**Project: Binary Encoding **

In this project:

Use binary (bit-string) encoding, with 15 bits for x1, 20 bits for x2, and 25 bits for x3.

The algorithm parameters (population size, crossover rate, etc.) do not have to be the same as the ones used in Project #1 and may be taken from the user on the command line or provided at the beginning of execution, or may be stored in a file to be read in.

The output should include the best, mean and standard deviation of the best-of-run fitnesses from 30 independent runs (no generation-wise details needed). Also, show the vector (the three x values) of the best of the 30 best-of-run solutions. Please do not use an off-the-shelf implementation from packages. Please submit a single doc/docx/pdf/ipynb file (no other file type, please, with the following exception: if you are submitting an ipynb file, please ALSO submit the corresponding html) containing the source code and all output. Submission of multiple files is discouraged but may be resorted to only if you absolutely cannot manage to produce a single file. Physical files are to be uploaded – not a link to some web site. At the beginning of your report, you may add notes for any other special issues/techniques that you think might be important in your implementation.

**Issues faced:** I encountered issue while encoding the numbers to the binary system. I was not able to specify the number of bits while converting floating point numbers to binary. On converting floating point to binary, I was able to generate a string of either 32-bits or 64 bits.
Hence, the current code works for only integers.

**Parameters:**

Population size, N = 30

Number of independent runs, nRun = 30

Number of generations, nGen= 80

Crossover probability, p_c= 0.8

Mutation Probability, p_m=0.1

**Function to minimize:** X1^2 + X2^2 + x3^2

**Range for values of X:**

X_MIN= -1.0

X_MAX= 5.0

**Output:**

The average of the best-of-run fitness is 60.379620051557396

The corresponding standard deviation is 48.524933538699585

best-of-the-run vector: [0, 0, 0]

