GitHub - dvillavicencio/n-queens-problem: Small Jupyter Notebook that solves chess' N-Queens problem using analytical evolutionary algorithms.

Project 4: Solving N-Queens Problem using Genetic Algorithms

CSC 180 Intelligent Systems

Dr. Haiquan Chen, California State University, Sacramento

Part I: Position-index-based board representation

# Insert your name, your id, course title, assignment id, and due date here as comment 
# CSC180 Intelligent Systems
# Mini-Project 4
# Daniel E. Villavicencio Mena (302262597), Niravkumar Tandel (220218142), Mariya Cherednichenko (302037411)

import random
import numpy as np
!pip install deap
from deap import algorithms, base, creator, tools

creator.create("FitnessMin", base.Fitness, weights=(-1.0,))
creator.create("Individual", list, fitness=creator.FitnessMin)

Requirement already satisfied: deap in /usr/local/lib/python3.7/dist-packages (1.3.1)
Requirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from deap) (1.21.6)


/usr/local/lib/python3.7/dist-packages/deap/creator.py:141: RuntimeWarning: A class named 'FitnessMin' has already been created and it will be overwritten. Consider deleting previous creation of that class or rename it.
  RuntimeWarning)
/usr/local/lib/python3.7/dist-packages/deap/creator.py:141: RuntimeWarning: A class named 'Individual' has already been created and it will be overwritten. Consider deleting previous creation of that class or rename it.
  RuntimeWarning)

def create_individual():
  n = random.sample(range(64), 8)
  n.sort()
  return n

print(create_individual())

[4, 6, 7, 11, 28, 39, 50, 52]

def show_grid(board):
    
    n = [0]*64
    for i in board:
        n[i] = 1
    
    
    for i in range(8):
        for j in range(64):
            if j // 8 == i:
                if n[j] == 1:
                    print('X',end="|")
                else:
                    print('-',end="|")
        print()
        print("----------------")

toolbox = base.Toolbox()

toolbox.register("individual", tools.initIterate, creator.Individual, create_individual)

toolbox.register("population", tools.initRepeat, list, toolbox.individual)

pop = toolbox.population(n=5)

print(pop[0])

[25, 28, 30, 42, 44, 45, 54, 63]

show_grid(pop[0])

-|-|-|-|-|-|-|-|
----------------
-|-|-|-|-|-|-|-|
----------------
-|-|-|-|-|-|-|-|
----------------
-|X|-|-|X|-|X|-|
----------------
-|-|-|-|-|-|-|-|
----------------
-|-|X|-|X|X|-|-|
----------------
-|-|-|-|-|-|X|-|
----------------
-|-|-|-|-|-|-|X|
----------------

10 pts: Write your code in the cell below to define the "evaFitness" function, which returns the fitness of any given board.

Noticed that in this case, mutation may generate invalid board, e.g., the board with dupliciate positions. Think about [5, 32, 8, 8, 41, 3, 55, 49]
How to exclude those invalid boards from each generation? One way is to add some penalty to the fitness value of invalid boards. In that case, any invalid board will have a very high fitness value (remember that our goal is to find the board with least fitness value). To do that, let's write a function checkDuplicate() to calculate the number of queen pairs in the same position for any given board. Give each duplicate a high penalty (i.e., multiply by 20, 50) and add the penalty to the fitness value.
evaFitness() returns the total number of duplicate position pair (with penalty) plus the total number of distinct pairs of queens that attack each other.

#fitness function
def evaFitness(individual):
    
    individual = board_representation_2d(individual)
    conflict = 0

    for i in range(0, len(individual)-1):
      for k in range(i, len(individual)-1):
        ax, ay, bx, by = (individual[i][0], individual[i][1], individual[k+1][0], individual[k+1][1])
        # print('For run ', k, ' (ax, ay)=(', ax,', ', ay, ') ', '(bx, by)=(', bx, ', ', by, ')')
        if(ax == bx or ay == by or (bx-ax == by-ay) or (ax-bx == by-ay)):
          conflict = conflict + 1

    return (checkDuplicate(individual)*50 + conflict,)

def board_representation_2d(individual):
  n = []
  for i in individual:
      n.append([int(i//8), int(i%8)])
  return n
    
    
# Calculate the number of queen pairs in the same position for any given board
def checkDuplicate(individual):
    dups = 0
    for i in range(0,len(individual)):
      for k in range(i, len(individual)-1):
        if(individual[k+1] == individual[i]):
          dups = dups + 1
    return dups

board = create_individual()
show_grid(board)

print('duplicates: ', checkDuplicate(board))
print('conflicts: ', evaFitness(board))

