使用 genetic algorithm 來求解非線性問題。如 y = [ sin(1*x0) * sin(2*x1) ] + ... + [ sin(49*x48) * sin(50*x49) ]，求 y 的最大值

問題描述： 指定 0,1,2,.........49 等50個數字給 x0~x49(不可重複)，且

y = [ sin(1*x0) * sin(2*x1) ] + [ sin(3*x2) * sin(4*x3) ] + ... + [ sin(49*x48) * sin(50*x49) ]

請求解 y 之最大值?

本問題我使用 pyevolve 函式庫來幫我處理染色體的突變、重組、交配工作。我只需要提供目標函數(eval_func)的計算方式即可。本問題我的 y 最佳解是 20.4676 ，決策變數是 [33, 26, 36, 16, 45, 28, 37, 1, 19, 2, 25, 14, 0, 22, 6, 17, 35, 24, 11, 12, 27, 42, 49, 32, 13, 20, 23, 43, 41, 30, 4, 9, 21, 3, 10, 34, 38, 15, 18, 5, 47, 39, 44, 40, 8, 7, 31, 48, 46, 29] 。

 1 from pyevolve import G1DList
 2 from pyevolve import GSimpleGA
 3 from pyevolve import Selectors
 4 from pyevolve import Statistics
 5 from pyevolve import DBAdapters
 6 import pyevolve
 7 from math import sin
 8 
 9 """ 指定 (0,1,2,.........49 等50個數字不可重複）給 x0~x49，例如  x0=12,  x1= 33, ....
10     y = [ sin(1*x0) * sin(2*x1) ] + [ sin(3*x2) * sin(4*x3) ] + ... + [ sin(49*x48) * sin(50*x49) ]
11     求解 y 之 最大值＝?
12 """
13 
14 def eval_func(chromosome):
15     score = 20.0 #為了不讓 score 的值小於 0，因為 pyevolve 不支援適存值小於 0 。
16     list = map(lambda a,b: (a, b), xrange(50), chromosome)
17     list.sort(key=lambda a: a[1])
18     for i in xrange(25):
19         score += sin((2*i+1)*list[i*2][0]) * sin((2*i+2)*list[i*2+1][0])
20 
21     return score
22 
23 # Enable the pyevolve logging system
24 pyevolve.logEnable()
25 # Genome instance, 1D List of 50 elements
26 genome = G1DList.G1DList(50)
27 # Sets the range max and min of the 1D List
28 genome.setParams(rangemin=0, rangemax=500)
29 # The evaluator function (evaluation function)
30 genome.evaluator.set(eval_func)
31 # Genetic Algorithm Instance
32 ga = GSimpleGA.GSimpleGA(genome)
33 # Set the Roulette Wheel selector method, the number of generations and
34 # the termination criteria
35 ga.selector.set(Selectors.GRouletteWheel)
36 ga.setGenerations(5000)
37 ga.terminationCriteria.set(GSimpleGA.ConvergenceCriteria)
38 # Sets the DB Adapter, the resetDB flag will make the Adapter recreate
39 # the database and erase all data every run, you should use this flag
40 # just in the first time, after the pyevolve.db was created, you can
41 # omit it.
42 sqlite_adapter = DBAdapters.DBSQLite(identify="ex1", resetDB=True)
43 ga.setDBAdapter(sqlite_adapter)
44 # Do the evolution, with stats dump
45 # frequency of 20 generations
46 ga.evolve(freq_stats=20)
47 # Best individual
48 print ga.bestIndividual()

CMClass: GA 演算法

老師出了一題求函數最小化的問題，要我們用 Partical Swarm 求解，它與螞蟻王國演算法很類似，但尚未認真研究。先用 GA 求解。再來用 Partical Swarm 求解。

題目是：

f(x)= (x1/x2)* (sin(x2))^2 + (x2-x1)* cos(x1+10)
where
10<= x1 <= 30
30<= x2 <= 50
考題：
x1, x2 = any real value
try to find the minimum f(x)

我自已寫了一個 GA 物件(請到 https://ssvn.hoamon.info/OpenRelease/GA-0.1.py 下載，帳/密： guest/guest)

而解題的 ConvVar, FUNC 函式如下：

 1 def ConvVar(chromosom):     #轉換基因組到決策變數
 2     variables = []
 3     variables.append((int(chromosom[0]*3) + 1)*10)
 4     variables[0] += int(chromosom[1]*10)
 5     variables[0] += int(chromosom[2]*10)*0.1
 6     variables[0] += int(chromosom[3]*10)*0.01
 7     variables[0] += int(chromosom[4]*10)*0.001
 8 
 9     variables.append((int(chromosom[5]*3) + 3)*10)
10     variables[1] += int(chromosom[6]*10)
11     variables[1] += int(chromosom[7]*10)*0.1
12     variables[1] += int(chromosom[8]*10)*0.01
13     variables[1] += int(chromosom[9]*10)*0.001
14 
15     return variables
16 
17 from math import sin, cos
18 def FUNC(variables):        #定義目標函數
19     (x1, x2) = variables
20     if x1 > 30 or x1 < 10: return float('infinity')
21     if x2 > 50 or x2 < 30: return float('infinity')
22     sum = (x1/x2) * (sin(x2)) * (sin(x2)) + (x2-x1) * cos(x1+10)
23     return sum