Overview and Development:
Particle Swarm Optimization is one of the most important algorithms used in modern data analysis and mathematical programming. This algorithm aims to find the best solution or feasible solution for a given optimization problems. The basic idea is that you keep a set of similar differentiable functions placed in a cluster, and then you try to optimize the objective function until it converges to a solution.
It has a very limited hyperparameter:
1. Procedure has many representatives that comprise a swarm roaming in the search section, finding the finest result.
2. Here algorithms work to solve a problem, the social interaction concept is used.
3. Global best that is known as Gbest offers the best value which is tracked by PSO.
4. In the solution space, each particle finds its positional coordinates in relation to the optimal
What is a particle swarm?
Particle Swarm Optimization is a method used to search for important specifications for a new machine to be built. It is based on the observation that immobility in a fluid is a property shared by many objects of similar structure, and that immobility of a part or part of a system is a property of the whole.
Particle swarm optimization problem seeks to find the most efficient way to screen through scenarios that occur in the real world, to quickly find the most efficient path for a specific set of business challenges. Optimization algorithms are used for industrial applications in the field of AI.
The behavior of Optimization problem & Optimal solution
Different algorithms have been introduced at different times and many of them were dissipated but PSO is still in the attention of many researchers. PSO was developed by Eberhart and Kennedy in the year 1995.
Particle swarm optimization simulation is a mathematical program that involves organized groups of particles, or particles that are not in an isolated state, as well as how to organize them in a way that minimizes the search space and provides optimum output through a fixed number of iterations.
There are a variety of different aspects to PSO and most of them are related to how the group members’ behavior is reflected in the search space. The main goal of PSO is to create smaller and closer-together groups that minimize the search space. It is one of the most important algorithms in the field of computer science.
As the flock bird’s movement can be simulated, here each is capable to find the best feasible solutions in the solution space of high dimension, and hence the greatest solution is found by the flock. This is called a heuristic solution. As the real global optimal solution cannot be approved.
Determine the developed model of Optimization Problems:
To design the system with the optimal values of the lowest cost with the modern scientific parameter is known as Optimization. If you want to find the greatest solution to any problem, so optimization provides it.
If a CEO needs to take different types of plans at different periods of time. That person with try to minimize the hard work he is doing through different steps to maximize the profit for him.
For maximizing and minimizing tasks Optimization is highly referred to. Now the problems in optimization can be linear or nonlinear functions. The Non-Liner problems are more difficult to solve.
There are different types of Optimizations, constraints, dynamic, local, and global.
PSO Algorithm Parameters to solve an objective function
For different optimization problems, there are different parameters
1. Swarm size
2. Iteration number
3. Velocity components
4. Acceleration Coefficients
Building the PSO Algorithm
The Particle swarm is majorly based on the algorithms. It is the most natural algorithm. A class of independents known as debris move in specific steps in a complete area. Evaluation is done at every position which in terms decides and lots a completely new pace to each of the elements.
The Particle Swarm Algorithm’s major steps are Initialization, objective function evaluation, Iteration, and stopping. The complete process is as:
1. Making the Initial particles
2. Particles should be assigned with initial velocities
3. At every particle location, the objective function needs to be evaluated, referred to as the personal best pBest
4. It will find the best shortest value and location
5. The updated new velocities will be selected by the simulation, which is based on current velocities and the best positions of particles and their nearest particles
6. Then repetitively modernize the location of the particles
7. This repetition will continue until the stopping criteria are reached by the algorithm
Particle swarm optimization algorithm Matlab code Explanation
In this example, the requirement is to find the global minimum, in order to implement PSO Matlab code to an objective function.
The optimized method is affected by a variety of control parameters, including the dimension of the problem, the number of swarms, inertia weight, acceleration coefficients, number of iterations, and the random value that influence social and cognitive components.