-|-|-|-|-|-|-|-|
----------------
-|X|-|-|-|-|-|-|
----------------
-|-|-|X|-|-|-|-|
----------------
-|-|X|-|-|-|X|X|
----------------
-|-|-|X|-|-|-|X|
----------------
-|-|-|-|-|-|-|-|
----------------
-|-|-|-|-|-|-|-|
----------------
-|-|-|X|-|-|-|-|
----------------
duplicates:  0
conflicts:  (12,)

5 pts: Writer your code in the cell below to register "evaluate" function to toolbox

Mutation: mutUniformInt Crossover: cxTwoPoint Population size: 1000 Generations: 100

toolbox.register("evaluate", evaFitness)

toolbox.register("mate", tools.cxTwoPoint)

toolbox.register("mutate", tools.mutUniformInt, low = 0, up = 63, indpb=0.1)

toolbox.register("select", tools.selTournament, tournsize=3)

stats = tools.Statistics(key=lambda ind: ind.fitness.values)

stats.register("avg", np.mean)
stats.register("min", np.min)

10 pts: Writer your code in the cell below to create the first generation, the hall of fame, and launch the genetic algorithm: eaSimple(). How many individuals you want to have for each generation and how many generations you want GA to go thourgh for each run? Vary those two parameters to see the change.

import matplotlib.pyplot as plt
%matplotlib inline 
pop = toolbox.population(n=1000)

hof = tools.HallOfFame(maxsize=1)

pop, log = algorithms.eaSimple(pop, toolbox, cxpb=0.5, mutpb=0.1, ngen=100, stats=stats, halloffame=hof, verbose=True)

gen	nevals	avg   	min
0  	1000  	10.236	4  
1  	531   	12.05 	3  
2  	549   	10.662	3  
3  	566   	9.437 	3  
4  	531   	9.53  	2  
5  	553   	8.725 	1  
6  	553   	8.603 	1  
7  	594   	7.764 	1  
8  	567   	7.565 	1  
9  	571   	6.893 	1  
10 	524   	6.028 	1  
11 	563   	5.823 	1  
12 	546   	5.559 	1  
13 	569   	4.889 	1  
14 	547   	4.745 	1  
15 	535   	3.505 	1  
16 	566   	2.621 	1  
17 	552   	1.999 	1  
18 	564   	1.612 	1  
19 	542   	1.508 	1  
20 	544   	1.387 	1  
21 	526   	1.579 	1  
22 	556   	1.499 	1  
23 	528   	1.5   	1  
24 	571   	1.697 	1  
25 	540   	1.913 	1  
26 	529   	1.627 	1  
27 	575   	1.403 	1  
28 	557   	2.05  	1  
29 	574   	1.413 	1  
30 	526   	1.591 	1  
31 	527   	1.657 	1  
32 	551   	1.629 	1  
33 	545   	1.952 	1  
34 	545   	1.636 	1  
35 	585   	1.625 	1  
36 	577   	1.772 	1  
37 	573   	1.541 	1  
38 	558   	1.631 	1  
39 	586   	1.652 	1  
40 	524   	1.63  	1  
41 	584   	1.565 	1  
42 	561   	1.594 	1  
43 	557   	1.418 	1  
44 	557   	1.531 	1  
45 	550   	1.476 	1  
46 	524   	1.62  	1  
47 	548   	1.72  	1  
48 	583   	1.743 	1  
49 	514   	1.527 	1  
50 	579   	1.462 	1  
51 	553   	1.629 	1  
52 	539   	1.397 	1  
53 	508   	1.498 	1  
54 	538   	1.462 	1  
55 	536   	1.479 	1  
56 	550   	1.904 	1  
57 	566   	1.566 	1  
58 	528   	1.415 	1  
59 	541   	1.485 	1  
60 	550   	1.413 	1  
61 	523   	1.583 	1  
62 	537   	1.873 	1  
63 	553   	1.3   	1  
64 	529   	1.298 	1  
65 	499   	1.516 	1  
66 	571   	1.654 	1  
67 	568   	1.769 	1  
68 	562   	1.346 	1  
69 	538   	1.618 	1  
70 	568   	1.779 	1  
71 	508   	1.63  	1  
72 	592   	1.595 	1  
73 	573   	1.497 	1  
74 	540   	1.626 	1  
75 	530   	1.634 	1  
76 	521   	1.687 	1  
77 	548   	1.508 	1  
78 	552   	1.362 	1  
79 	549   	1.818 	1  
80 	569   	1.692 	1  
81 	611   	1.754 	1  
82 	560   	1.565 	1  
83 	581   	1.581 	1  
84 	515   	1.758 	1  
85 	564   	1.341 	1  
86 	549   	1.562 	1  
87 	545   	1.751 	1  
88 	541   	1.395 	1  
89 	544   	1.547 	1  
90 	556   	1.396 	1  
91 	522   	1.306 	1  
92 	551   	1.708 	1  
93 	556   	1.309 	1  
94 	557   	1.831 	1  
95 	542   	1.621 	1  
96 	564   	1.601 	1  
97 	565   	1.914 	1  
98 	562   	1.579 	1  
99 	541   	1.542 	1  
100	517   	1.799 	1

