fix algorithm

The visited minimum was not updated. This improves benchmarks, too.

README.md

@@ -45,9 +45,9 @@ Number of function evaluations for
 
 |  | ShiftedQuadratic | Griewank | LevyMontalvo2 | Rastrigin | Rosenbrock |
 | ---- | ---- | ---- | ---- | ---- | ---- |
-| `LN_BOBYQA` | 554 | 2656 | 4223 | **FAIL** | 11297 |
-| `LN_NELDERMEAD` | 15677 | 17255 | 33117 | **FAIL** | 50334 |
-| `LN_NEWUOA_BOUND` | 580 | 2059 | 2183 | **FAIL** | 17811 |
-| `LN_SBPLX` | 12318 | 11787 | 11280 | **FAIL** | 6788573 |
-| `LN_COBYLA` | 16922 | **FAIL** | 32810 | **FAIL** | **FAIL** |
-| `LN_PRAXIS` | 1856 | 10154 | 8144 | **FAIL** | 15198 |
+| `LN_BOBYQA` | 569 | 2633 | 4235 | **FAIL** | 10995 |
+| `LN_NELDERMEAD` | 15750 | 17108 | 33088 | **FAIL** | 42785 |
+| `LN_NEWUOA_BOUND` | 580 | 2088 | 2253 | **FAIL** | 13409 |
+| `LN_SBPLX` | 12329 | 11806 | 11447 | **FAIL** | 7020038 |
+| `LN_COBYLA` | 16943 | 37414 | 32792 | **FAIL** | 985676 |
+| `LN_PRAXIS` | 1850 | 9886 | 8548 | **FAIL** | 15436 |

src/MultistartOptimization.jl

@@ -182,10 +182,11 @@ function multistart_minimization(multistart_method::TikTak, local_method,
     @unpack quasirandom_N, initial_N, θ_min, θ_max, θ_pow = multistart_method
     quasirandom_points = sobol_starting_points(minimization_problem, quasirandom_N)
     initial_points = _keep_lowest(quasirandom_points, initial_N)
-    function _step(best_point, (i, initial_point))
+    function _step(visited_minimum, (i, initial_point))
         θ = _weight_parameter(multistart_method, i)
-        x = @. (1 - θ) * initial_point.location + θ * best_point.location
-        local_minimization(local_method, minimization_problem, x)
+        x = @. (1 - θ) * initial_point.location + θ * visited_minimum.location
+        local_minimum = local_minimization(local_method, minimization_problem, x)
+        local_minimum.value < visited_minimum.value ? local_minimum : visited_minimum
     end
     foldl(_step, enumerate(initial_points); init = first(initial_points))
 end