Dr.PandaHello everyone. In this video, I’m going to show you a Python code of Particle Swarm Optimization (PSO) algorithm and test its performance in solving 2 simple optimization problems (one is maximization problem and another one is minimization problem).
In addition, I will show you how to customize this Python code of PSO to solve other optimization problems. If you have any questions, please leave your comments below. I will try to answer your questions as soon as possible.
Let’s get started.
For more videos like this, check my YouTube channel here.
import random
import math
import matplotlib.pyplot as plt
#------------------------------------------------------------------------------
# TO CUSTOMIZE THIS PSO CODE TO SOLVE UNCONSTRAINED OPTIMIZATION PROBLEMS, CHANGE THE PARAMETERS IN THIS SECTION ONLY:
# THE FOLLOWING PARAMETERS MUST BE CHANGED.
def objective_function(x):
y = 3*(1-x[0])**2*math.exp(-x[0]**2 - (x[1]+1)**2) - 10*(x[0]/5 - x[0]**3 - x[1]**5)*math.exp(-x[0]**2 - x[1]**2) -1/3*math.exp(-(x[0]+1)**2 - x[1]**2);
return y
bounds=[(-3,3),(-3,3)] # upper and lower bounds of variables
nv = 2 # number of variables
mm = -1 # if minimization problem, mm = -1; if maximization problem, mm = 1
# THE FOLLOWING PARAMETERS ARE OPTINAL.
particle_size=100 # number of particles
iterations=200 # max number of iterations
w=0.85 # inertia constant
c1=1 # cognative constant
c2=2 # social constant
# END OF THE CUSTOMIZATION SECTION
#------------------------------------------------------------------------------
class Particle:
def __init__(self,bounds):
self.particle_position=[] # particle position
self.particle_velocity=[] # particle velocity
self.local_best_particle_position=[] # best position of the particle
.
.
.
def evaluate(self,objective_function):
self.fitness_particle_position=objective_function(self.particle_position)
if mm == -1:
if self.fitness_particle_position < self.fitness_local_best_particle_position:
self.local_best_particle_position=self.particle_position # update the local best
self.fitness_local_best_particle_position=self.fitness_particle_position # update the fitness of the local best
.
.
.
def update_velocity(self,global_best_particle_position):
for i in range(nv):
r1=random.random()
r2=random.random()
cognitive_velocity = c1*r1*(self.local_best_particle_position[i] - self.particle_position[i])
social_velocity = c2*r2*(global_best_particle_position[i] - self.particle_position[i])
self.particle_velocity[i] = w*self.particle_velocity[i]+ cognitive_velocity + social_velocity
def update_position(self,bounds):
for i in range(nv):
self.particle_position[i]=self.particle_position[i]+self.particle_velocity[i]
# check and repair to satisfy the upper bounds
if self.particle_position[i]>bounds[i][1]:
self.particle_position[i]=bounds[i][1]
.
.
.
class PSO():
def __init__(self,objective_function,bounds,particle_size,iterations):
fitness_global_best_particle_position=initial_fitness
global_best_particle_position=[]
swarm_particle=[]
for i in range(particle_size):
swarm_particle.append(Particle(bounds))
A=[]
for i in range(iterations):
for j in range(particle_size):
swarm_particle[j].evaluate(objective_function)
.
.
.
Sorry! This is only a half of the code.
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No need to build the Python code from scratch because it’s very time-consuming. My idol, Jim Rohn, once said: “Time is more value than money. You can get more money, but you cannot get more time”. If you think this code can be used in your research/teaching work, you should download it and then customize/modify/apply it to your work, without any obligation of citing the original source if you don’t want. However, redistribution (i.e., downloading the code/script here and then making it available on another site on the Internet) is strictly prohibited.
If you have any question or problem, please contact Dr. Panda by email: learnwithpanda2018@gmail.com
Thank you very much and good luck with your research!
How would you add stopping criteria, to stop when the global best particle is not improving anymore?
Hi, record the fitness value of the global best particle, check it in every iteration to see if it is improving or not. Set the number of iterations, in which the best fitness is not improving, to stop the algorithm. Use the function ”break” to jump out of the loop to stop your PSO. Good luck!
Thanks, how would you use PSO to find the optimal values for the inertia (w) and acceleration coefficients (c1 and c2)
Hi, to optimize that parameters, I usually use Taguchi experimental design as shown here: https://youtu.be/0XbzneD_ZfI
Hello Sir,
I want to use this code to solve the problem of optimal capacitor sizing and placement
Can you please help me with the editing?
Hi, thanks for interest in my PSO code. To solve a new problem, we must update the objective function and constraints.
Can you please help me, i would pay for your services,
its very urgent
Hi, currently, I give general advice for FREE. I don’t have time to solve research problems for other people. I don’t accept money from anyone. Thanks for your interest!
Can you please help me with that?
Would pay for your services..
