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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
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<a name="math_toolkit.jso"></a><a class="link" href="jso.html" title="Algorithm jSO">Algorithm jSO</a>
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</h2></div></div></div>
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<h4>
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<a name="math_toolkit.jso.h0"></a>
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<span class="phrase"><a name="math_toolkit.jso.synopsis"></a></span><a class="link" href="jso.html#math_toolkit.jso.synopsis">Synopsis</a>
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</h4>
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<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>
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<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>
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<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>
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<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>
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<span class="identifier">ArgumentContainer</span> <span class="identifier">lower_bounds</span><span class="special">;</span>
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<span class="identifier">ArgumentContainer</span> <span class="identifier">upper_bounds</span><span class="special">;</span>
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<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>
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<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>
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<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>
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<span class="special">};</span>
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<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>
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<span class="identifier">ArgumentContainer</span> <span class="identifier">jso</span><span class="special">(</span>
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<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>
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<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>
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<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>
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<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>
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<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>
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<span class="special">}</span> <span class="comment">// namespaces</span>
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</pre>
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<p>
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The <code class="computeroutput"><span class="identifier">jso</span></code> function provides a
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(hopefully) faithful implementation of Algorithm jSO, described in Brest et
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al 2017. This algorithm came in second place in the 2017 conference on evolutionary
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computing competition. It is an improvement on the classical differential evolution
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algorithm, which adapts the parameters in such as way that exploration is favored
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during early stages of the algorithm, and exploitation is favored during the
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later stages. In particular, it incorporates numerous ideas in the literature
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(in particular SHADE and L-SHADE) which aid in fast convergence. There are:
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Use of a historical archive of rejected vectors to provide information about
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convergence direction, adapting crossover and mutation parameters based on
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whether they were associated with successful updates, linear population size
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reduction, and use of "current-to-p-best" mutation.
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</p>
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<p>
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Like our implementation of differential evolution, it minimizes a cost function
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defined on a continuous space represented by a set of bounds. Again this function
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has been designed more for progress observability, graceful cancellation, and
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post-hoc data analysis than for speed of convergence.
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</p>
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<h4>
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<a name="math_toolkit.jso.h1"></a>
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<span class="phrase"><a name="math_toolkit.jso.parameters"></a></span><a class="link" href="jso.html#math_toolkit.jso.parameters">Parameters</a>
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</h4>
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<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
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<li class="listitem">
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<code class="computeroutput"><span class="identifier">lower_bounds</span></code>: A container
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representing the lower bounds of the optimization space along each dimension.
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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
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of the problem.
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</li>
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<li class="listitem">
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<code class="computeroutput"><span class="identifier">upper_bounds</span></code>: A container
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representing the upper bounds of the optimization space along each dimension.
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It should have the same size of <code class="computeroutput"><span class="identifier">lower_bounds</span></code>,
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and each element should be >= the corresponding element of <code class="computeroutput"><span class="identifier">lower_bounds</span></code>.
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</li>
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<li class="listitem">
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<code class="computeroutput"><span class="identifier">initial_population_size</span></code>:
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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>
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where <code class="computeroutput"><span class="identifier">D</span></code> is the dimension
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of the problem.
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</li>
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<li class="listitem">
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<code class="computeroutput"><span class="identifier">max_function_evaluations</span></code>:
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Defaults to 10000D, where <code class="computeroutput"><span class="identifier">D</span></code>
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is the dimension of the space.
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</li>
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<li class="listitem">
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<code class="computeroutput"><span class="identifier">initial_guess</span></code>: An optional
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guess for where we should start looking for solutions.
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</li>
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</ul></div>
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<p>
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The defaults were chosen from a reading of Brest 2017.
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</p>
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<h4>
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<a name="math_toolkit.jso.h2"></a>
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<span class="phrase"><a name="math_toolkit.jso.the_function"></a></span><a class="link" href="jso.html#math_toolkit.jso.the_function">The
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function</a>
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</h4>
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<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>
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<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>
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<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>
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<span class="identifier">URBG</span> <span class="special">&</span><span class="identifier">gen</span><span class="special">,</span>
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<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>
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<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>
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<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>
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||
<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>
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||
<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>
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</pre>
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<p>
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Parameters:
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</p>
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<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
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<li class="listitem">
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<code class="computeroutput"><span class="identifier">cost_function</span></code>: The cost
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function to be minimized.
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</li>
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<li class="listitem">
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<code class="computeroutput"><span class="identifier">jso_params</span></code>: The parameters
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to the algorithm as described above.
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</li>
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<li class="listitem">
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<code class="computeroutput"><span class="identifier">gen</span></code>: A uniform random bit
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generator, like <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">mt19937_64</span></code>.
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</li>
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<li class="listitem">
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<code class="computeroutput"><span class="identifier">value_to_reach</span></code>: An optional
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value that, if reached, stops the optimization. This is the most robust
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way to terminate the calculation, but in most cases the optimal value of
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the cost function is unknown. If it is, use it! Physical considerations
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can often be used to find optimal values for cost functions.
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</li>
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<li class="listitem">
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<code class="computeroutput"><span class="identifier">cancellation</span></code>: An optional
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atomic boolean to allow the user to stop the computation and gracefully
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return the best result found up to that point. N.B.: Cancellation is not
|
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immediate; the in-progress generation finishes.
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</li>
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<li class="listitem">
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<code class="computeroutput"><span class="identifier">current_minimum_cost</span></code>: An
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optional atomic variable to store the current minimum cost during optimization.
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This allows developers to (e.g.) plot the progress of the minimization
|
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over time and in conjunction with the <code class="computeroutput"><span class="identifier">cancellation</span></code>
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argument allow halting the computation when the progress stagnates.
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</li>
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<li class="listitem">
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<code class="computeroutput"><span class="identifier">queries</span></code>: An optional vector
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||
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>
|
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</ul></div>
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<p>
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Returns:
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</p>
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<p>
|
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The argument vector corresponding to the minimum cost found by the optimization.
|
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</p>
|
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<p>
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N.B.: The termination criteria is an "OR", not an "AND".
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So if the maximum generations is hit, the iteration stops, even if (say) a
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<code class="computeroutput"><span class="identifier">value_to_reach</span></code> has not been
|
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attained.
|
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</p>
|
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<p>
|
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If you want more observability into what the optimization is doing, compile
|
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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>
|
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<h5>
|
||
<a name="math_toolkit.jso.h3"></a>
|
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<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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</div>
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