# Print out the last generation

pop

[[0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 22, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 19, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 3, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 3, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 40, 31, 33, 44, 50, 18],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 7, 19, 51, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 35, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 33, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 13, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 35, 31, 33, 44, 50, 61],
 [0, 14, 20, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 47],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 3, 44, 50, 56],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 13, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 3, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 51, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 54, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 20],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
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 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
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 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
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 [0, 52, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
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 [0, 14, 19, 31, 33, 44, 50, 60],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 20, 19, 26, 7, 44, 50, 57],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
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 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
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 [0, 14, 19, 31, 39, 44, 50, 61],
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 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
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 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 9, 31, 28, 44, 26, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 27, 12, 23, 50, 9],
 [0, 14, 20, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 0, 19, 31, 39, 44, 50, 31],
 [42, 14, 26, 31, 33, 44, 50, 61],
 [0, 14, 19, 7, 33, 44, 30, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 6, 47, 31, 49, 48, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 3, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 3, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [26, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 3, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 10, 31, 33, 44, 50, 61],
 [0, 14, 63, 31, 33, 44, 48, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 39, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [59, 14, 13, 31, 61, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61],
 [0, 14, 19, 31, 33, 44, 50, 61]]

5 pts: Plot the "avg" and "min" for each generation

import matplotlib.pyplot as plt
%matplotlib inline  

gen, avg, min_= log.select("gen", "avg", "min")

plt.plot(gen, avg, label="average")
plt.plot(gen, min_, label="minimum")
plt.xlabel("Generation")
plt.ylabel("Fitness")
plt.legend(loc="lower right")
plt.show()

5 pts: Print out the best individual found and its fitness value. Show the best individual as chessboard

best_ind = tools.selBest(pop, k=1)[0]

print('Best individual is:', best_ind)

show_grid(best_ind)

Best individual is: [0, 14, 19, 31, 33, 44, 50, 61]
X|-|-|-|-|-|-|-|
----------------
-|-|-|-|-|-|X|-|
----------------
-|-|-|X|-|-|-|-|
----------------
-|-|-|-|-|-|-|X|
----------------
-|X|-|-|-|-|-|-|
----------------
-|-|-|-|X|-|-|-|
----------------
-|-|X|-|-|-|-|-|
----------------
-|-|-|-|-|X|-|-|
----------------

print('With fitness: ', toolbox.evaluate(best_ind))

With fitness:  (1,)

Mutation: mutUniformInt Crossover: cxOnePoint Population size: 100 Generations: 10

toolbox.register("evaluate", evaFitness)
toolbox.register("mate", tools.cxOnePoint)

toolbox.register("mutate", tools.mutUniformInt, low = 0, up = 63, indpb=0.1)

toolbox.register("select", tools.selTournament, tournsize=3)

stats = tools.Statistics(key=lambda ind: ind.fitness.values)

stats.register("avg", np.mean)
stats.register("min", np.min)

import matplotlib.pyplot as plt
%matplotlib inline 
pop = toolbox.population(n=100)

hof = tools.HallOfFame(maxsize=1)

pop, log = algorithms.eaSimple(pop, toolbox, cxpb=0.5, mutpb=0.1, ngen=100, stats=stats, halloffame=hof, verbose=True)

