I am using PSO algorithm to search optimum value for parameters within range. I have 5 parameters such as: x0, x1, x2, x3, x4, and x5. Each parameter has own range.
x0 = [10,320]
x1=[65,100]
x2= [1, 16]
x3= [1,4]
x4 =[1,3]
x5 = [150,230]
In program, I am setting the lower and upper position as:
X0-min = 10;
X0-max= 320
Similar for the other parameters (x1,x2.....).
As, in PSO the particle position is changing based on velocity. I am confused on configuring a value for the velocity. How I can control velocity of a particle. I mean how to set limits of the velocity for each parameter? Should I use similar value for v0-min and v0-max as I used for the x0-min and x0-max?
A simple rule of thumb is to set initially the maximum velocity for each Design Variable at a value equal to 10% of Xmax-Xmin and make some preliminary runs. Keep track of the time histories reporting the velocity of the particles and a) increase by a small amount the maximum velocity for speedier convergence if the maximum velocity is reached often or b) decrease otherwise.
The "optimum" value is also problem depedent. If you have a vague idea about the shape of the objective function then a) choose a small maximum velocity in the case of non-smooth objectives to avoid overshooting and b) choose a confortably large value otherwise.
Please bear in mind that in literature values up to 20% or even 40% of the Xmax-Xmin are reported for different problems.
First, we've had problems before in search spaces with different ranges for each search term -- the differing scales affect trajectories/velocities which distorted our search behaviour. Things worked better if we made the search technique work in a [0,1] hypercube, and the have each solution scaled to the actual search ranges before evaluating them.
Second, our claim in the attached paper is that minimum step-size (which is directly related to velocity in PSO) is not generally considered. We found improved results by just filtering out moves of insufficient size. Subsequently, by preventing convergence, the size of the attraction vectors will maintain a high average velocity (although any given step might be smaller).
Hope that helps.
Conference Paper Particle Swarm Optimization with Thresheld Convergence
We need to set velocities of each particle when you initialize the swarm. Afterwards, we compute velocity of each particle by the standard PSO equation. If position of a particle goes beyond search space (limit), we clamp position of the particle. If you want to control the velocities read papers related to inertia weight and constriction factor.
A simple rule of thumb is to set initially the maximum velocity for each Design Variable at a value equal to 10% of Xmax-Xmin and make some preliminary runs. Keep track of the time histories reporting the velocity of the particles and a) increase by a small amount the maximum velocity for speedier convergence if the maximum velocity is reached often or b) decrease otherwise.
The "optimum" value is also problem depedent. If you have a vague idea about the shape of the objective function then a) choose a small maximum velocity in the case of non-smooth objectives to avoid overshooting and b) choose a confortably large value otherwise.
Please bear in mind that in literature values up to 20% or even 40% of the Xmax-Xmin are reported for different problems.
Thank you very much all of you, Stephen, Pramond and C.K. Dimon for your valuable suggestions. I have applied the suggestion of Dimon and I think it is working for me. Many thanks again.
Happy New Year 2015
Best regards,
PSO codes in MATLAB
https://www.researchgate.net/publication/296636431_Codes_in_MATLAB_for_Particle_Swarm_Optimization?ev=prf_pub
Code Codes in MATLAB for Particle Swarm Optimization
https://www.researchgate.net/publication/280244004_A_comparative_study_of_metaheuristic_optimization_approaches_for_directional_overcurrent_relays_coordination?ev=prf_pub
Article A comparative study of metaheuristic optimization approaches...
https://www.researchgate.net/publication/297245624_Particle_Swarm_Optimization_Algorithm_and_its_Codes_in_MATLAB
Research Particle Swarm Optimization: Algorithm and its Codes in MATLAB
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