Develop Reference

Find minimum number of elements in a list that covers specific values

A recruiter wants to form a team with different skills and he wants to pick the minimum number of persons which can cover all the required skills.
N represents number of persons and K is the number of distinct skills that need to be included. list spec_skill = [[1,3],[0,1,2],[0,2,4]] provides information about skills of each person. e.g. person 0 has skills 1 and 3, person 1 has skills 0, 1 and 2 and so on.
The code should outputs the size of the smallest team that recruiter could find (the minimum number of persons) and values indicating the specific IDs of the people to recruit onto the team.
I implemented the code with brute force as below but since some data are more than thousands, it seems I need to be solved with heuristic approaches. In this case it is possible to have approximate answer.
Any suggestion how to solve it with heuristic methods will be appreciated.
N,K = 3,5
spec_skill = [[1,3],[0,1,2],[0,2,4]]
A = list(range(K))
set_a = set(A)
solved = False
for L in range(0, len(spec_skill)+1):
for subset in itertools.combinations(spec_skill, L):
s = set(item for sublist in subset for item in sublist)
if set_a.issubset(s):
print(str(len(subset)) + '\n' + ' '.join([str(spec_skill.index(item)) for item in subset]))
solved = True
break
if solved: break

Here is my way of doing this. There might be potential optimization possibilities in the code, but the base idea should be understandable.
import random
import time
def man_power(lst, K, iterations=None, period=0):
"""
Specify a fixed number of iterations
or a period in seconds to limit the total computation time.
"""
# mapping each sublist into a (sublist, original_index) tuple
lst2 = [(lst[i], i) for i in range(len(lst))]
mini_sample = [0]*(len(lst)+1)
if period<0 or (period == 0 and iterations is None):
raise AttributeError("You must specify iterations or a positive period")
def shuffle_and_pick(lst, iterations):
mini = [0]*len(lst)
for _ in range(iterations):
random.shuffle(lst2)
skillset = set()
chosen_ones = []
idx = 0
fullset = True
# Breaks from the loop when all skillsets are found
while len(skillset) < K:
# No need to go further, we didn't find a better combination
if len(chosen_ones) >= len(mini):
fullset = False
break
before = len(skillset)
skillset.update(lst2[idx][0])
after = len(skillset)
if after > before:
# We append with the orginal index of the sublist
chosen_ones.append(lst2[idx][1])
idx += 1
if fullset:
mini = chosen_ones.copy()
return mini
# Estimates how many iterations we can do in the specified period
if iterations is None:
t0 = time.perf_counter()
mini_sample = shuffle_and_pick(lst, 1)
iterations = int(period / (time.perf_counter() - t0)) - 1
mini_result = shuffle_and_pick(lst, iterations)
if len(mini_sample)<len(mini_result):
return mini_sample, len(mini_sample)
else:
return mini_result, len(mini_result)

Genetic Algorithm for 8 queens puzzle

I'm trying to apply genetic algorithm for 8 queens puzzle. I've coded whole algorithm but it keeps getting stuck when it finds solution with 6 unhit queens and can't get over it. I feel like there's some diversity problem but I can't figure out what to do with it. My question is what is wrong with this realisation and why it keeps getting stuck on 6 unhit queens and can't make a final move? I've already examined every bit of code and I think there's some misinterpretation of algorithm itself evolved. That's why I attached whole code. So I hope that someone would tell me where I did wrong. Thanks in advance.
def mutate(self, children):
rnd.seed()
count = 0
for child in children:
count += 1
if rnd.random() < self.mut_prob:
i = rnd.randrange(0, 7)
ind = child[i].index(1)
child[i][ind] = 0
j = rnd.randrange(0, 7)
child[i][j] = 1
def solve(self, min_fitness= 7, max_epochs=100):
prev_pop = self.initial_population()
epochs = 0
max_fitness = 0
while (max_fitness <= min_fitness) and (epochs < max_epochs):
fitness = self.fitness_function(prev_pop)
fitness.sort(key=lambda tup: tup[1])
best_sol = fitness[len(fitness) - 1][0]
max_fitness = fitness[len(fitness) - 1][1]
mating = self.roulette(fitness)
mating_chromes = []
pop = copy.deepcopy(prev_pop)
for chrom in mating:
mating_chromes.append(pop[chrom])
pop.clear()
children = self.crossover(mating_chromes)
self.mutate(children)
fit = self.fitness_function(prev_pop)
to_destroy = self.reduction(fitness)
for el in to_destroy:
prev_pop[el] = children.pop(0)
epochs += 1
print(max_fitness)
print(epochs)
for el in prev_pop[best_sol]:
print(el)
print("\n")
print("im fine")
return 0
s = Solver_8_queens()
arr = s.solve()

One problem with your code is the way you use Python function random.randrange(). The documentation says that randrange(a, b) will return a random number x such that a <= x < b (note that b is not included).
When you write something like i = random.randrange(0, 7) you will get a random number from the semi-open interval [0, 7), while what you (most likely) want is the number from closed interval [0, 7], because board size is 8x8. So check all calls to randrange(), fix them if they are incorrect and see whether it solves the problem.

