
problems.
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