gen	nevals	avg  	min
0  	100   	10.26	5  
1  	55    	10.15	5  
2  	60    	11.16	5  
3  	66    	9.8  	4  
4  	48    	8.12 	5  
5  	59    	7.94 	4  
6  	48    	7.71 	3  
7  	67    	6.73 	3  
8  	57    	4.91 	3  
9  	60    	5.54 	3  
10 	57    	4.92 	1  
11 	61    	3.54 	2  
12 	55    	4.67 	2  
13 	49    	3.47 	2  
14 	51    	2.67 	2  
15 	60    	2.49 	2  
16 	56    	2.32 	2  
17 	52    	4.83 	2  
18 	60    	2.3  	2  
19 	43    	2.7  	2  
20 	62    	4.04 	2  
21 	47    	2.28 	2  
22 	50    	2.29 	2  
23 	46    	2.75 	2  
24 	59    	3.18 	2  
25 	47    	2.84 	2  
26 	50    	2.29 	2  
27 	57    	2.7  	2  
28 	52    	2.68 	2  
29 	65    	2.2  	2  
30 	58    	2.24 	2  
31 	55    	2.11 	2  
32 	55    	2.77 	2  
33 	52    	2.08 	2  
34 	46    	2.1  	2  
35 	49    	3.2  	2  
36 	54    	2.06 	2  
37 	63    	2.69 	2  
38 	57    	2.13 	2  
39 	63    	2.1  	2  
40 	61    	2.59 	2  
41 	55    	2.73 	2  
42 	59    	2.68 	2  
43 	59    	3.37 	2  
44 	56    	2.04 	2  
45 	45    	2.03 	2  
46 	46    	2.58 	2  
47 	47    	2.61 	2  
48 	66    	3.16 	2  
49 	59    	2.16 	2  
50 	49    	2.17 	2  
51 	51    	2.22 	2  
52 	56    	2.24 	2  
53 	44    	2.6  	2  
54 	56    	3.86 	2  
55 	51    	2.15 	2  
56 	62    	3.12 	2  
57 	56    	2.6  	2  
58 	61    	2.59 	2  
59 	67    	2.68 	2  
60 	40    	2.14 	2  
61 	66    	2.12 	2  
62 	64    	2.23 	2  
63 	51    	2.61 	2  
64 	45    	3.16 	2  
65 	67    	2.61 	2  
66 	61    	3.12 	2  
67 	63    	2.19 	2  
68 	59    	2.64 	2  
69 	43    	3.12 	2  
70 	54    	2.6  	2  
71 	62    	2.73 	2  
72 	56    	2.3  	2  
73 	49    	2.34 	2  
74 	58    	2.55 	2  
75 	45    	2.15 	2  
76 	52    	2.09 	2  
77 	47    	2.07 	2  
78 	59    	3.23 	2  
79 	55    	2.74 	2  
80 	54    	2.67 	2  
81 	49    	3.17 	2  
82 	51    	2.19 	2  
83 	58    	2.09 	2  
84 	54    	3.17 	2  
85 	49    	3.17 	2  
86 	58    	2.68 	2  
87 	64    	2.72 	2  
88 	54    	2.65 	2  
89 	45    	2.53 	2  
90 	54    	2.13 	2  
91 	58    	2.11 	2  
92 	58    	3.1  	2  
93 	45    	3.14 	2  
94 	63    	3.14 	2  
95 	62    	2.69 	2  
96 	53    	2.76 	2  
97 	57    	2.16 	2  
98 	51    	2.54 	2  
99 	67    	2.15 	2  
100	54    	2.14 	2

import matplotlib.pyplot as plt
%matplotlib inline  

gen, avg, min_= log.select("gen", "avg", "min")

plt.plot(gen, avg, label="average")
plt.plot(gen, min_, label="minimum")
plt.xlabel("Generation")
plt.ylabel("Fitness")
plt.legend(loc="lower right")
plt.show()

best_ind = tools.selBest(pop, k=1)[0]

print('Best individual is:', best_ind)

show_grid(best_ind)

Best individual is: [0, 13, 17, 25, 38, 42, 55, 60]
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print('With fitness: ', toolbox.evaluate(best_ind))

With fitness:  (2,)

Mutation: mutShuffleIndexes Crossover: cxTwoPoint Population size: 200 Generations: 20

toolbox.register("evaluate", evaFitness)
toolbox.register("mate", tools.cxTwoPoint)

toolbox.register("mutate", tools.mutShuffleIndexes, indpb=0.1) #low = 0, up = 63,

toolbox.register("select", tools.selTournament, tournsize=3)

stats = tools.Statistics(key=lambda ind: ind.fitness.values)

stats.register("avg", np.mean)
stats.register("min", np.min)

import matplotlib.pyplot as plt
%matplotlib inline 
pop = toolbox.population(n=200)

hof = tools.HallOfFame(maxsize=1)

pop, log = algorithms.eaSimple(pop, toolbox, cxpb=0.5, mutpb=0.1, ngen=20, stats=stats, halloffame=hof, verbose=True)

gen	nevals	avg   	min
0  	200   	10.135	4  
1  	95    	13.145	4  
2  	126   	9.63  	4  
3  	95    	10.62 	4  
4  	113   	9.255 	3  
5  	102   	7.17  	3  
6  	112   	7.02  	3  
7  	100   	6.71  	3  
8  	118   	7.16  	3  
9  	103   	5.9   	3  
10 	107   	7.01  	2  
11 	123   	7.295 	2  
12 	113   	5.915 	2  
13 	113   	7.605 	2  
14 	95    	6.7   	2  
15 	105   	6.77  	2  
16 	116   	10.315	2  
17 	105   	9.345 	2  
18 	117   	11.425	2  
19 	101   	6.055 	2  
20 	106   	9.275 	2

import matplotlib.pyplot as plt
%matplotlib inline  

gen, avg, min_= log.select("gen", "avg", "min")

plt.plot(gen, avg, label="average")
plt.plot(gen, min_, label="minimum")
plt.xlabel("Generation")
plt.ylabel("Fitness")
plt.legend(loc="lower right")
plt.show()

best_ind = tools.selBest(pop, k=1)[0]

print('Best individual is:', best_ind)

show_grid(best_ind)
print('With fitness: ', toolbox.evaluate(best_ind))

