Particle swarm intelligence
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The particle swarm optimization (PSO) algorithm was developed in 1995 as a metaheuristic algorithm based on swarm intelligence. It uses a population of candidate solutions called particles that search through the problem space to find the best solution. Each particle adjusts its trajectory based on its own experience and the experience of neighboring particles. The algorithm keeps track of each particle's best solution (personal best) and the best solution in the swarm (global best) to determine the particle's new velocity and position in the search space iteration by iteration until an optimal solution is found.
![PSO Algorithm
Goal of an optimization problem
Determine a variable represented by a vector
x = [x1, x2, x3,…, xd]
that minimizes or maximizes the fitness or objective function f(X)
based on the proposed optimization formulation
Let
n be the number of particles in a swarm
xi be the position vector for particle i
vi be the velocity for particle i](https://image.slidesharecdn.com/3-210827100624/85/Particle-swarm-intelligence-4-320.jpg)
Particle swarm intelligence
- 2. Introduction Developed by James Kennedy & Russell Eberhart in 1995 Metaheuristic algorithm based on the concept of swarm intelligence
- 3. PSO Algorithm – Basic Concept Uses the population (called a swarm) of candidate solutions (called particles) Particles searches through the space of an objective function looking for the best solution Each particle in search space adjusts its trajectories according to its own best known position as well as entire swarm's best known position Trajectories: Path described by an object moving in air or space under the influence of forces
- 4. PSO Algorithm Goal of an optimization problem Determine a variable represented by a vector x = [x1, x2, x3,…, xd] that minimizes or maximizes the fitness or objective function f(X) based on the proposed optimization formulation Let n be the number of particles in a swarm xi be the position vector for particle i vi be the velocity for particle i
- 5. PSO Algorithm Each particle keeps track: its best solution, personal best, pbest the best value of any particle, global best, gbest
- 6. Pseudo code
- 7. Update Velocity Vector Determine the new velocity vector xt i be the position vector for particle i at t iteration vt i be the velocity for particle i at t iteration 1 and 2 are two random vectors α and β are the learning parameters or acceleration constants, α ≈ β ≈ 2
- 8. Update Position Vector Determine the new velocity vector xi be the position vector for particle i vi be the velocity for particle I 1 and 2 are two random vectors α and β are the learning parameters or acceleration constants, α ≈ β ≈ 2
- 9. Introduction to the PSO: Algorithm Particle’s velocity: • Makes the particle move in the same direction and with the same velocity 1. Inertia 2. Personal Influence 3. Social Influence • Improves the individual • Makes the particle return to a previous position, better than the current • Conservative • Makes the particle follow the best neighbors direction
- 10. Velocity Vector Makes the particle move in the same direction and with the same velocity 1. Inertia 2. Personal Influence 3. Social Influence Improves the individual Makes the particle return to a previous position, better than the current Conservative Makes the particle follow the best neighbors direction
- 11. Velocity Vector Intensification: explores the previous solutions, finds the best solution of a given region Diversification: searches new solutions, finds the regions with potentially the best solutions
- 12. THANK YOU