def f14(domain=(-65.54, 65.54), dimensions=2):
"""
M. Shekel's Foxholes Function
Dimensions: 2
Domain: -65.54 -> 65.54
Minimum value: f(31.95) = 0.998 (~1)
:param domain:
:param dimensions:
:return:
"""
def function(x):
sum = 0
for j in range(24):
secondsum = 0
for i in range(2):
secondsum += (x[i] -
ComparativeBenchmarks.a_matrix[i][j])**6
sum += (j + 1 + secondsum)**-1
total = ((1 / 500) + sum)**-1
return total
return Benchmark(function=function,
domain=domain,
dimensions=dimensions,
min_value=0.998,
name="14")
def f12(domain=(-50, 50), dimensions=30):
"""
Generalised Penalised Function
Domain: -50 -> 50
Minimum value: f(-1) = 0
:param domain:
:param dimensions:
:return:
"""
def function(x):
n = len(x)
sum = 0
secondsum = 0
for i in range(n):
if i < n - 1:
sum += (
(((ComparativeBenchmarks.y(x[i]) - 1)**2) *
(1 + 10 *
(math.sin(math.pi *
ComparativeBenchmarks.y(x[i + 1])))**2)) +
(ComparativeBenchmarks.y(x[n - 1]) - 1)**2)
secondsum += ComparativeBenchmarks.u(x[i], 10, 100, 4)
total = (math.pi / n) * (
(10 * math.sin(math.pi * ComparativeBenchmarks.y(x[1])))**2 +
sum) + secondsum
return total
return Benchmark(function=function,
domain=domain,
dimensions=dimensions,
min_value=0,
name="12")
def f13(domain=(-50, 50), dimensions=30):
"""
TODO CHECK AGAIN
Generalised Penalised Function
Domain: -50 -> 50
Minimum value: f(1,...,1) = 0
:param domain:
:param dimensions:
:return:
"""
def function(x):
n = len(x)
sum = 0
secondsum = 0
for i in range(n - 2):
sum += (x[i] - 1)**2 * (1 + np.sin(
3 * np.pi * x[i + 1])**2) + (x[n - 1] - 1)**2 * (
1 + np.sin(2 * np.pi * x[n - 1])**2)
for i in range(n - 1):
secondsum += ComparativeBenchmarks.u(x[i], 5, 100, 4)
total = 0.1 * (np.sin(np.pi * 3 * x[0])**2 + sum) + secondsum
return total
return Benchmark(function=function,
domain=domain,
dimensions=dimensions,
min_value=0,
name="13")
def f10(domain=(-32, 32), dimensions=30):
"""
Ackley's Function
Domain: -32 -> 32
Minimum value: f(0) = 0
:param domain:
:param dimensions:
:return:
"""
def function(x):
sum = 0
n = len(x)
a = 0
b = 0
for i in range(n):
a += x[i]**2
b += np.cos(2 * np.pi * x[i])
sum = -20 * np.exp(-0.2 * ((1 / n) * a**0.5)) - np.exp(
(1 / n) * b) + 20 + np.e
return sum
return Benchmark(function=function,
domain=domain,
dimensions=dimensions,
min_value=0,
name="10")
def f20(domain=(0, 1), dimensions=6):
"""
R. Hartman's Family
Dimensions: 6
Domain: 0 -> 1
Minimum value: f(0.201,0.150,0.477,0.275,0.311,0.657) = -3.32
:param domain:
:param dimensions:
:return:
"""
def function(x):
sum = 0
for i in range(4):
secondsum = 0
for j in range(6):
secondsum += ComparativeBenchmarks.a_hartman20[i][j] * \
((x[j]-ComparativeBenchmarks.p_hartman20[i][j])**2)
sum += ComparativeBenchmarks.c_hartman[i] * math.exp(
-secondsum)
return -sum
return Benchmark(function=function,
domain=domain,
dimensions=dimensions,
min_value=-3.32,
name="20")
def f19(domain=(0, 1), dimensions=3):
"""
R. Hartman's Family
Dimensions: 3
Domain: 0 -> 1
Minimum value: f(0.114,0.556,0.852) = -3.86
:param domain:
:param dimensions:
:return:
"""
def function(x):
sum = 0
for i in range(4):
secondsum = 0
for j in range(3):
secondsum += ComparativeBenchmarks.a_hartman19[i][j] * \
((x[j]-ComparativeBenchmarks.p_hartman19[i][j])**2)
sum += ComparativeBenchmarks.c_hartman[i] * math.exp(
