Solving Linear Equations
这个问题要我们求解线性方程组。
linearEquationTests.py 完整代码如下：
import unittest
import datetime
import genetic
import fractions
import random
class LinearEquationTests(unittest.TestCase):
def solve_unknowns(self, numUnknowns, geneset, equations, fnGenesToInputs):
startTime = datetime.datetime.now()
maxAge = 50
window = Window(max(1, int(len(geneset) / (2 * maxAge))),
max(1, int(len(geneset) / 3)),
int(len(geneset) / 2))
geneIndexes = [i for i in range(numUnknowns)]
sortedGeneset = sorted(geneset)
def fnMutate(genes):
mutate(genes, sortedGeneset, window, geneIndexes)
def fnDisplay(candidate):
display(candidate, startTime, fnGenesToInputs)
def fnGetFitness(genes):
return get_fitness(genes, equations)
optimalFitness = Fitness(0)
best = genetic.get_best(fnGetFitness, numUnknowns, optimalFitness,
geneset, fnDisplay, fnMutate, maxAge=maxAge)
self.assertTrue(not optimalFitness > best.Fitness)
def test_4_unknowns(self):
geneRange = [i for i in range(-13, 13) if i != 0]
geneset = [i for i in set(
fractions.Fraction(d, e)
for d in geneRange
for e in geneRange if e != 0)]
def fnGenesToInputs(genes):
return genes
def e1(genes):
x, y, z, a= genes
return fractions.Fraction(1, 15) * x
- 2 * y
- 15 * z
- fractions.Fraction(4,5) * a
- 3
def e2(genes):
x,y,z,a = genes
return - fractions.Fraction(5,2) * x
- fractions.Fraction(9,4) * y
+ 12 * z
- a
- 17
def e3(genes):
x,y,z,a = genes
return -13 * x
+ fractions.Fraction(3,10) * y
- 6 * z
- fractions.Fraction(2,5) * a
- 17
def e4(genes):
x,y,z,a = genes
return fractions.Fraction(1,2) * x
+ 2 * y
+ fractions.Fraction(7, 4) * z
+ fractions.Fraction(4, 3) * a
+ 9
equations = [e1, e2, e3, e4]
self.solve_unknowns(4, geneset, equations, fnGenesToInputs)
def test_benchmark(self):
genetic.Benchmark.run(lambda :self.test_4_unknowns())
def test_3_unknowns(self):
geneRange = [i for i in range(-5, 5) if i != 0]
geneset = [i for i in set(
fractions.Fraction(d, e)
for d in geneRange
for e in geneRange if e!=0)]
def fnGenesToInputs(genes):
return genes
def e1(genes):
x, y, z = genes
return 6 * x - 2 * y + 8 * z - 20
def e2(genes):
x,y,z = genes
return y + 8 * x * z + 1
def e3(genes):
x,y,z = genes
return 2 * z * fractions.Fraction(6, x) + 3* fractions.Fraction(y, 2) - 6
equations = [e1,e2,e3]
self.solve_unknowns(3, geneset, equations, fnGenesToInputs)
def get_fitness(genes, equations):
fitness = Fitness(sum(abs(e(genes)) for e in equations))
return fitness
class Fitness:
def __init__(self, totalDifference):
self.TotalDifference = totalDifference
def __gt__(self, other):
return self.TotalDifference < other.TotalDifference
def __str__(self):
return "diff: {:0.2f}".format(float(self.TotalDifference))
def display(candidate, startTime, fnGenesToInputs):
timeDiff = datetime.datetime.now() - startTime
symbols = "xyza"
result = ', '.join("{} = {}".format(s,v)
for s, v in zip(symbols, fnGenesToInputs(candidate.Genes)))
print("{} {} {}".format(
result,
candidate.Fitness,
timeDiff))
class Window:
def __init__(self, minimum, maximum, size):
self.Min = minimum
self.Max = maximum
self.Size = size
def slide(self):
self.Size = self.Size - 1
if self.Size > self.Min else self.Max
def mutate(genes, sortedGeneset, window, geneIndexes):
indexes = random.sample(geneIndexes, random.randint(1, len(genes)))
if random.randint(0, 10) == 0 else [random.choice(geneIndexes)]
window.slide()
while len(indexes) > 0:
index = indexes.pop()
genesetIndex = sortedGeneset.index(genes[index])
start = max(0, genesetIndex - window.Size)
stop = min(len(sortedGeneset)- 1, genesetIndex + window.Size)
genesetIndex = random.randint(start, stop)
genes[index] = sortedGeneset[genesetIndex]
需要注意的是这里使用maxAge来防止进入局部解，利用滑窗的方法提高效率，基因采用分数的形式，适应值计算的是等式的值，目标适应值为0.