Best individual is: [6, 10, 23, 25, 33, 47, 59, 53]
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With fitness:  (2,)

Part II: Row-index-based board representation

import random
import numpy as np
from deap import algorithms, base, creator, tools

creator.create("FitnessMin", base.Fitness, weights=(-1.0,))
creator.create("Individual", list, fitness=creator.FitnessMin)

/usr/local/lib/python3.7/dist-packages/deap/creator.py:141: RuntimeWarning: A class named 'FitnessMin' has already been created and it will be overwritten. Consider deleting previous creation of that class or rename it.
  RuntimeWarning)
/usr/local/lib/python3.7/dist-packages/deap/creator.py:141: RuntimeWarning: A class named 'Individual' has already been created and it will be overwritten. Consider deleting previous creation of that class or rename it.
  RuntimeWarning)

Each row of the chess row is indexed from 0->7 . we place different queens on different rows initially. The sequence [ a b c d .... ] means that in $0^{th}$ row, $a^{th}$ column, the queen is present and so on

toolbox = base.Toolbox()

toolbox.register("attr_int", random.randint, 0, 7)
toolbox.register("individual", tools.initRepeat, creator.Individual,
                 toolbox.attr_int, n=8)

toolbox.individual()

[5, 3, 2, 3, 0, 2, 5, 5]

def show_grid(board):
    
    n = [0]*64
    
    for i in range(len(board)):
        n[board[i] + i*8] = 1
      
    
    for i in range(8):
        for j in range(64):
            if j // 8 == i:
                if n[j] == 1:
                    print('X',end="|")
                else:
                    print('-',end="|")
        print()
        print("----------------")

toolbox.register("population", tools.initRepeat, list, toolbox.individual)

pop = toolbox.population(n=5)

print(pop[0])

[5, 2, 7, 1, 1, 0, 0, 0]

show_grid(pop[0])

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10 pts: Write your code in the cell below to define the "evaFitness" function, which return the fitness of any given board

evaFitness() returns the total number of distinct pairs of queens that attack each other.
The following are some test cases you may use to verify the correctness of the evaFitness() function:

evaFitness([0, 2, 6, 7, 7, 4, 1, 6]) should return (4,)
evaFitness([7, 5, 2, 4, 3, 1, 3, 5]) should return (6,)
evaFitness([3, 1, 6, 0, 5, 7, 2, 1]) should return (5,)
evaFitness([7, 3, 1, 4, 5, 1, 3, 5]) should return (6,)

#fitness function
def evaFitness(individual):
    
    individual = board_representation_2d(individual)

    conflict = 0

    for i in range(0, len(individual)-1):
      ax,ay = (individual[i][1], individual[i][0])
      axDP = ax
      ayDP = ay
      while(not(ayDP + 1 > 7 or axDP + 1 > 7)):
        axDP = axDP + 1
        ayDP = ayDP + 1
        for j in range(i+1, len(individual)):
          if(axDP == individual[j][1] and ayDP == individual[j][0]):
            conflict = conflict + 1
      axDP = ax
      ayDP = ay
      while(not(ayDP + 1 > 7 or axDP - 1 < 0)):
        axDP = axDP - 1
        ayDP = ayDP + 1
        for e in range(i+1, len(individual)):
          if(axDP == individual[e][1] and ayDP == individual[e][0]):
            conflict = conflict + 1
      for k in range(i+1, len(individual)):
        bx, by = (individual[k][1], individual[k][0])
        if(ax == bx):
          conflict = conflict + 1
          

    return (checkDuplicate(individual)*50 + conflict,)

def board_representation_2d(individual):

  n = []
  k = 0
  for i in individual:
      n.append([k, int(i%8)])
      k = k + 1
        
  return n
    
    
# Calculate the number of queen pairs in the same position for any given board
def checkDuplicate(individual):
    dups = 0
    for i in range(0,len(individual)):
      for k in range(i, len(individual)-1):
        if(individual[k+1] == individual[i]):
          dups = dups + 1
          break
    return dups

board = [3, 1, 6, 0, 5, 7, 2, 1]
print(board_representation_2d(board))
show_grid(board)

# print('duplicates: ', checkDuplicate(board))
print('conflicts: ', evaFitness(board))

[[0, 3], [1, 1], [2, 6], [3, 0], [4, 5], [5, 7], [6, 2], [7, 1]]
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conflicts:  (5,)

5 pts: Writer your code in the cell below to register "evaluate" function to toolbox

Mutation: mutUniformInt Crossover: cxTwoPoint Population size: 1000 Generations: 100

toolbox.register("evaluate", evaFitness)

toolbox.register("mate", tools.cxTwoPoint)

toolbox.register("mutate", tools.mutUniformInt, low = 0, up = 7, indpb=0.1)

toolbox.register("select", tools.selTournament, tournsize=3)

stats = tools.Statistics(key=lambda ind: ind.fitness.values)


stats.register("avg", np.mean)
stats.register("min", np.min)

