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<title>GNU Scientific Library &ndash; Reference Manual: Simulated Annealing</title>

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<a name="Simulated-Annealing"></a>
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<p>
Next: <a href="Ordinary-Differential-Equations.html#Ordinary-Differential-Equations" accesskey="n" rel="next">Ordinary Differential Equations</a>, Previous: <a href="Monte-Carlo-Integration.html#Monte-Carlo-Integration" accesskey="p" rel="previous">Monte Carlo Integration</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Simulated-Annealing-1"></a>
<h2 class="chapter">26 Simulated Annealing</h2>
<a name="index-simulated-annealing"></a>
<a name="index-combinatorial-optimization"></a>
<a name="index-optimization_002c-combinatorial"></a>
<a name="index-energy-function"></a>
<a name="index-cost-function"></a>
<p>Stochastic search techniques are used when the structure of a space is
not well understood or is not smooth, so that techniques like Newton&rsquo;s
method (which requires calculating Jacobian derivative matrices) cannot
be used. In particular, these techniques are frequently used to solve
combinatorial optimization problems, such as the traveling salesman
problem.
</p>
<p>The goal is to find a point in the space at which a real valued
<em>energy function</em> (or <em>cost function</em>) is minimized.  Simulated
annealing is a minimization technique which has given good results in
avoiding local minima; it is based on the idea of taking a random walk
through the space at successively lower temperatures, where the
probability of taking a step is given by a Boltzmann distribution.
</p>
<p>The functions described in this chapter are declared in the header file
<samp>gsl_siman.h</samp>.
</p>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">&bull; <a href="Simulated-Annealing-algorithm.html#Simulated-Annealing-algorithm" accesskey="1">Simulated Annealing algorithm</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Simulated-Annealing-functions.html#Simulated-Annealing-functions" accesskey="2">Simulated Annealing functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Examples-with-Simulated-Annealing.html#Examples-with-Simulated-Annealing" accesskey="3">Examples with Simulated Annealing</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Simulated-Annealing-References-and-Further-Reading.html#Simulated-Annealing-References-and-Further-Reading" accesskey="4">Simulated Annealing References and Further Reading</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
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