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軟件簡(jiǎn)介
這是一個(gè)處理全局最優(yōu)化問(wèn)題的算法，叫模擬褪火法 ( Simulated annealing)。它采用Monte-Carlo思想可以處理多維（譬如100個(gè)自由度）的全局最優(yōu)化搜索問(wèn)題。通常的最優(yōu)化搜索算法，譬如牛頓下山法，在處理局域最優(yōu)化問(wèn)題時(shí)比較成功。但是要求初值在最小值附近，如果要研究的問(wèn)題有多個(gè)極小值，（大多數情況都是這樣），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。
該算法的缺點(diǎn)就是需要多次計算函數值以確保找到全局最小。如果用戶(hù)的函數每計算一次的代價(jià)很小，譬如只是一個(gè)解析表達式，那么這個(gè)算法就非常合適。反之，如果用戶(hù)的函數每計算一次需要的時(shí)間很長(cháng)，譬如該函數本身就是一個(gè)多維積分，這個(gè)算法就非常耗時(shí)。
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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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