10 pts: Writer your code in the cell below to create the first generation, the hall of fame, and launch the genetic algorithm: eaSimple(). How many individuals you want to have for each generation and how many generations you want GA to go thourgh for each run? Vary those two parameters to see the change.

import matplotlib.pyplot as plt
%matplotlib inline 
pop = toolbox.population(n=1000)

hof = tools.HallOfFame(maxsize=1)

pop, log = algorithms.eaSimple(pop, toolbox, cxpb=0.5, mutpb=0.1, ngen=100, stats=stats, halloffame=hof, verbose=True)

gen	nevals	avg  	min
0  	1000  	7.894	2  
1  	529   	6.44 	2  
2  	504   	5.563	1  
3  	559   	5.102	2  
4  	546   	4.631	1  
5  	548   	4.222	1  
6  	519   	3.914	1  
7  	552   	3.786	1  
8  	569   	3.707	0  
9  	577   	3.484	0  
10 	540   	3.326	0  
11 	555   	3.143	0  
12 	555   	3.056	0  
13 	560   	2.852	0  
14 	556   	2.63 	0  
15 	543   	2.415	0  
16 	564   	2.218	0  
17 	557   	2.007	0  
18 	550   	1.816	0  
19 	527   	1.859	0  
20 	584   	1.838	0  
21 	577   	1.624	0  
22 	510   	1.394	0  
23 	568   	1.175	0  
24 	583   	1.063	0  
25 	553   	0.783	0  
26 	584   	0.594	0  
27 	521   	0.385	0  
28 	564   	0.262	0  
29 	543   	0.209	0  
30 	519   	0.151	0  
31 	578   	0.174	0  
32 	512   	0.186	0  
33 	546   	0.166	0  
34 	569   	0.159	0  
35 	553   	0.201	0  
36 	580   	0.158	0  
37 	531   	0.148	0  
38 	586   	0.128	0  
39 	554   	0.141	0  
40 	585   	0.137	0  
41 	520   	0.143	0  
42 	574   	0.171	0  
43 	569   	0.128	0  
44 	528   	0.155	0  
45 	545   	0.17 	0  
46 	497   	0.154	0  
47 	548   	0.133	0  
48 	522   	0.17 	0  
49 	539   	0.18 	0  
50 	540   	0.114	0  
51 	558   	0.13 	0  
52 	546   	0.141	0  
53 	517   	0.118	0  
54 	596   	0.157	0  
55 	565   	0.184	0  
56 	531   	0.114	0  
57 	564   	0.125	0  
58 	575   	0.123	0  
59 	532   	0.183	0  
60 	572   	0.117	0  
61 	556   	0.167	0  
62 	522   	0.195	0  
63 	593   	0.15 	0  
64 	533   	0.11 	0  
65 	511   	0.086	0  
66 	552   	0.135	0  
67 	546   	0.128	0  
68 	532   	0.155	0  
69 	542   	0.139	0  
70 	535   	0.145	0  
71 	562   	0.128	0  
72 	545   	0.14 	0  
73 	547   	0.112	0  
74 	510   	0.153	0  
75 	575   	0.19 	0  
76 	514   	0.112	0  
77 	598   	0.128	0  
78 	570   	0.098	0  
79 	557   	0.128	0  
80 	589   	0.148	0  
81 	551   	0.139	0  
82 	542   	0.139	0  
83 	536   	0.155	0  
84 	546   	0.17 	0  
85 	561   	0.151	0  
86 	534   	0.143	0  
87 	522   	0.172	0  
88 	518   	0.14 	0  
89 	538   	0.172	0  
90 	542   	0.172	0  
91 	560   	0.159	0  
92 	552   	0.195	0  
93 	526   	0.122	0  
94 	584   	0.129	0  
95 	560   	0.14 	0  
96 	542   	0.143	0  
97 	546   	0.142	0  
98 	531   	0.19 	0  
99 	573   	0.147	0  
100	543   	0.116	0

5 pts: Plot the "avg" and "min" for each generation

# Plot the "avg" and "min" for each generation

import matplotlib.pyplot as plt
%matplotlib inline   

gen, avg, min_= log.select("gen", "avg", "min")

plt.plot(gen, avg, label="average")
plt.plot(gen, min_, label="minimum")
plt.xlabel("Generation")
plt.ylabel("Fitness")
plt.legend(loc="lower right")
plt.show()

5 pts: Print out the best individual found and its fitness value. Show the best individual as chessboard

best_ind = tools.selBest(pop, k=1)[0]

print('Best individual is:', best_ind)

show_grid(best_ind)

print('With fitness: ', toolbox.evaluate(best_ind))

