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benchmarks.py
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benchmarks.py
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# -*- coding: utf-8 -*-
"""
Created on Tue May 17 12:46:20 2016
@author: Hossam Faris
"""
import numpy
import math
# define the function blocks
def prod(it):
p = 1
for n in it:
p *= n
return p
def Ufun(x, a, k, m):
y = k * ((x - a) ** m) * (x > a) + k * ((-x - a) ** m) * (x < (-a))
return y
def F1(x):
s = numpy.sum(x ** 2)
return s
def F2(x):
o = sum(abs(x)) + prod(abs(x))
return o
def F3(x):
dim = len(x) + 1
o = 0
for i in range(1, dim):
o = o + (numpy.sum(x[0:i])) ** 2
return o
def F4(x):
o = max(abs(x))
return o
def F5(x):
dim = len(x)
o = numpy.sum(
100 * (x[1:dim] - (x[0 : dim - 1] ** 2)) ** 2 + (x[0 : dim - 1] - 1) ** 2
)
return o
def F6(x):
o = numpy.sum(abs((x + 0.5)) ** 2)
return o
def F7(x):
dim = len(x)
w = [i for i in range(len(x))]
for i in range(0, dim):
w[i] = i + 1
o = numpy.sum(w * (x ** 4)) + numpy.random.uniform(0, 1)
return o
def F8(x):
o = sum(-x * (numpy.sin(numpy.sqrt(abs(x)))))
return o
def F9(x):
dim = len(x)
o = numpy.sum(x ** 2 - 10 * numpy.cos(2 * math.pi * x)) + 10 * dim
return o
def F10(x):
dim = len(x)
o = (
-20 * numpy.exp(-0.2 * numpy.sqrt(numpy.sum(x ** 2) / dim))
- numpy.exp(numpy.sum(numpy.cos(2 * math.pi * x)) / dim)
+ 20
+ numpy.exp(1)
)
return o
def F11(x):
dim = len(x)
w = [i for i in range(len(x))]
w = [i + 1 for i in w]
o = numpy.sum(x ** 2) / 4000 - prod(numpy.cos(x / numpy.sqrt(w))) + 1
return o
def F12(x):
dim = len(x)
o = (math.pi / dim) * (
10 * ((numpy.sin(math.pi * (1 + (x[0] + 1) / 4))) ** 2)
+ numpy.sum(
(((x[: dim - 1] + 1) / 4) ** 2)
* (1 + 10 * ((numpy.sin(math.pi * (1 + (x[1 :] + 1) / 4)))) ** 2)
)
+ ((x[dim - 1] + 1) / 4) ** 2
) + numpy.sum(Ufun(x, 10, 100, 4))
return o
def F13(x):
if x.ndim==1:
x = x.reshape(1,-1)
o = 0.1 * (
(numpy.sin(3 * numpy.pi * x[:,0])) ** 2
+ numpy.sum(
(x[:,:-1] - 1) ** 2
* (1 + (numpy.sin(3 * numpy.pi * x[:,1:])) ** 2), axis=1
)
+ ((x[:,-1] - 1) ** 2) * (1 + (numpy.sin(2 * numpy.pi * x[:,-1])) ** 2)
) + numpy.sum(Ufun(x, 5, 100, 4))
return o
def F14(x):
aS = [
[
-32, -16, 0, 16, 32,
-32, -16, 0, 16, 32,
-32, -16, 0, 16, 32,
-32, -16, 0, 16, 32,
-32, -16, 0, 16, 32,
],
[
-32, -32, -32, -32, -32,
-16, -16, -16, -16, -16,
0, 0, 0, 0, 0,
16, 16, 16, 16, 16,
32, 32, 32, 32, 32,
],
]
aS = numpy.asarray(aS)
bS = numpy.zeros(25)
v = numpy.matrix(x)
for i in range(0, 25):
H = v - aS[:, i]
bS[i] = numpy.sum((numpy.power(H, 6)))
w = [i for i in range(25)]
for i in range(0, 24):
w[i] = i + 1
o = ((1.0 / 500) + numpy.sum(1.0 / (w + bS))) ** (-1)
return o
def F15(L):
aK = [
0.1957, 0.1947, 0.1735, 0.16, 0.0844, 0.0627,
0.0456, 0.0342, 0.0323, 0.0235, 0.0246,
]
bK = [0.25, 0.5, 1, 2, 4, 6, 8, 10, 12, 14, 16]