Finding the optimal location for router placement

I am looking for an optimization algorithm that takes a text file encoded with 0s, 1s, and -1s:
1's denoting target cells that requires Wi-Fi coverage
0's denoting cells that are walls
1's denoting cells that are void (do not require Wi-Fi coverage)
Example of text file:
I have created a solution function along with other helper functions, but I can't seem to get the optimal positions of the routers to be placed to ensure proper coverage. There is another file that does the printing, I am struggling with finding the optimal location. I basically need to change the get_random_position function to get the optimal one, but I am unsure how to do that. The area covered by the various routers are:
This is the kind of output I am getting:
Each router covers a square area of at most (2S+1)^2
Type 1: S=5; Cost=180
Type 2: S=9; Cost=360
Type 3: S=15; Cost=480
My code is as follows:
import numpy as np
import time
from random import randint
def is_taken(taken, i, j):
for coords in taken:
if coords[0] == i and coords[1] == j:
return True
return False
def get_random_position(floor, taken , nrows, ncols):
i = randint(0, nrows-1)
j = randint(0, ncols-1)
while floor[i][j] == 0 or floor[i][j] == -1 or is_taken(taken, i, j):
i = randint(0, nrows-1)
j = randint(0, ncols-1)
return (i, j)
def solution(floor):
start_time = time.time()
router_types = [1,2,3]
nrows, ncols = floor.shape
ratio = 0.1
router_scale = int(nrows*ncols*0.0001)
if router_scale == 0:
router_scale = 1
row_ratio = int(nrows*ratio)
col_ratio = int(ncols*ratio)
print('Row : ',nrows, ', Col: ', ncols, ', Router scale :', router_scale)
global_best = [0, ([],[],[])]
taken = []
while True:
found_better = False
best = [global_best[0], (list(global_best[1][0]), list(global_best[1][1]), list(global_best[1][2]))]
for times in range(0, row_ratio+col_ratio):
if time.time() - start_time > 27.0:
print('Time ran out! Using what I got : ', time.time() - start_time)
return global_best[1]
fit = []
for rtype in router_types:
interim = (list(global_best[1][0]), list(global_best[1][1]), list(global_best[1][2]))
for i in range(0, router_scale):
pos = get_random_position(floor, taken, nrows, ncols)
interim[0].append(pos[0])
interim[1].append(pos[1])
interim[2].append(rtype)
fit.append((fitness(floor, interim), interim))
highest_fitness = fit[0]
for index in range(1, len(fit)):
if fit[index][0] > highest_fitness[0]:
highest_fitness = fit[index]
if highest_fitness[0] > best[0]:
best[0] = highest_fitness[0]
best[1] = (highest_fitness[1][0],highest_fitness[1][1], highest_fitness[1][2])
found_better = True
global_best = best
taken.append((best[1][0][-1],best[1][1][-1]))
break
if found_better == False:
break
print('Best:')
print(global_best)
end_time = time.time()
run_time = end_time - start_time
print("Run Time:", run_time)
return global_best[1]
def available_cells(floor):
available = 0
for i in range(0, len(floor)):
for j in range(0, len(floor[i])):
if floor[i][j] != 0:
available += 1
return available
def fitness(building, args):
render = np.array(building, dtype=int, copy=True)
cov_factor = 220
cost_factor = 22
router_types = { # type: [coverage, cost]
1: {'size' : 5, 'cost' : 180},
2: {'size' : 9, 'cost' : 360},
3: {'size' : 15, 'cost' : 480},
}
routers_used = args[-1]
for r, c, t in zip(*args):
size = router_types[t]['size']
nrows, ncols = render.shape
rows = range(max(0, r-size), min(nrows, r+size+1))
cols = range(max(0, c-size), min(ncols, c+size+1))
walls = []
for ri in rows:
for ci in cols:
if building[ri, ci] == 0:
walls.append((ri, ci))
def blocked(ri, ci):
for w in walls:
if min(r, ri) <= w[0] and max(r, ri) >= w[0]:
if min(c, ci) <= w[1] and max(c, ci) >= w[1]:
return True
return False
for ri in rows:
for ci in cols:
if blocked(ri, ci):
continue
if render[ri, ci] == 2:
render[ri, ci] = 4
if render[ri, ci] == 1:
render[ri, ci] = 2
render[r, c] = 5
return (
cov_factor * np.sum(render > 1) -
cost_factor * np.sum([router_types[x]['cost'] for x in routers_used])
)

