cec2020: implement Composition1 func

bench/cec2020/benchFunctions.go

@@ -184,7 +184,44 @@ func Hybrid3(x []float64) float64 {
 }
 
 // Composition1 is the "Composition Function 1" of CEC2020.
-func Composition1(x []float64) float64 { return 0 }
+func Composition1(x []float64) float64 {
+	nx := len(x)
+	fnx := float64(nx)
+
+	// optimum positions.
+	o := newOpt(nx)
+	sigma := []float64{10, 20, 30}
+	lambda := []float64{1, 10, 1}
+	bias := []float64{0, 100, 200}
+	omega := make([]float64, nx)
+	funcs := []func([]float64) float64{
+		Rastrigin,
+		Griewank,
+		SchwefelModified,
+	}
+
+	var sum float64
+
+	var weights []float64
+
+	for i := range funcs {
+		wi := getWeight(x, o, sigma[i], fnx)
+
+		weights = append(weights, wi)
+
+		var wsum float64
+
+		for j := range weights {
+			wsum += weights[j]
+		}
+
+		omega = append(omega, wi/wsum)
+
+		sum += (omega[i] * (lambda[i]*funcs[i](x) + bias[i])) + funcs[i](x)
+	}
+
+	return sum
+}
 
 // Composition2 is the "Composition Function 2" of CEC2020.
 func Composition2(x []float64) float64 { return 0 }

bench/cec2020/helperFunctions.go

@@ -191,3 +191,14 @@ func getMz(x []float64, z []float64) []float64 {
 
 	return mz
 }
+
+func getWeight(x, o []float64, sigma, nx float64) float64 {
+	var sum float64
+
+	for i := range x {
+		sum += math.Pow(x[i]-o[i], 2)
+	}
+
+	// w.
+	return (1 / (math.Sqrt(sum))) * math.Exp(-(sum / 2 * nx * math.Pow(sigma, 2)))
+}