Benchmark ackley opt method

docs/src/ackley.md

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+# Ackley function
+
+The Ackley function is defined as:
+``f(x) = -a*exp(-b\sqrt{\frac{1}{d}\sum_{i=1}^d x_i^2}) - exp(\frac{1}{d} \sum_{i=1}^d cos(cx_i)) + a + exp(1)``
+Usually the recommended values are: ``a =  20``, ``b = 0.2`` and ``c =  2\pi``
+
+Let's see the 1D case.
+
+```@example ackley
+using Surrogates
+using Plots
+default()
+```
+
+
+```@example ackley
+n = 100
+lb = -32.768
+ub = 32.768
+x = sample(n,lb,ub,SobolSample())
+y = f.(x)
+xs = lb:0.001:ub
+plot(x, y, seriestype=:scatter, label="Sampled points", xlims=(lb, ub), ylims=(0,30), legend=:top)
+plot!(xs,f.(xs), label="True function", legend=:top)
+```
+
+```@example ackley
+my_rad = RadialBasis(x,y,lb,ub)
+my_krig = Kriging(x,y,lb,ub)
+my_loba = LobacheskySurrogate(x,y,lb,ub)
+```
+
+```@example ackley
+plot(x, y, seriestype=:scatter, label="Sampled points", xlims=(lb, ub), ylims=(0, 30), legend=:top)
+plot!(xs,f.(xs), label="True function", legend=:top)
+plot!(xs, my_rad.(xs), label="Polynomial expansion", legend=:top)
+plot!(xs, my_krig.(xs), label="Lobachesky", legend=:top)
+plot!(xs, my_loba.(xs), label="Kriging", legend=:top)
+```
+
+The fit looks good. Let's now see if we are able to find the minimum value using
+optimization methods:
+
+```@example ackley
+surrogate_optimize(f,DYCORS(),lb,ub,my_rad,UniformSample())
+plot(x, y, seriestype=:scatter, label="Sampled points", xlims=(lb, ub), ylims=(0, 30), legend=:top)
+plot!(xs,f.(xs), label="True function", legend=:top)
+plot!(xs, my_rad.(xs), label="Radial basis optimized", legend=:top)
+```
+
+The DYCORS methods successfully finds the minimum.