Best individual is: [7, 1, 3, 0, 6, 4, 2, 5]
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With fitness:  (0,)

Mutation: mutUniformInt Crossover: cxOnePoint Population size: 100 Generations: 10

toolbox.register("evaluate", evaFitness)
toolbox.register("mate", tools.cxOnePoint)

toolbox.register("mutate", tools.mutUniformInt, low = 0, up = 63, indpb=0.1)

toolbox.register("select", tools.selTournament, tournsize=3)

stats = tools.Statistics(key=lambda ind: ind.fitness.values)

stats.register("avg", np.mean)
stats.register("min", np.min)

import matplotlib.pyplot as plt
%matplotlib inline 
pop = toolbox.population(n=100)

hof = tools.HallOfFame(maxsize=1)

pop, log = algorithms.eaSimple(pop, toolbox, cxpb=0.5, mutpb=0.1, ngen=100, stats=stats, halloffame=hof, verbose=True)

gen	nevals	avg	min
0  	100   	9.9	5  
1  	66    	10.7	4  
2  	59    	10.13	4  
3  	60    	6.69 	3  
4  	53    	5.61 	3  
5  	52    	7.24 	3  
6  	46    	5.45 	3  
7  	64    	4.91 	3  
8  	51    	3.78 	3  
9  	37    	4.61 	3  
10 	63    	3.61 	3  
11 	60    	4.19 	3  
12 	50    	4.57 	3  
13 	46    	3.78 	3  
14 	64    	4.17 	3  
15 	44    	4.12 	1  
16 	54    	4.11 	1  
17 	55    	3.42 	1  
18 	52    	2.54 	1  
19 	61    	2.1  	1  
20 	60    	2.33 	1  
21 	30    	1.13 	1  
22 	63    	1.03 	1  
23 	56    	1.25 	1  
24 	69    	1.64 	1  
25 	55    	1.09 	1  
26 	48    	1.6  	1  
27 	64    	1.81 	1  
28 	48    	1.21 	1  
29 	56    	1.33 	1  
30 	53    	1.18 	1  
31 	60    	1.77 	1  
32 	61    	2.68 	1  
33 	54    	1.14 	1  
34 	53    	1.75 	1  
35 	58    	2.23 	1  
36 	47    	1.07 	1  
37 	49    	1.13 	1  
38 	50    	1.55 	1  
39 	42    	1.67 	1  
40 	58    	1.71 	1  
41 	50    	3.23 	1  
42 	60    	1.14 	1  
43 	59    	1.62 	1  
44 	56    	1.68 	1  
45 	44    	1.62 	1  
46 	53    	1.87 	1  
47 	65    	2.23 	1  
48 	47    	1.14 	1  
49 	57    	1.1  	1  
50 	62    	2.19 	1  
51 	53    	2.15 	1  
52 	68    	1.65 	1  
53 	59    	1.73 	1  
54 	63    	1.62 	1  
55 	58    	1.25 	1  
56 	45    	1.07 	1  
57 	58    	2.22 	1  
58 	51    	1.52 	1  
59 	60    	1.62 	1  
60 	56    	1.06 	1  
61 	47    	2.12 	1  
62 	41    	1.24 	1  
63 	53    	2.2  	1  
64 	56    	1.1  	1  
65 	44    	1.57 	1  
66 	51    	1.17 	1  
67 	53    	1.2  	1  
68 	60    	1.12 	1  
69 	62    	2.92 	1  
70 	58    	1.03 	1  
71 	48    	1.12 	1  
72 	60    	1.81 	1  
73 	56    	1.15 	1  
74 	60    	1.06 	1  
75 	54    	1.64 	1  
76 	50    	1.11 	1  
77 	50    	1.82 	1  
78 	55    	1.14 	1  
79 	62    	1.71 	1  
80 	56    	1.78 	1  
81 	58    	1.82 	1  
82 	60    	1.23 	1  
83 	51    	1.35 	1  
84 	42    	1.1  	1  
85 	60    	1.74 	1  
86 	60    	1.02 	1  
87 	51    	1.58 	1  
88 	58    	1.09 	1  
89 	51    	1.08 	1  
90 	65    	1.18 	1  
91 	49    	1.7  	1  
92 	51    	2.2  	1  
93 	55    	1.59 	1  
94 	47    	2.07 	1  
95 	48    	1.69 	1  
96 	62    	2.43 	1  
97 	47    	1.71 	1  
98 	52    	1.21 	1  
99 	45    	2.22 	1  
100	71    	1.68 	1

import matplotlib.pyplot as plt
%matplotlib inline  

gen, avg, min_= log.select("gen", "avg", "min")

plt.plot(gen, avg, label="average")
plt.plot(gen, min_, label="minimum")
plt.xlabel("Generation")
plt.ylabel("Fitness")
plt.legend(loc="lower right")
plt.show()

best_ind = tools.selBest(pop, k=1)[0]

print('Best individual is:', best_ind)

show_grid(best_ind)
print('With fitness: ', toolbox.evaluate(best_ind))

