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<title>Algorithm jSO</title>
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<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.jso"></a><a class="link" href="jso.html" title="Algorithm jSO">Algorithm jSO</a>
</h2></div></div></div>
<h4>
<a name="math_toolkit.jso.h0"></a>
<span class="phrase"><a name="math_toolkit.jso.synopsis"></a></span><a class="link" href="jso.html#math_toolkit.jso.synopsis">Synopsis</a>
</h4>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">optimization</span><span class="special">/</span><span class="identifier">jso</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
<span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">optimization</span> <span class="special">{</span>
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">typename</span> <span class="identifier">ArgumentContainer</span><span class="special">></span> <span class="keyword">struct</span> <span class="identifier">jso_parameters</span> <span class="special">{</span>
<span class="keyword">using</span> <span class="identifier">Real</span> <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">ArgumentContainer</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">;</span>
<span class="identifier">ArgumentContainer</span> <span class="identifier">lower_bounds</span><span class="special">;</span>
<span class="identifier">ArgumentContainer</span> <span class="identifier">upper_bounds</span><span class="special">;</span>
<span class="identifier">size_t</span> <span class="identifier">initial_population_size</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span>
<span class="identifier">size_t</span> <span class="identifier">max_function_evaluations</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span>
<span class="identifier">ArgumentContainer</span> <span class="keyword">const</span> <span class="special">*</span> <span class="identifier">initial_guess</span> <span class="special">=</span> <span class="keyword">nullptr</span><span class="special">;</span>
<span class="special">};</span>
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">typename</span> <span class="identifier">ArgumentContainer</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Func</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">URBG</span><span class="special">></span>
<span class="identifier">ArgumentContainer</span> <span class="identifier">jso</span><span class="special">(</span>
<span class="keyword">const</span> <span class="identifier">Func</span> <span class="identifier">cost_function</span><span class="special">,</span> <span class="identifier">jso_parameters</span><span class="special"><</span><span class="identifier">ArgumentContainer</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">jso_params</span><span class="special">,</span> <span class="identifier">URBG</span> <span class="special">&</span><span class="identifier">gen</span><span class="special">,</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">invoke_result_t</span><span class="special"><</span><span class="identifier">Func</span><span class="special">,</span> <span class="identifier">ArgumentContainer</span><span class="special">></span> <span class="identifier">target_value</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">invoke_result_t</span><span class="special"><</span><span class="identifier">Func</span><span class="special">,</span> <span class="identifier">ArgumentContainer</span><span class="special">>>::</span><span class="identifier">quiet_NaN</span><span class="special">(),</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">atomic</span><span class="special"><</span><span class="keyword">bool</span><span class="special">></span> <span class="special">*</span><span class="identifier">cancellation</span> <span class="special">=</span> <span class="keyword">nullptr</span><span class="special">,</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">atomic</span><span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">invoke_result_t</span><span class="special"><</span><span class="identifier">Func</span><span class="special">,</span> <span class="identifier">ArgumentContainer</span><span class="special">>></span> <span class="special">*</span><span class="identifier">current_minimum_cost</span> <span class="special">=</span> <span class="keyword">nullptr</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">ArgumentContainer</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">invoke_result_t</span><span class="special"><</span><span class="identifier">Func</span><span class="special">,</span> <span class="identifier">ArgumentContainer</span><span class="special">>>></span> <span class="special">*</span><span class="identifier">queries</span> <span class="special">=</span> <span class="keyword">nullptr</span><span class="special">);</span>
<span class="special">}</span> <span class="comment">// namespaces</span>
</pre>
<p>
The <code class="computeroutput"><span class="identifier">jso</span></code> function provides a
(hopefully) faithful implementation of Algorithm jSO, described in Brest et
al 2017. This algorithm came in second place in the 2017 conference on evolutionary
computing competition. It is an improvement on the classical differential evolution
algorithm, which adapts the parameters in such as way that exploration is favored
during early stages of the algorithm, and exploitation is favored during the
later stages. In particular, it incorporates numerous ideas in the literature
(in particular SHADE and L-SHADE) which aid in fast convergence. There are:
Use of a historical archive of rejected vectors to provide information about
convergence direction, adapting crossover and mutation parameters based on
whether they were associated with successful updates, linear population size
reduction, and use of "current-to-p-best" mutation.
</p>
<p>
Like our implementation of differential evolution, it minimizes a cost function
defined on a continuous space represented by a set of bounds. Again this function
has been designed more for progress observability, graceful cancellation, and
post-hoc data analysis than for speed of convergence.
</p>
<h4>
<a name="math_toolkit.jso.h1"></a>
<span class="phrase"><a name="math_toolkit.jso.parameters"></a></span><a class="link" href="jso.html#math_toolkit.jso.parameters">Parameters</a>
</h4>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
<code class="computeroutput"><span class="identifier">lower_bounds</span></code>: A container
representing the lower bounds of the optimization space along each dimension.
The <code class="computeroutput"><span class="special">.</span><span class="identifier">size</span><span class="special">()</span></code> of the bounds should return the dimension
of the problem.
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">upper_bounds</span></code>: A container
representing the upper bounds of the optimization space along each dimension.
It should have the same size of <code class="computeroutput"><span class="identifier">lower_bounds</span></code>,
and each element should be >= the corresponding element of <code class="computeroutput"><span class="identifier">lower_bounds</span></code>.
