Add BasinHopping global optimization algorithm

- Implements the basin-hopping algorithm for global optimization based on the approach in SciPy.
- Basin-hopping combines Monte Carlo random displacement with local minimization to efficiently find global minima in complex energy landscapes.
- Depends on PR mathnet#1119 (ILeastSquaresMinimizer interface) which must be merged first.

Author: diluculo

src/Numerics.Tests/OptimizationTests/NonLinearCurveFittingTests.cs

@@ -201,6 +201,29 @@ public void Rat43_TRNCG_Dif()
             }
         }
 
+        [Test]
+        public void Rat43_BasinHopping()
+        {
+            // Local Minimizer: LevenbergMarquardtMinimizer
+            var obj = ObjectiveFunction.NonlinearModel(Rat43Model, Rat43X, Rat43Y, accuracyOrder: 6);
+            var solver = new BasinHopping(localMinimizer: new LevenbergMarquardtMinimizer());
+            var result = solver.FindMinimum(obj, Rat43Start2);
+
+            for (var i = 0; i < result.MinimizingPoint.Count; i++)
+            {
+                AssertHelpers.AlmostEqualRelative(Rat43Pbest[i], result.MinimizingPoint[i], 2);
+            }
+
+            // Local Minimizer: TrustRegionNewtonCGMinimizer
+            solver = new BasinHopping(localMinimizer: new TrustRegionNewtonCGMinimizer());
+            result = solver.FindMinimum(obj.Fork(), Rat43Start2);
+
+            for (var i = 0; i < result.MinimizingPoint.Count; i++)
+            {
+                AssertHelpers.AlmostEqualRelative(Rat43Pbest[i], result.MinimizingPoint[i], 2);
+            }
+        }
+
         [Test]
         public void Rat43_Bfgs_Dif()
         {
@@ -411,6 +434,42 @@ public void BoxBod_TRNCG_Dif()
             }
         }
 
+        [Test]
+        public void BoxBod_BasinHopping()
+        {
+            // Local minimizer: LevenbergMarquardtMinimizer
+
+            var obj = ObjectiveFunction.NonlinearModel(BoxBodModel, BoxBodX, BoxBodY, accuracyOrder: 2);
+            var solver = new BasinHopping(localMinimizer: new LevenbergMarquardtMinimizer());
+            var result = solver.FindMinimum(obj, BoxBodStart2);
+
+            for (var i = 0; i < result.MinimizingPoint.Count; i++)
+            {
+                AssertHelpers.AlmostEqualRelative(BoxBodPbest[i], result.MinimizingPoint[i], 3);
+                AssertHelpers.AlmostEqualRelative(BoxBodPstd[i], result.StandardErrors[i], 3);
+            }
+
+            // Local Minimizer: TrustRegionDogLegMinimizer
+            solver = new BasinHopping(localMinimizer: new TrustRegionDogLegMinimizer());
+            result = solver.FindMinimum(obj.Fork(), BoxBodStart2);
+
+            for (var i = 0; i < result.MinimizingPoint.Count; i++)
+            {
+                AssertHelpers.AlmostEqualRelative(BoxBodPbest[i], result.MinimizingPoint[i], 3);
+                AssertHelpers.AlmostEqualRelative(BoxBodPstd[i], result.StandardErrors[i], 3);
+            }
+
+            // Local minimizer: TrustRegionNewtonCGMinimizer
+            solver = new BasinHopping(localMinimizer: new TrustRegionNewtonCGMinimizer());
+            result = solver.FindMinimum(obj.Fork(), BoxBodStart2);
+
+            for (var i = 0; i < result.MinimizingPoint.Count; i++)
+            {
+                AssertHelpers.AlmostEqualRelative(BoxBodPbest[i], result.MinimizingPoint[i], 3);
+                AssertHelpers.AlmostEqualRelative(BoxBodPstd[i], result.StandardErrors[i], 3);
+            }
+        }
+
         [Test]
         public void BoxBod_Bfgs_Der()
         {