aK = numpy.asarray(aK)
bK = numpy.asarray(bK)
bK = 1 / bK
fit = numpy.sum(
(aK - ((L[0] * (bK ** 2 + L[1] * bK)) / (bK ** 2 + L[2] * bK + L[3]))) ** 2
)
return fit
def F16(L):
o = (
4 * (L[0] ** 2)
- 2.1 * (L[0] ** 4)
+ (L[0] ** 6) / 3
+ L[0] * L[1]
- 4 * (L[1] ** 2)
+ 4 * (L[1] ** 4)
)
return o
def F17(L):
o = (
(L[1] - (L[0] ** 2) * 5.1 / (4 * (numpy.pi ** 2)) + 5 / numpy.pi * L[0] - 6)
** 2
+ 10 * (1 - 1 / (8 * numpy.pi)) * numpy.cos(L[0])
+ 10
)
return o
def F18(L):
o = (
1
+ (L[0] + L[1] + 1) ** 2
* (
19
- 14 * L[0]
+ 3 * (L[0] ** 2)
- 14 * L[1]
+ 6 * L[0] * L[1]
+ 3 * L[1] ** 2
)
) * (
30
+ (2 * L[0] - 3 * L[1]) ** 2
* (
18
- 32 * L[0]
+ 12 * (L[0] ** 2)
+ 48 * L[1]
- 36 * L[0] * L[1]
+ 27 * (L[1] ** 2)
)
)
return o
# map the inputs to the function blocks
def F19(L):
aH = [[3, 10, 30], [0.1, 10, 35], [3, 10, 30], [0.1, 10, 35]]
aH = numpy.asarray(aH)
cH = [1, 1.2, 3, 3.2]
cH = numpy.asarray(cH)
pH = [
[0.3689, 0.117, 0.2673],
[0.4699, 0.4387, 0.747],
[0.1091, 0.8732, 0.5547],
[0.03815, 0.5743, 0.8828],
]
pH = numpy.asarray(pH)
o = 0
for i in range(0, 4):
o = o - cH[i] * numpy.exp(-(numpy.sum(aH[i, :] * ((L - pH[i, :]) ** 2))))
return o
def F20(L):
aH = [
[10, 3, 17, 3.5, 1.7, 8],
[0.05, 10, 17, 0.1, 8, 14],
[3, 3.5, 1.7, 10, 17, 8],
[17, 8, 0.05, 10, 0.1, 14],
]
aH = numpy.asarray(aH)
cH = [1, 1.2, 3, 3.2]
cH = numpy.asarray(cH)
pH = [
[0.1312, 0.1696, 0.5569, 0.0124, 0.8283, 0.5886],
[0.2329, 0.4135, 0.8307, 0.3736, 0.1004, 0.9991],
[0.2348, 0.1415, 0.3522, 0.2883, 0.3047, 0.6650],
[0.4047, 0.8828, 0.8732, 0.5743, 0.1091, 0.0381],
]
pH = numpy.asarray(pH)
o = 0
for i in range(0, 4):
o = o - cH[i] * numpy.exp(-(numpy.sum(aH[i, :] * ((L - pH[i, :]) ** 2))))
return o
def F21(L):
aSH = [
[4, 4, 4, 4],
[1, 1, 1, 1],
[8, 8, 8, 8],
[6, 6, 6, 6],
[3, 7, 3, 7],
[2, 9, 2, 9],
[5, 5, 3, 3],
[8, 1, 8, 1],
[6, 2, 6, 2],
[7, 3.6, 7, 3.6],
]
cSH = [0.1, 0.2, 0.2, 0.4, 0.4, 0.6, 0.3, 0.7, 0.5, 0.5]
aSH = numpy.asarray(aSH)
cSH = numpy.asarray(cSH)
fit = 0
for i in range(5):
v = numpy.matrix(L - aSH[i, :])
fit = fit - ((v) * (v.T) + cSH[i]) ** (-1)
o = fit.item(0)
return o
def F22(L):
aSH = [
[4, 4, 4, 4],
[1, 1, 1, 1],
[8, 8, 8, 8],
[6, 6, 6, 6],
[3, 7, 3, 7],
[2, 9, 2, 9],
[5, 5, 3, 3],
[8, 1, 8, 1],
[6, 2, 6, 2],
[7, 3.6, 7, 3.6],
]
cSH = [0.1, 0.2, 0.2, 0.4, 0.4, 0.6, 0.3, 0.7, 0.5, 0.5]
aSH = numpy.asarray(aSH)
cSH = numpy.asarray(cSH)
fit = 0
for i in range(7):
v = numpy.matrix(L - aSH[i, :])
fit = fit - ((v) * (v.T) + cSH[i]) ** (-1)
o = fit.item(0)
return o
def F23(L):
aSH = [
[4, 4, 4, 4],
[1, 1, 1, 1],
[8, 8, 8, 8],
[6, 6, 6, 6],
[3, 7, 3, 7],
[2, 9, 2, 9],
[5, 5, 3, 3],
[8, 1, 8, 1],
[6, 2, 6, 2],
[7, 3.6, 7, 3.6],
]
cSH = [0.1, 0.2, 0.2, 0.4, 0.4, 0.6, 0.3, 0.7, 0.5, 0.5]
aSH = numpy.asarray(aSH)
cSH = numpy.asarray(cSH)