-secondsum)
return -sum
return Benchmark(function=function,
domain=domain,
dimensions=dimensions,
min_value=-3.86,
name="19")
def f15(domain=(-5, 5), dimensions=4):
"""
N. Kowalik's Function
Dimensions: 4
Domain: -5 -> 5
Minimum value: f(0.19,0.19,0.12,0.14) = 0.0003075
:param domain:
:param dimensions:
:return:
"""
def function(x):
sum = 0
for i in range(10):
sum += (ComparativeBenchmarks.a_vector[i] -
((x[0] * ((ComparativeBenchmarks.b_vector[i]**2) +
ComparativeBenchmarks.b_vector[i] * x[1])) /
((ComparativeBenchmarks.b_vector[i]**2) +
ComparativeBenchmarks.b_vector[i] * x[2] + x[3])))**2
return sum
return Benchmark(function=function,
domain=domain,
dimensions=dimensions,
min_value=-1.1428,
name="15")
def f23(domain=(0, 10), dimensions=4):
"""
S. Shekel's Family
Dimensions: 4
Domain: 0 -> 10
Minimum value: f(~4) = -10.5
:param domain:
:param dimensions:
:return:
"""
def function(x):
sum = 0
for i in range(9):
vector_1 = ComparativeBenchmarks.subtract_vectors(
x, ComparativeBenchmarks.a_shekel[i])
vector_2 = ComparativeBenchmarks.subtract_vectors(
x, ComparativeBenchmarks.a_shekel[i])
sum += (ComparativeBenchmarks.dot_product(vector_1, vector_2) +
ComparativeBenchmarks.c_shekel[i])**-1
return -sum
return Benchmark(function=function,
domain=domain,
dimensions=dimensions,
min_value=-10.5,
name="23")
def f16(domain=(-5, 5), dimensions=2):
"""
O. Six-Hump Camel-Back Function
Dimensions: 2
Domain: -5 -> 5
Minimum value: f(-0.09,0.71) = -1.0316
:param domain:
:param dimensions:
:return:
"""
def function(x):
return 4 * x[0]**2 - 2.1 * x[0]**4 + (
1 / 3) * x[0]**6 + x[0] * x[1] - 4 * x[1]**2 + 4 * x[1]**4
return Benchmark(function=function,
domain=domain,
dimensions=dimensions,
min_value=-1.0316,
name="16")
def f17(domain=(-5, 15), dimensions=2):
"""
P. Branin Function
Dimensions: 2
Domain: -5 -> 15
Minimum value: f(9.42,2.47) = 0.398
:param domain:
:param dimensions:
:return:
"""
def function(x):
return ((x[1] - (5.1 / (4*(math.pi**2))) * (x[0]**2) + (5/math.pi)*x[0] - 6)**2) + 10*(1 - (1/(8*math.pi))) * \
math.cos(x[0])+10
return Benchmark(function=function,
domain=domain,
dimensions=dimensions,
min_value=0.398,
name="17")
def f9(domain=(-5.12, 5.12), dimensions=30):
"""
Generalised Rastrigin's Function
Domain: -5.12 -> 5.12
Minimum value: f(0) = 0
:param domain:
:param dimensions:
:return:
"""
def function(x):
sum = 0
for i in range(len(x)):
sum += (x[i]**2) - 10 * math.cos(2 * math.pi * x[i]) + 10
return sum
return Benchmark(function=function,
domain=domain,
dimensions=dimensions,
min_value=0,
name="9")
def f6(domain=(-100, 100), dimensions=30):
"""
Step Function
Domain: -100 -> 100
Minimum value: f(p) = 0, -0.5 <= p <= 0.5
:param domain:
:param dimensions:
:return:
"""
def function(x):
sum = 0
for i in range(len(x)):
sum += (abs(x[i] + 0.5))**2
return sum
return Benchmark(function=function,
domain=domain,
dimensions=dimensions,
min_value=0,
name="6")
def f5(domain=(-30, 30), dimensions=30):
"""
Generalised Rosenbrock's Function
Domain: -30 -> 30
Minimum value: f(1) = 0
:param domain:
:param dimensions:
:return:
"""
def function(x):
sum = 0
for i in range(len(x) - 1):
sum += 100 * (x[i + 1] - (x[i]**2))**2 + (x[i] - 1)**2
return sum
return Benchmark(function=function,
domain=domain,
dimensions=dimensions,