Here's a suggestion on how to solve the problem; however I don't affirm this is the best approach, and it's certainly not the only one.
Main idea
Your problem can be modelised as a weighted minimum set cover problem.
Good news, this is a well known optimization problem:
It is easy to find algorithm descriptions for approximate solutions
A quick search on the web shows many implementations of approximation algorithms in Python.
Bad news, this is a NP-hard optimization problem:
If you need an exact solution: algorithms will work only for "small" sized problems in a reasonable amount of time(in your case: size of the problem <=> number of "1" cells).
Approximate (a.k.a greedy) algorithms are trade-off between computation requirements, and a risk do deliver far from optimal solutions in certain cases.
Note that the following part does not prove that your problem is NP-hard. The general minimum set cover problem is NP-hard. In your case the subsets have several properties that might help to design a better algorithm. I have no idea how though.
Translating into a cover set problem
Let's define some sets:
U: the set of "1" cells (requiring Wifi).
P(U): the power set of U (the set of subsets of U).
P: the set of cells on which you can place a router (not sure if P=U in your original post).
T: the set of router type (3 values in your case).
R+: positive Real number (used to describe prices).
Let's define a function (pseudo Python):
# Domain of definition : T,P --> R+,P(U)
# This function takes a router type and a position, and returns
# a tuple containing:
# - the price of a router of the given type.
# - the subset of U containing all the position covered by a router
# of the given type placed at the given position.
def weighted_subset(routerType, position):
pass # TODO: implementation
Now, we define a last set, as the image of the function we've just described: S=weighted_subset(T,P). Each element of this set is a subset of U, weighted by a price in R+.
With all this formalism, finding the router types & positions that:
gives coverage to all the desirable locations
minimize the cost
Is equivalent to finding a sub-collection of S:
whose union of their P(U) is equal to U
which minimise the sum of the associated weights
Which is the weighted minimal set cover problem.

python genetic algorithm found optimum solution

I explain, I am trying to develop a program to optimize a system based on the parameters it receives. My program will have to vary these parameters to try to find the best possible combination.
here is a code to simplify my problem:
parameters=[["toto1","toto2","toto3"],["tutu1","tutu2","tutu3"],["titi1","titi2","titi3"],["tata1","tata2","tata3"]]
def MySysteme(param1,param2,param3,param4):
result=0
for i in range(0,len(param1)):
result+=ord(param1[i])
for i in range(0,len(param2)):
result+=ord(param1[i])
for i in range(0,len(param3)):
result+=ord(param1[i])
for i in range(0,len(param4)):
result+=ord(param1[i])
return result
print(MySysteme(parameters[0][0],parameters[1][2],parameters[2][2],parameters[3][0]))
print(MySysteme(parameters[1][0],parameters[2][2],parameters[3][2],parameters[0][0]))
print(MySysteme(parameters[3][1],parameters[1][2],parameters[2][2],parameters[0][0]))
#how to find the highest value?
I try to (try) find the highest number, without testing all the parameters naively. hence the use of a genetic algorithm. 1 parameter is a list contained in the list parameters, the contents of the list is a varariante of my parameter
knowing that in my function / my system, one should not have 2 times the same parameter, for example this should not happen: print (MySystem (parameters [1] [0], parameters [1] [0])) or this print (MySystem (parameters [2] [1], parameters [2] [0]))
on the other hand the number of parameters is included in 1 and 4 (there can be 1,2,3 or 4 parameters)
To solve my problem here is the data that I consider: Individual: it is a variant of parameter which carries a name ("toto1", "tata3", "toto2 = 12" ... etc.) Population: set of the variants of the parameters fitness : it is the result of the function according to the parameters a circuit: a set of parameters
but unlike the commercial traveler, I have no starting data => that is to say that I do not have GPS coordinates. and it is at this level that I am stuck for the resolution of my problem.
can anyone help me?
edit:
I have been looking some examples of how I could find the points at which a function achieves its maxium using a genetic algorithm approach in Python. I looked at this tutorial
https://lethain.com/genetic-algorithms-cool-name-damn-simple/
my objective is to found the smaller number to "mySysteme" function
i set a new code :
je re-explique mon probleme plus simplement. J’ai mets un code plus complet, plus clair avec un algo génétique.
from random import randint, random
from operator import add
from functools import reduce
parameters=[["toto123","toto27","toto3000"],["tu","tut","tutu378694245"],["t","choicezaert","titi3=78965"],["blabla","2","conjoncture_is_enable"]]
def individual(length, min, max):
return [ randint(min,max) for x in range(length) ]
def population(count, length, min, max):
return [ individual(length, min, max) for x in range(count) ]
def fitness(individual, target):
sum = reduce(add, individual, 0)
return abs(target-sum)
def grade(pop, target):
individu_number_parameters=randint(1, len(parameters)-1)
for j in range(0,individu_number_parameters):
position=randint(1, len(parameters)-1)
parameter=parameters[position]
if isinstance(parameter, list):
parameter=parameters[position][randint(1, len(parameters[position])-1)]
result=0
for i in range(0,len(parameter)):
result+=ord(parameter[i])
return result
def evolve(pop, target, retain=0.2, random_select=0.05, mutate=0.01):
graded = [ (fitness(x, target), x) for x in pop]
graded = [ x[1] for x in sorted(graded)]
retain_length = int(len(graded)*retain)
parents = graded[:retain_length]
for individual in graded[retain_length:]:
if random_select > random():
parents.append(individual)
for individual in parents:
if mutate > random():
pos_to_mutate = randint(0, len(individual)-1)
individual[pos_to_mutate] = randint(
min(individual), max(individual))
parents_length = len(parents)
desired_length = len(pop) - parents_length
children = []
while len(children) < desired_length:
male = randint(0, parents_length-1)
female = randint(0, parents_length-1)
if male != female:
male = parents[male]
female = parents[female]
half = int(len(male) / 2)
child = male[:half] + female[half:]
children.append(child)
parents.extend(children)
return parents
target = 0
p_count = 100
i_length = 6
i_min = 0
i_max = 100
p = population(p_count, i_length, i_min, i_max)
fitness_history = [grade(p, target),]
for i in range(1000):
p = evolve(p, target)
fitness_history.append(grade(p, target))
for datum in fitness_history:
print(datum)
print(len(fitness_history))
I updated with new code. My ask : i want that my program found smaller number