fit = 0
for i in range(10):
v = numpy.matrix(L - aSH[i, :])
fit = fit - ((v) * (v.T) + cSH[i]) ** (-1)
o = fit.item(0)
return o
def getFunctionDetails(a):
# [name, lb, ub, dim]
param = {
"F1": ["F1", -100, 100, 30],
"F2": ["F2", -10, 10, 30],
"F3": ["F3", -100, 100, 30],
"F4": ["F4", -100, 100, 30],
"F5": ["F5", -30, 30, 30],
"F6": ["F6", -100, 100, 30],
"F7": ["F7", -1.28, 1.28, 30],
"F8": ["F8", -500, 500, 30],
"F9": ["F9", -5.12, 5.12, 30],
"F10": ["F10", -32, 32, 30],
"F11": ["F11", -600, 600, 30],
"F12": ["F12", -50, 50, 30],
"F13": ["F13", -50, 50, 30],
"F14": ["F14", -65.536, 65.536, 2],
"F15": ["F15", -5, 5, 4],
"F16": ["F16", -5, 5, 2],
"F17": ["F17", -5, 15, 2],
"F18": ["F18", -2, 2, 2],
"F19": ["F19", 0, 1, 3],
"F20": ["F20", 0, 1, 6],
"F21": ["F21", 0, 10, 4],
"F22": ["F22", 0, 10, 4],
"F23": ["F23", 0, 10, 4],
}
return param.get(a, "nothing")
'''
# ESAs space mission design benchmarks https://www.esa.int/gsp/ACT/projects/gtop/
from fcmaes.astro import (
MessFull,
Messenger,
Gtoc1,
Cassini1,
Cassini2,
Rosetta,
Tandem,
Sagas,
)
def Ca1(x):
return Cassini1().fun(x)
def Ca2(x):
return Cassini2().fun(x)
def Ros(x):
return Rosetta().fun(x)
def Tan(x):
return Tandem(5).fun(x)
def Sag(x):
return Sagas().fun(x)
def Mef(x):
return MessFull().fun(x)
def Mes(x):
return Messenger().fun(x)
def Gt1(x):
return Gtoc1().fun(x)
def getFunctionDetails(a):
# [name, lb, ub, dim]
param = {
"F1": ["F1", -100, 100, 30],
"F2": ["F2", -10, 10, 30],
"F3": ["F3", -100, 100, 30],
"F4": ["F4", -100, 100, 30],
"F5": ["F5", -30, 30, 30],
"F6": ["F6", -100, 100, 30],
"F7": ["F7", -1.28, 1.28, 30],
"F8": ["F8", -500, 500, 30],
"F9": ["F9", -5.12, 5.12, 30],
"F10": ["F10", -32, 32, 30],
"F11": ["F11", -600, 600, 30],
"F12": ["F12", -50, 50, 30],
"F13": ["F13", -50, 50, 30],
"F14": ["F14", -65.536, 65.536, 2],
"F15": ["F15", -5, 5, 4],
"F16": ["F16", -5, 5, 2],
"F17": ["F17", -5, 15, 2],
"F18": ["F18", -2, 2, 2],
"F19": ["F19", 0, 1, 3],
"F20": ["F20", 0, 1, 6],
"F21": ["F21", 0, 10, 4],
"F22": ["F22", 0, 10, 4],
"F23": ["F23", 0, 10, 4],
"Ca1": [
"Ca1",
Cassini1().bounds.lb,
Cassini1().bounds.ub,
len(Cassini1().bounds.lb),
],
"Ca2": [
"Ca2",
Cassini2().bounds.lb,
Cassini2().bounds.ub,
len(Cassini2().bounds.lb),
],
"Gt1": ["Gt1", Gtoc1().bounds.lb, Gtoc1().bounds.ub, len(Gtoc1().bounds.lb)],
"Mes": [
"Mes",
Messenger().bounds.lb,
Messenger().bounds.ub,
len(Messenger().bounds.lb),
],
"Mef": [
"Mef",
MessFull().bounds.lb,
MessFull().bounds.ub,
len(MessFull().bounds.lb),
],
"Sag": ["Sag", Sagas().bounds.lb, Sagas().bounds.ub, len(Sagas().bounds.lb)],
"Tan": [
"Tan",
Tandem(5).bounds.lb,
Tandem(5).bounds.ub,
len(Tandem(5).bounds.lb),
],
"Ros": [
"Ros",
Rosetta().bounds.lb,
Rosetta().bounds.ub,
len(Rosetta().bounds.lb),
],
}
return param.get(a, "nothing")
'''