PSO Matlab Initialization
The inertial weight greatly impacts the PSO algorithm code in the convergence of optimization. This factor maintains the particle/swarms inertial motion and redirects the change of particle velocity. PSO code correction factor is a suitable approach to ensure convergence of the Matlab particle swarm optimization. Let’s demonstrate the PSO code in Matlab
clear clc iterations = 1000; inertia = 1.0; correction_factor = 2.0; swarms = 5000;
I will attach the download link for particle swarm optimization Matlab code at the end of this post, so keep the focus on the understanding.
Here in the below, 50 rows are created, in the case of 5000 particles, there will be 5000 rows as well. Considered columns are 7 as 1, 2 represent particle position, and 3, 4 represent the particle velocity. PSO algorithm Matlab code updates the position, and velocity on each iteration.
% ---- initial swarm position ----- swarm=zeros(5000,7); step = 1; for i = 1 : 5000 swarm(step, 1:7) = i; step = step + 1; end swarm(:, 7) = 1000; % Greater than maximum possible value swarm(:, 5) = 0; % initial velocity swarm(:, 6) = 0; % initial velocity
In 5, 6 column velocity vector consideration based on inertia and correction factor is done and then it will be updated on 3, 4 columns.
Interested to implement different objective functions then you have to adjust the PSO Optimization Matlab program a bit.
%-- position of Swarms --- for i = 1 : swarms swarm(i, 1) = swarm(i, 1) + swarm(i, 5)/1.2 ; %update u position swarm(i, 2) = swarm(i, 2) + swarm(i, 6)/1.2 ; %update v position u = swarm(i, 1); v = swarm(i, 2); value = (u - 20)^2 + (v - 10)^2; %Objective function if value < swarm(i, 7) % Always True swarm(i, 3) = swarm(i, 1); % update best position of u, swarm(i, 4) = swarm(i, 2); % update best postions of v, swarm(i, 7) = value; % best updated minimum value end end
In the case of 5000 swarms, the cluster looks like this, which have to finally converge at a point closer to each other.
Differences between PSO and Genetic Algorithm (GA):
Optimization techniques like Particle swarm optimization and Genetic Algorithm (GA) both have many features that are similar as mostly both are used in a similar type of problem programs, but there are some differences too.
To reach a faster convergence PSO needs to normalize the Input parameters, whereas the genetic algorithm uses discrete as well as continuous.
Swam optimization requires no evolution operators, whereas GA has crossover etc.
PSO provides both local searchers and global searchers, whereas GA provides only local searchers.
In PSO the independent individual is neither created nor deleted.
From research, the performance of PSO is found to be much better than GA, as it provides both global and local searches.
Advantages and Disadvantages of Particle Swarm Optimization
1. The whole concept is quite simple
2. Implementation is not very complex
3. Without difficulty parallelized for concurrent processing
4. A completely green international seek set of rules
5. It has very few amounts of algorithm parameters
6. Provides both global and local searches
There are very few disadvantages as well
1. Its convergence rate is low
2. It is weak in the local search
In the field of Artificial Intelligence PSO plays an important role. It has many new advanced features. It is an optimization algorithm that is global and local and has many different unique strategies. It helps a lot in improving the solution of problems.
You should read this article with a positive attitude, interest, and hopefully, find out really helpful what we have done and how you can implement yours.
If you are interested to get the code, click the below link
PSO algorithm Matlab code free download
Interested to learn more take a look at recent popular content
 Kennedy, J., and R. Eberhart. “Particle Swarm Optimization.” Proceedings of the IEEE International Conference on Neural Networks. Perth, Australia, 1995, pp. 1942–1945.
 Mezura-Montes, E., and C. A. Coello Coello. “Constraint-handling in nature-inspired numerical optimization: Past, present and future.” Swarm and Evolutionary Computation. 2011, pp. 173–194.
 Pedersen, M. E. “Good Parameters for Particle Swarm Optimization.” Luxembourg: Hvass Laboratories, 2010.