[genetic search] Scale fitness before selection

Using an unscaled fitness value for selection is problematic:

-Outstanding individuals take over very quickly, this leads to
premature convergence.

-When fitness values are close together, very litle selection
pressure is applied and selection is almost uniformly random.
Having slightly better fitness does not improve an individual's
survival chances.

-Transposing the fitness function (e.g. adding a constant value)
changes the selection probabilities even though the location of the
optimum (and the "shape" of the fitness) remain unchanged.

Scaling the fitness function helps ameliorate those issues.

Sigma scaling is used:

fitness' = max(fitness - (mean_fitness - 2 * std_fitness), 0)

Author: Theodoros Theodoridis

tc/autotuner/genetic_search.cc

@@ -16,6 +16,8 @@
 
 #include "tc/autotuner/genetic_search.h"
 
+#include <algorithm>
+#include <numeric>
 #include <random>
 #include <sstream>
 
@@ -72,9 +74,35 @@ void mutate(
   }
 }
 
-void normalizeVector(std::vector<double>& v) {
+double mean(std::vector<double>& v) {
+  if (v.empty()) {
+    throw std::invalid_argument("Cannot compute the mean of an empty vector.");
+  }
   auto sum = std::accumulate(v.begin(), v.end(), 0.0);
+  return sum / v.size();
+}
+
+double stdv(std::vector<double>& v, double mean) {
+  std::vector<double> diffs(v.size());
+  std::transform(v.begin(), v.end(), diffs.begin(), [mean](double val) {
+    return val - mean;
+  });
+
+  auto squareSum =
+      std::inner_product(diffs.begin(), diffs.end(), diffs.begin(), 0.0);
+  return std::sqrt(squareSum / v.size());
+}
+
+void sigmaScale(std::vector<double>& v) {
+  auto m = mean(v);
+  auto s = stdv(v, m);
+  std::transform(v.begin(), v.end(), v.begin(), [m, s](double val) {
+    return std::max(val - (m - 2 * s), 0.0);
+  });
+}
 
+void normalizeVector(std::vector<double>& v) {
+  auto sum = std::accumulate(v.begin(), v.end(), 0.0);
   std::transform(
       v.begin(), v.end(), v.begin(), [sum](double v) { return v / sum; });
 }
@@ -90,6 +118,7 @@ std::vector<double> computeNormalizedFitness(
       [](const std::unique_ptr<CandidateConfiguration>& c) {
         return 1.0 / c->runtime.toMicroSeconds();
       });
+  sigmaScale(fitness);
   normalizeVector(fitness);
   return fitness;
 }