My work is a constrained optimization problem of optimal sizing and placement of capacitors
Hi, currently, I give general advice for FREE. I don’t have time to solve research problems for other people. I don’t accept money from anyone. Thanks for your interest!
ok sir, please then i need your advice in editing and updating the code to solve optimal capacitor size and placement problems
Hi, to solve a new problem, we need to update objective function and constraints. That’s all. The rest of the PSO code can be the same.
ok thank you sir,
last thing, what does the bounds mean
Bounds are the max and min values of variables. For example, bound of x = -5 to 5, bound of y = 0 to 7.
ok sir,
i remember seeing in one your replies to someone on youtube, you said edititng this code for another purpose is a bit complex for constrained optimization….my problem is a constrained one
how do i edit this…for the capacitor sizing problem
To handle the constraints, we can use penalty function or repairing method. Here is one example – PSO for constrained optimization: https://learnwithpanda.com/2020/05/19/particle-swarm-optimization-pso-for-constrained-optimization-problems/
Hello. Just wanna clarify something. Does the generated random number for the acceleration coefficients r1 and r2 in line 48 and 49 stay the same throughout the optimization process or does it draw a random number at every iteration step?
Hi, they are random numbers in each iteration.
Hello Sir,
Can we incorporate hyperspectral images in this code? How to proceed it…
Hi, it is possible for the PSO code to work on image processing but we have to modify the objective function. “imread” can be used to load the images as far as I can remember.
Hello sir,
what does the number of variables (nV) in the code means.The result of the optimal solution is being displayed as a range what does that infer.
the number of variables is the number of decision variables or the variables you want to find the optimal values. for example, z = x + y, this problem has 2 variables, x and y
Hello,
Is it possible to bulit a confusion matrix with this code .How do we need to define the y_pred values …
I don’t know confusion matrix. So, I don’t know.
Good day sir,
Thanks for this really helpful code. However could you please explain what mm means in this code? I have read the comment out on it and I still don’t quite understand what it is for.
Any help would be appreciated.
Hi, mm is my notation for minimization or maximization problems (if minimization problem, mm = -1; if maximization problem, mm = 1). This code can solve both problems
Hello,
The code is great. Although how would you add code to add another grid showing the final placement of the particles at the end of the optimization.
Yes, it is possible to do that because we know the positions of the particles at the end of the optimization, i.e. final iteration.
Good day,
I just want to ask why you had to add [0] or [1] beside x when defining the function,
i.e. y = 3*(1-x[0])**2*math.exp(-x[0]**2 – (x[1]+1)**2) – 10*(x[0]/5 – x[0]**3 – x[1]**5)*math.exp(-x[0]**2 – x[1]**2) -1/3*math.exp(-(x[0]+1)**2 – x[1]**2)
What is the purpose of those and how do I know if I need to put a number 1 or 0 beside x?
Hi, they are indexes to determine the elements of the vector x. For example, x[0] is the first element in x, x[1] is the second element in x. Hope it’s clear.
Hello,
thank you for the PSO Algorithm
If I have 3 variables what I should change
bounds=[(-3,3,4),(-3,3,6)]
nv =3
and how i can change this
for i in range(nv):
self.particle_position.append(
random.uniform(bounds[i][0], bounds[i][1])) # generate random initial position
self.particle_velocity.append(random.uniform(-1, 1))
Hi,that’s correct. No need to change anything
but it shows me an error message
File “C:/Users/Yousra/Documents/PSO.py”, line 44, in __init__
self.particle_position.append(random.uniform(bounds[i][0], bounds[i][1])) # generate random initial position
IndexError: list index out of range
Hi, check the bounds of variables
Hello, I can’t find the Python code
Hi, try to use your PC or ipad. It will not shown up on mobile phone. Thanks
The problem is i can’t subsribe to your websitr with my email. the loading page loops
After subscribing, you should receive an email to confirm. If not, maybe, check you spam folder. Thanks
dear sir
I like to ask you about when should the iteration stops if I use python to solve some equation ??
thank you
We should tests by running several times to see if the best solution can’t be better. So that we can set the number of iterations or computing time.
Hello Sir,
How to i implement the constraint like this 0≤𝑤𝑖≤1; and𝑖=1,2. . .,𝑁(4) as the boundary for the problem
Please have a look at the code for more details. It’s hard to explain in words
Hello Sir’
How can I use this code along with vector support regression code? I have a set of data (having 7 independent variable and two dependent variables) and want to find the optimal solution to maximize dependent variables.
Thanks for the interesting suggestion. I will make that video as soon as possible.
Hello Sir
Upon implementing your code it throws an error for “if self.fitness_particle_position < self.fitness_local_best_particle_position:" saying that "TypeError: '<' not supported between instances of 'float' and 'list'"
You should check the format of each function carefully
Hello sir,
I have a such question but I am not sure how should I change parameters for the given problem. There are not any boundaries:
A child’s rectangular playground is to be built next to the house. To make the three sides of the playpen, 24 feet of fencing are available. What should be dimensions of the sides to make a maximum area?
Are you available to help?
Hello, thanks for your interest. Sorry, currently I am not available.
How does one use this code to obtain results for load flow with and without DGs for comparison
Sorry, I don’t know the DGs.