Differential evolution (#1062)

* Differential evolution

---------

Co-authored-by: Matt Borland <matt@mattborland.com>

example/differential_evolution.cpp

@@ -0,0 +1,41 @@
+/*
+ * Copyright Nick Thompson, 2023
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+#include <iostream>
+#include <boost/math/tools/differential_evolution.hpp>
+
+using boost::math::tools::differential_evolution_parameters;
+using boost::math::tools::differential_evolution;
+
+double rosenbrock(std::vector<double> const & x) {
+   double result = 0;
+   for (size_t i = 0; i < x.size() - 1; ++i) {
+       double tmp = x[i+1] - x[i]*x[i];
+       result += 100*tmp*tmp + (1-x[i])*(1-x[i]); 
+   }
+   return result;
+}
+
+int main() {
+    auto de_params = differential_evolution_parameters<std::vector<double>>();
+    constexpr const size_t dimension = 10;
+    // Search on [0, 2]^dimension:
+    de_params.lower_bounds.resize(dimension, 0);
+    de_params.upper_bounds.resize(dimension, 2);
+    // This is a challenging function, increase the max generations 10x from default so we don't terminate prematurely:
+    de_params.max_generations *= 10;
+    std::random_device rd;
+    std::mt19937_64 rng(rd());
+    // The global minima is exactly zero-but some leeway is required:
+    double value_to_reach = 1e-5;
+    auto local_minima = differential_evolution(rosenbrock, de_params, rng, value_to_reach);
+    std::cout << "Minima: {";
+    for (auto l : local_minima) {
+        std::cout << l << ", ";
+    }
+    std::cout << "}\n";
+    std::cout << "Value of cost function at minima: " << rosenbrock(local_minima) << "\n";
+}