**Code Implementation**

```
import random
import math
N = 10 # size of population
X_MIN = -1.0
X_MAX = 5.0
p_c = 0.8
p_m = 0.1
def run_ga(N, n_gen, plot=False):
"""Run Genentic algorithm
N - size of population
n_gen - number of generation
plot - if equals True function plot the graphs
"""
population = initialize(N)
results = []
for i in range(n_gen):
results.append(get_best_worst(population))
population = crossover(population, p_c)
population = mutate(population, p_m)
if plot:
show_results(results)
best_of_run = get_best_of_run(results)
return best_of_run, results
def initialize(N):
"""Create initial population of length N
The X_MIN and X_MAX are global parameters
"""
population = [ [round(random.uniform(X_MIN, X_MAX)) for _ in range(3)] for _ in range(N)]
for i in population:
i[0]='{0:015b}'.format(i[0])
i[1]='{0:020b}'.format(i[1])
i[2]='{0:025b}'.format(i[2])
return population
def fit_fun(X):
"""Calculate a fitness function to minimize
X1**2 + X2**2 + ... + Xn**2
"""
decimal=[int(i,2) for i in X]
s = sum([x**2 for x in decimal])
return 1/(s+0.01)
def get_best_worst(population):
"""Find and return best and worst fitness functions along with corresponding
vectors for a population, also return afrage fitness.
Return format:
((best_f, best_x), (worst_f, worst_x), avrg_f)
"""
best_f = 0
best_x = None
worst_f = 999999
worst_x = None
s = 0
for x in population:
f = fit_fun(x)
if f > best_f:
best_f = f
best_x = x
if f < worst_f:
worst_f = f
worst_x = x
s += f
avrg_f = s / len(population)
return ((best_f, best_x), (worst_f, worst_x), avrg_f)
def crossover(population, p_c):
"""Form a new population from an old one using crossover
with probability p_c
"""
N = len(population)
f = [fit_fun(x) for x in population]
new_pop = []
for _ in range(N//2):
xx = random.choices(population, weights=f, k=2)
if random.random() < p_c:
crossover_gen(xx)
new_pop += [xx[0][:], xx[1][:]] # add a copy
return new_pop
def crossover_gen(x):
"""Do crossoving in the pair of chromosomes x[0] and x[1] using
linear combination
"""
# single point crossover
# select a gen to crossover
i = random.randrange(len(x[0]))
s, t = x[0][i], x[1][i]
x[0][i]=t
x[1][i]=s
# generate a random parameter
def mutate(population, p_m):
"""Mutate a population with probability p_m
"""
new_pop = []
for x in population:
if random.random() < p_m:
mutate_gen(x)
new_pop.append(x)
return new_pop
def mutate_gen(x):
"""Mutate a single chromosome using by flipping one random bit
"""
# form the chromosome by concatinating the genes
x_full=''
for i in x:
x_full+=i
# select a random position
j=random.randrange(1,len(x_full))
# flip the bit
x_list=list(x_full)
if x_list[j]=='0':
x_list[j]='1'
else:
x_list[j]='0'
# mutated chromosome
x=["".join(x_list[:15]),"".join(x_list[15:35]),"".join(x_list[35:])]
def get_best_of_run(results):
"""Find the best fitness funcion value and vector among all generations
results is tuple return by get_best_wost funcion:
((best_f, best_x), (worst_f, worst_x), avrg_f)
"""
the_best_f = 0
the_best_x = None
for (f, x), worst, avrg in results:
if f > the_best_f:
the_best_f = f
the_best_x = x
return the_best_f, the_best_x
def show_results(results):
"""Plot best, worst and average fitness value vs generation
results is a list of tuples return by get_best_wost funcion:
((best_f, best_x), (worst_f, worst_x), avrg_f)
"""
import matplotlib.pyplot as plt
best = []
worst = []
avrg = []
for (b, x), (w, x), a in results:
best.append(b)
worst.append(w)
avrg.append(a)
g = range(len(best))
plt.plot(g, best, label="best")
plt.plot(g, worst, label="worst")
plt.plot(g, avrg, label="average")
plt.legend()
plt.xlabel('Generation')
plt.ylabel('Fitness function')
plt.show()
def do_ga_stats(nRuns, N, nGens, plot=False):
"""Do nRuns independent runs of GA and collect statistics
nRuns a number of times to run
N a size of population
nGens a number of generations
if plot is True show a graph
Return list of best-of-generation avarage values, list of standad deviations,
avarage value of the best-of-run fitness, standard deviation of the best-of-run
"""
s = [0.0] * nGens # sum of best-of_generation
s2 = [0.0] * nGens # sum of best-of_generation squares
bof = 0.0 # best-of-run
bof2 = 0.0 # best-of-run square
for _ in range(nRuns):
(best_of_run, x), results = run_ga(N, nGens)
bof += best_of_run
bof2 += best_of_run**2
for gen, result in enumerate(results):
(b, x), (w, x), a = result
s[gen] += b
s2[gen] += b**2
avg = []
std = []
for i in range(nGens):
avg.append(s[i]/nRuns)
x = math.sqrt(s2[i]/nRuns - avg[i]**2)
std.append(x)
if plot:
show_stat(avg, std)
avg_bof = bof/nRuns
std_bof = math.sqrt(bof2/nRuns - avg_bof**2)
(b, x), (w, y), a = result
return avg, std, avg_bof, std_bof,x
def show_stat(avg, std):
"""Plot average value of the best-of-generation and standard deviation
"""
import matplotlib.pyplot as plt
g = range(len(avg))
plt.plot(g, avg)
plt.xlabel('Generation')
plt.ylabel('Avarage of fitness function')
plt.show()
plt.figure()
plt.plot(g, std)
plt.xlabel('Generation')
plt.ylabel('Standard deviation of fitness function')
plt.show()
```

```
random.seed(0)
avg, std, avg_bof, std_bof,vector = do_ga_stats(30, 30, 80, plot=False)
print(f'The average of the best-of-run fitness is {avg_bof}')
print(f'The corresponding standard deviation is {std_bof}')
print('\nbest-of-the-run vector:',[int(i,2) for i in vector])
```

Output:

The average of the best-of-run fitness is 60.379620051557396

The corresponding standard deviation is 48.524933538699585

best-of-the-run vector: [0, 0, 0]

*For more details you can contact Us at:*

realcode4you@gmail.com

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