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">initial_population_size</span></code>:
How big the first generation should be. Defaults to <code class="computeroutput"><span class="identifier">ceil</span><span class="special">(</span><span class="number">25l</span><span class="identifier">og</span><span class="special">(</span><span class="identifier">D</span><span class="special">+</span><span class="number">1</span><span class="special">)</span><span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">D</span><span class="special">))</span></code>
where <code class="computeroutput"><span class="identifier">D</span></code> is the dimension
of the problem.
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">max_function_evaluations</span></code>:
Defaults to 10000D, where <code class="computeroutput"><span class="identifier">D</span></code>
is the dimension of the space.
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">initial_guess</span></code>: An optional
guess for where we should start looking for solutions.
</li>
</ul></div>
<p>
The defaults were chosen from a reading of Brest 2017.
</p>
<h4>
<a name="math_toolkit.jso.h2"></a>
<span class="phrase"><a name="math_toolkit.jso.the_function"></a></span><a class="link" href="jso.html#math_toolkit.jso.the_function">The
function</a>
</h4>
<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">typename</span> <span class="identifier">ArgumentContainer</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Func</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">URBG</span><span class="special">></span>
<span class="identifier">ArgumentContainer</span> <span class="identifier">jso</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Func</span> <span class="identifier">cost_function</span><span class="special">,</span>
<span class="identifier">jso_parameters</span><span class="special"><</span><span class="identifier">ArgumentContainer</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">jso_params</span><span class="special">,</span>
<span class="identifier">URBG</span> <span class="special">&</span><span class="identifier">gen</span><span class="special">,</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">invoke_result_t</span><span class="special"><</span><span class="identifier">Func</span><span class="special">,</span> <span class="identifier">ArgumentContainer</span><span class="special">></span> <span class="identifier">value_to_reach</span>
<span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">invoke_result_t</span><span class="special"><</span><span class="identifier">Func</span><span class="special">,</span> <span class="identifier">ArgumentContainer</span><span class="special">>>::</span><span class="identifier">quiet_NaN</span><span class="special">(),</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">atomic</span><span class="special"><</span><span class="keyword">bool</span><span class="special">></span> <span class="special">*</span><span class="identifier">cancellation</span> <span class="special">=</span> <span class="keyword">nullptr</span><span class="special">,</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">atomic</span><span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">invoke_result_t</span><span class="special"><</span><span class="identifier">Func</span><span class="special">,</span> <span class="identifier">ArgumentContainer</span><span class="special">>></span> <span class="special">*</span><span class="identifier">current_minimum_cost</span> <span class="special">=</span> <span class="keyword">nullptr</span><span class="special">,</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">ArgumentContainer</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">invoke_result_t</span><span class="special"><</span><span class="identifier">Func</span><span class="special">,</span> <span class="identifier">ArgumentContainer</span><span class="special">>>></span> <span class="special">*</span><span class="identifier">queries</span> <span class="special">=</span> <span class="keyword">nullptr</span><span class="special">)</span>
</pre>
<p>
Parameters:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
<code class="computeroutput"><span class="identifier">cost_function</span></code>: The cost
function to be minimized.
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">jso_params</span></code>: The parameters
to the algorithm as described above.
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">gen</span></code>: A uniform random bit
generator, like <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">mt19937_64</span></code>.
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">value_to_reach</span></code>: An optional
value that, if reached, stops the optimization. This is the most robust
way to terminate the calculation, but in most cases the optimal value of
the cost function is unknown. If it is, use it! Physical considerations
can often be used to find optimal values for cost functions.
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">cancellation</span></code>: An optional
atomic boolean to allow the user to stop the computation and gracefully
return the best result found up to that point. N.B.: Cancellation is not
immediate; the in-progress generation finishes.
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">current_minimum_cost</span></code>: An
optional atomic variable to store the current minimum cost during optimization.
This allows developers to (e.g.) plot the progress of the minimization
over time and in conjunction with the <code class="computeroutput"><span class="identifier">cancellation</span></code>
argument allow halting the computation when the progress stagnates.
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">queries</span></code>: An optional vector
to store intermediate results during optimization. This is useful for debugging
and perhaps volume rendering of the objective function after the calculation
is complete.
</li>
</ul></div>
<p>
Returns:
</p>
<p>
The argument vector corresponding to the minimum cost found by the optimization.
</p>
<p>
N.B.: The termination criteria is an "OR", not an "AND".
So if the maximum generations is hit, the iteration stops, even if (say) a
<code class="computeroutput"><span class="identifier">value_to_reach</span></code> has not been
attained.
</p>
<p>
If you want more observability into what the optimization is doing, compile
with <code class="computeroutput"><span class="special">-</span><span class="identifier">DBOOST_MATH_DEBUG_JSO</span><span class="special">=</span><span class="number">1</span></code>
</p>
<h5>
<a name="math_toolkit.jso.h3"></a>
<span class="phrase"><a name="math_toolkit.jso.examples"></a></span><a class="link" href="jso.html#math_toolkit.jso.examples">Examples</a>
</h5>
<p>
An example exhibiting graceful cancellation and progress observability can
be studied in <a href="../../../example/jso_example.cpp" target="_top">jso_example.cpp</a>.
</p>
<h5>
<a name="math_toolkit.jso.h4"></a>
<span class="phrase"><a name="math_toolkit.jso.references"></a></span><a class="link" href="jso.html#math_toolkit.jso.references">References</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
Brest, Janez, Mirjam Sepesy Maučec, and Borko Bošković. <span class="emphasis"><em>Single
objective real-parameter optimization: Algorithm jSO.</em></span> 2017 IEEE
congress on evolutionary computation (CEC). IEEE, 2017.
</li></ul></div>
</div>
<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
Walker and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
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