Implementation of Whale Optimization Algorithm

# python implementation of whale optimization algorithm (WOA)
# minimizing rastrigin and sphere function


import random
import math  # cos() for Rastrigin
import copy  # array-copying convenience
import sys  # max float


# -------fitness functions---------

# rastrigin function
def fitness_rastrigin(position):
    fitness_value = 0.0
    for i in range(len(position)):
        xi = position[i]
        fitness_value += (xi * xi) - (10 * math.cos(2 * math.pi * xi)) + 10
    return fitness_value


# sphere function
def fitness_sphere(position):
    fitness_value = 0.0
    for i in range(len(position)):
        xi = position[i]
        fitness_value += (xi * xi);
    return fitness_value;


# -------------------------


# whale class
class whale:
    def __init__(self, fitness, dim, minx, maxx, seed):
        self.rnd = random.Random(seed)
        self.position = [0.0 for i in range(dim)]

        for i in range(dim):
            self.position[i] = ((maxx - minx) * self.rnd.random() + minx)

        self.fitness = fitness(self.position)  # curr fitness


# whale optimization algorithm(WOA)
def woa(fitness, max_iter, n, dim, minx, maxx):
    rnd = random.Random(0)

    # create n random whales
    whalePopulation = [whale(fitness, dim, minx, maxx, i) for i in range(n)]

    # compute the value of best_position and best_fitness in the whale Population
    Xbest = [0.0 for i in range(dim)]
    Fbest = sys.float_info.max

    for i in range(n):  # check each whale
        if whalePopulation[i].fitness < Fbest:
            Fbest = whalePopulation[i].fitness
            Xbest = copy.copy(whalePopulation[i].position)

    # main loop of woa
    Iter = 0
    while Iter < max_iter:

        # after every 10 iterations
        # print iteration number and best fitness value so far
        if Iter % 10 == 0 and Iter > 1:
            print("Iter = " + str(Iter) + " best fitness = %.3f" % Fbest)

        # linearly decreased from 2 to 0
        a = 2 * (1 - Iter / max_iter)
        a2=-1+Iter*((-1)/max_iter)

        for i in range(n):
            A = 2 * a * rnd.random() - a
            C = 2 * rnd.random()
            b = 1
            l = (a2-1)*rnd.random()+1;
            p = rnd.random()

            D = [0.0 for i in range(dim)]
            D1 = [0.0 for i in range(dim)]
            Xnew = [0.0 for i in range(dim)]
            Xrand = [0.0 for i in range(dim)]
            if p < 0.5:
                if abs(A) > 1:
                    for j in range(dim):
                        D[j] = abs(C * Xbest[j] - whalePopulation[i].position[j])
                        Xnew[j] = Xbest[j] - A * D[j]
                else:
                    p = random.randint(0, n - 1)
                    while (p == i):
                        p = random.randint(0, n - 1)

                    Xrand = whalePopulation[p].position

                    for j in range(dim):
                        D[j] = abs(C * Xrand[j] - whalePopulation[i].position[j])
                        Xnew[j] = Xrand[j] - A * D[j]
            else:
                for j in range(dim):
                    D1[j] = abs(Xbest[j] - whalePopulation[i].position[j])
                    Xnew[j] = D1[j] * math.exp(b * l) * math.cos(2 * math.pi * l) + Xbest[j]

            for j in range(dim):
                whalePopulation[i].position[j] = Xnew[j]

        for i in range(n):
            # if Xnew < minx OR Xnew > maxx
            # then clip it
            for j in range(dim):
                whalePopulation[i].position[j] = max(whalePopulation[i].position[j], minx)
                whalePopulation[i].position[j] = min(whalePopulation[i].position[j], maxx)

            whalePopulation[i].fitness = fitness(whalePopulation[i].position)

            if (whalePopulation[i].fitness < Fbest):
                Xbest = copy.copy(whalePopulation[i].position)
                Fbest = whalePopulation[i].fitness


        Iter += 1
    # end-while

    # returning the best solution
    return Xbest


# ----------------------------


# Driver code for rastrigin function

print("\nBegin whale optimization algorithm on rastrigin function\n")
dim = 3
fitness = fitness_rastrigin

print("Goal is to minimize Rastrigin's function in " + str(dim) + " variables")
print("Function has known min = 0.0 at (", end="")
for i in range(dim - 1):
    print("0, ", end="")
print("0)")

num_whales = 50
max_iter = 100

print("Setting num_whales = " + str(num_whales))
print("Setting max_iter    = " + str(max_iter))
print("\nStarting WOA algorithm\n")

best_position = woa(fitness, max_iter, num_whales, dim, -10.0, 10.0)

print("\nWOA completed\n")
print("\nBest solution found:")
print(["%.6f" % best_position[k] for k in range(dim)])
err = fitness(best_position)
print("fitness of best solution = %.6f" % err)

print("\nEnd WOA for rastrigin\n")

print()
print()

# Driver code for Sphere function
print("\nBegin whale optimization algorithm on sphere function\n")
dim = 3
fitness = fitness_sphere

print("Goal is to minimize sphere function in " + str(dim) + " variables")
print("Function has known min = 0.0 at (", end="")
for i in range(dim - 1):
    print("0, ", end="")
print("0)")

num_whales = 50
max_iter = 100

print("Setting num_whales = " + str(num_whales))
print("Setting max_iter    = " + str(max_iter))
print("\nStarting WOA algorithm\n")

best_position = woa(fitness, max_iter, num_whales, dim, -10.0, 10.0)

print("\nWOA completed\n")
print("\nBest solution found:")
print(["%.6f" % best_position[k] for k in range(dim)])
err = fitness(best_position)
print("fitness of best solution = %.6f" % err)

print("\nEnd WOA for sphere\n")