min_value=0,
name="5")
def f4(domain=(-100, 100), dimensions=30):
"""
Domain: -100 -> 100
Minimum value: f(0) = 0
:param domain:
:param dimensions:
:return:
"""
def function(x):
max = None
for i in range(len(x)):
if max is None or abs(x[i]) > max:
max = abs(x[i])
return max
return Benchmark(function=function,
domain=domain,
dimensions=dimensions,
min_value=0,
name="4")
def f1(domain=(-5.12, 5.12), dimensions=30):
"""
Sphere Model
Domain: -5.12 -> 5.12
Minimum Value: f(0) = 0
:param domain:
:param dimensions:
:return:
"""
def function(x):
sum = 0
for i in range(len(x)):
sum += x[i]**2
return sum
return Benchmark(function=function,
domain=domain,
dimensions=dimensions,
min_value=0,
name="1")
def f7(domain=(-1.28, 1.28), dimensions=30):
"""
Quartic Function i.e. Noise
Domain: -1.28 -> 1.28
Minimum value: f(0) = 0
:param domain:
:param dimensions:
:return:
"""
def function(x):
sum = 0
for i in range(len(x)):
sum += (i + 1) * x[i]**4
sum += random.uniform(0, 1)
return sum
return Benchmark(function=function,
domain=domain,
dimensions=dimensions,
min_value=0,
name="7")
def f8(domain=(-500, 500), dimensions=30):
"""
Generalised Schwefel's Problem 2.26
Domain: -500 -> 500
Minimum value: f(420.97) = -12569.5(30)/41898.3(100)
:param domain:
:param dimensions:
:return:
"""
def function(x):
sum = 0
n = len(x)
for i in range(n):
sum += -x[i] * math.sin(math.sqrt(abs(x[i])))
return sum
min_value = -418.9829 * dimensions
return Benchmark(function=function,
domain=domain,
dimensions=dimensions,
min_value=min_value,
name="8")
def f11(domain=(-600, 600), dimensions=30):
"""
Generalised Griewank Function
Domain: -600 -> 600
Minimum value: f(0) = 0
:param domain:
:param dimensions:
:return:
"""
def function(x):
sum = 0
prod = 0
for i in range(len(x)):
sum += x[i]**2
prod *= math.cos(x[i] / (math.sqrt(i + 1)))
total = (1 / 4000) * sum + prod
return total
return Benchmark(function=function,
domain=domain,
dimensions=dimensions,
min_value=0,
name="11")
def f3(domain=(-100, 100), dimensions=30):
"""
Schwefel's Problem 1.2
Domain: -100 -> 100
Minimum value: f(0) = 0
:param domain:
:param dimensions:
:return:
"""
def function(x):
sum = 0
for i in range(len(x)):
secondsum = 0
for j in range(i):
secondsum += x[j]
sum += secondsum**2
return sum
return Benchmark(function=function,
domain=domain,
dimensions=dimensions,
min_value=0,
name="3")
def f18(domain=(-2, 2), dimensions=2):
"""
Q. Goldstein-Price Function
Dimensions: 2
Domain: -2 -> 2
Minimum value: f(0,-1) = 3
:param domain:
:param dimensions:
:return:
"""
def function(x):
return ((1 + ((x[0] + x[1] + 1)**2) *
(19 - (14 * x[0]) + ((3 * x[0])**2) - (14 * x[1]) +
(6 * x[0] * x[1]) + ((3 * x[1])**2))) *
(30 + (((2 * x[0]) - (3 * x[1]))**2) *
(18 - (32 * x[0]) + (12 * (x[0]**2)) + (48 * x[1]) -
(36 * x[0] * x[1]) + (27 * (x[1]**2)))))
return Benchmark(function=function,
domain=domain,
dimensions=dimensions,
min_value=3,
name="18")
def f2(domain=(-10, 10), dimensions=30):
"""
Schwefel's Problem 2.22
Domain: -10 -> 10
Minimum value: f(0) = 0
:param domain:
:param dimensions:
:return:
"""
def function(x):
sum = 0
prod = 0
for i in range(len(x)):
sum += abs(x[i])
prod *= abs(x[i])
total = sum + prod
return total
return Benchmark(function=function,
domain=domain,
dimensions=dimensions,
min_value=0,
name="2")