added schaffer2 function

added output for improvement of fitness
added CMAES algorithm, that requires further testing

solvers.py

@@ -10,7 +10,7 @@ class Solver(ABC):
         self.function = function
 
     @abstractmethod
-    def rank(self, samples: Iterable[Iterable[float]], elite_size: int) -> (Iterable[Tuple], Iterable[Tuple], float):
+    def rank(self, samples: Iterable[Iterable[float]], elite_size: int) -> (Iterable[Iterable[float]], float):
         pass
 
     @abstractmethod
@@ -18,7 +18,7 @@ class Solver(ABC):
         pass
 
     @abstractmethod
-    def update(elite: Iterable[Tuple]):
+    def update(elite: Iterable[Iterable[float]]):
         pass
 
 
@@ -33,7 +33,7 @@ class SimpleEvolutionStrategy(Solver):
         else:
             self.sigma = [1] * len(mu)
 
-    def rank(self, samples: Iterable[Iterable[float]], elite_size: int) -> (Iterable[Tuple], Iterable[float]):
+    def rank(self, samples: Iterable[Iterable[float]], elite_size: int) -> (Iterable[Iterable[float]], Iterable[float]):
         fitness = self.function.eval(*samples.transpose())
         samples = samples[np.argsort(fitness)]
         fitness = np.sort(fitness)
@@ -43,6 +43,41 @@ class SimpleEvolutionStrategy(Solver):
     def sample(self, n: int) -> Iterable[Iterable[float]]:
         return np.array([np.random.multivariate_normal(self.mu, np.diag(self.sigma)) for _ in range(n)])
 
-    def update(self, elite: Iterable[Tuple]):
+    def update(self, elite: Iterable[Iterable[float]]):
         self.mu = elite[0]
 
+
+class CMAEvolutionStrategy(Solver):
+    def __init__(self, function: Function, mu: Iterable[float], covariances: Iterable[float] = None):
+        if covariances is not None and len(mu) != covariances.shape[0] and len(mu) != covariances.shape[1]:
+            raise Exception('Length of mu and covariance matrix must match')
+        super().__init__(function)
+        self.mu = mu
+        if covariances is not None:
+            self.covariances = covariances
+        else:
+            self.covariances = np.array([[1.0, 0.0], [0.0, 1.0]])
+
+    def rank(self, samples: Iterable[Iterable[float]], elite_size: int) -> (Iterable[Iterable[float]], Iterable[float]):
+        fitness = self.function.eval(*samples.transpose())
+        samples = samples[np.argsort(fitness)]
+        fitness = np.sort(fitness)
+        elite = samples[0:elite_size]
+        return elite, fitness[0]
+
+    def sample(self, n: int) -> Iterable[Iterable[float]]:
+        return np.array([np.random.multivariate_normal(self.mu, self.covariances) for _ in range(n)])
+
+    def update(self, elite: Iterable[Iterable[float]]):
+        mu = self.mu
+        x = elite.transpose()[0]
+        y = elite.transpose()[1]
+        self.mu[0] = np.average(x)
+        self.mu[1] = np.average(y)
+        
+        # TODO fix covariance matrix calculation using the tutorial by Nikolaus Hansen
+        self.covariances[0][0] = np.average((x - mu[0])**2)
+        self.covariances[1][1] = np.average((y - mu[1])**2)
+        self.covariances[0][1] = np.average((x - mu[0]) * (y - mu[1]))
+        # self.covariances = np.cov(elite.transpose())
+