Compute Higher Moments of Data Matrix

this probably leads to scipy/numpy, but right now I'm happy with any functionality as I couldn't find anything in those packages. I have a matrix that contains data for a multi-variate distribution (let's say, 2, for the fun of it). Is there any function to compute (higher) moments of that? All I could find was numpy.mean() and numpy.cov() :o
Thanks :)
/edit:
So some more detail: I have multivariate data, that is, a matrix where rows display variables and columns observations. Now I would like to have a simple way of computing the joint moments of that data, as defined in http://en.wikipedia.org/wiki/Central_moment#Multivariate_moments .
I'm pretty new to python/scipy so I'm not sure I'd be the best person to code this one up, especially for the n-variables case (note that the wikipedia definition is for n=2), and I kind of expected there to be some out-of-the-box thing to use as I thought this would be a standard problem.
/edit2:
Just for the future, in case someone wants to do something similar, the following code (which is still under review) should give the sample equivalent of the raw moments E(X^2), E(Y^2), etc. It only works for two variables right now, but it should be extendable if one feels the need. If you see some mistakes or unclean/unpython-nish code, feel free to comment.
from numpy import *
# this function should return something as
# moments[0] = 1
# moments[1] = mean(X), mean(Y)
# moments[2] = 1/n*X'X, 1/n*X'Y, 1/n*Y'Y
# moments[3] = mean(X'X'X), mean(X'X'Y), mean(X'Y'Y),
# mean(Y'Y'Y)
# etc
def getRawMoments(data, moment, axis=0):
a = moment
if (axis==0):
n = float(data.shape[1])
X = matrix(data[0,:]).reshape((n,1))
Y = matrix(data[1,:]).reshape((n,1))
else:
n = float(data.shape[0])
X = matrix(data[:,0]).reshape((n,1))
Y = matrix(data[:,1]).reshape((n,11))
result = 1
Z = hstack((X,Y))
iota = ones((1,n))
moments = {}
moments[0] = 1
#first, generate huge-ass matrix containing all x-y combinations
# for every power-combination k,l such that k+l = i
# for all 0 <= i <= a
for i in arange(1,a):
if i==2:
moments[i] = moments[i-1]*Z
# if even, postmultiply with X.
elif i%2 == 1:
moments[i] = kron(moments[i-1], Z.T)
# Else, postmultiply with X.T
elif i%2==0:
temp = moments[i-1]
temp2 = temp[:,0:n]*Z
temp3 = temp[:,n:2*n]*Z
moments[i] = hstack((temp2, temp3))
# since now we have many multiple moments
# such as x**2*y and x*y*x, filter non-distinct elements
momentsDistinct = {}
momentsDistinct[0] = 1
for i in arange(1,a):
if i%2 == 0:
data = 1/n*moments[i]
elif i == 1:
temp = moments[i]
temp2 = temp[:,0:n]*iota.T
data = 1/n*hstack((temp2))
else:
temp = moments[i]
temp2 = temp[:,0:n]*iota.T
temp3 = temp[:,n:2*n]*iota.T
data = 1/n*hstack((temp2, temp3))
momentsDistinct[i] = unique(data.flat)
return momentsDistinct(result, axis=1)