Best individual is: [0, 46, 15, 20, 26, 32, 51, 61]
X|-|-|-|-|-|-|-|
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With fitness:  (1,)

Mutation: mutShuffleIndexes Crossover: cxTwoPoint Population size: 200 Generations: 20

toolbox.register("evaluate", evaFitness)
toolbox.register("mate", tools.cxTwoPoint)

toolbox.register("mutate", tools.mutShuffleIndexes, indpb=0.1) #low = 0, up = 63,

toolbox.register("select", tools.selTournament, tournsize=3)

stats = tools.Statistics(key=lambda ind: ind.fitness.values)

stats.register("avg", np.mean)
stats.register("min", np.min)

import matplotlib.pyplot as plt
%matplotlib inline 
pop = toolbox.population(n=200)

hof = tools.HallOfFame(maxsize=1)

pop, log = algorithms.eaSimple(pop, toolbox, cxpb=0.5, mutpb=0.1, ngen=20, stats=stats, halloffame=hof, verbose=True)

gen	nevals	avg   	min
0  	200   	10.105	4  
1  	121   	9.97  	4  
2  	119   	10.82 	4  
3  	115   	8.425 	3  
4  	106   	9.75  	3  
5  	115   	8.235 	3  
6  	95    	6.945 	2  
7  	117   	6.615 	2  
8  	92    	5.07  	2  
9  	113   	6.005 	2  
10 	109   	7.99  	2  
11 	104   	5.655 	2  
12 	118   	4.77  	2  
13 	96    	4.97  	1  
14 	90    	6.765 	1  
15 	113   	6.265 	1  
16 	94    	6.915 	1  
17 	120   	6.675 	1  
18 	124   	8.135 	1  
19 	97    	8.355 	1  
20 	113   	6.875 	1

import matplotlib.pyplot as plt
%matplotlib inline  

gen, avg, min_= log.select("gen", "avg", "min")

plt.plot(gen, avg, label="average")
plt.plot(gen, min_, label="minimum")
plt.xlabel("Generation")
plt.ylabel("Fitness")
plt.legend(loc="lower right")
plt.show()

best_ind = tools.selBest(pop, k=1)[0]

print('Best individual is:', best_ind)

show_grid(best_ind)
print('With fitness: ', toolbox.evaluate(best_ind))

Best individual is: [0, 10, 26, 23, 38, 43, 49, 60]
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With fitness:  (1,)

Reflection: Which board representaion is better in terms of ease of coding and final solution quality? Try different parameter values for mutation and crossover and vary the number of generations and the population size. Write your findings in the report.

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Project 4: Solving N-Queens Problem using Genetic Algorithms

CSC 180 Intelligent Systems

Dr. Haiquan Chen, California State University, Sacramento

Part I: Position-index-based board representation

10 pts: Write your code in the cell below to define the "evaFitness" function, which returns the fitness of any given board.

5 pts: Writer your code in the cell below to register "evaluate" function to toolbox

5 pts: Plot the "avg" and "min" for each generation

5 pts: Print out the best individual found and its fitness value. Show the best individual as chessboard

Part II: Row-index-based board representation

10 pts: Write your code in the cell below to define the "evaFitness" function, which return the fitness of any given board

5 pts: Writer your code in the cell below to register "evaluate" function to toolbox

5 pts: Plot the "avg" and "min" for each generation

5 pts: Print out the best individual found and its fitness value. Show the best individual as chessboard

Reflection: Which board representaion is better in terms of ease of coding and final solution quality? Try different parameter values for mutation and crossover and vary the number of generations and the population size. Write your findings in the report.

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Project 4: Solving N-Queens Problem using Genetic Algorithms

CSC 180 Intelligent Systems

Dr. Haiquan Chen, California State University, Sacramento

Part I: Position-index-based board representation

10 pts: Write your code in the cell below to define the "evaFitness" function, which returns the fitness of any given board.

5 pts: Writer your code in the cell below to register "evaluate" function to toolbox

5 pts: Plot the "avg" and "min" for each generation

5 pts: Print out the best individual found and its fitness value. Show the best individual as chessboard

Part II: Row-index-based board representation

10 pts: Write your code in the cell below to define the "evaFitness" function, which return the fitness of any given board

5 pts: Writer your code in the cell below to register "evaluate" function to toolbox

5 pts: Plot the "avg" and "min" for each generation

5 pts: Print out the best individual found and its fitness value. Show the best individual as chessboard

Reflection: Which board representaion is better in terms of ease of coding and final solution quality? Try different parameter values for mutation and crossover and vary the number of generations and the population size. Write your findings in the report.

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