Overview
Particle Swarm Optimization maintains candidate particles whose velocities are pulled toward each particle's best-known position and the swarm's best-known position.
CoreSource checked
Particle Swarm Optimization
Searches for good solutions by moving particles according to personal and group best positions.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Optimization
- Difficulty
- Intermediate
- Family
- Population-Based Optimization
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 5
- Code example
- Ready
- Visualization
- Ready
Core Concepts
swarm populationvelocity updatepersonal bestglobal best
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(p)
Average
O(iterations * p * cost)
Worst
O(iterations * p * cost)
Space
O(p)
When to Use
- Use when tuning model parameters needs swarm population.
- Use when the input matches the assumptions behind population-Based Optimization.
When Not to Use
- Avoid when the objective is cheap and convex enough for a simpler exact solver.
- Avoid when a simpler algorithm gives the required result with less setup.
What It Does
- Searches for good solutions by moving particles according to personal and group best positions
- Uses swarm population and velocity update to guide the work.
- Produces best candidate.
Use Cases
- Tuning model parameters
- Searching design spaces
- Fitting models to noisy data
Inputs
- Objective function
- Initial candidate or population
- Stopping rule
Outputs
- Best candidate
- Objective value
- Search history
Key Formulas (1)
Velocity update
v = w·v + c1·r1·(pbest − x) + c2·r2·(gbest − x)
v = w*v + c1*r1*(pbest - x) + c2*r2*(gbest - x)Moves a particle using inertia, personal memory, and swarm memory.
Pseudocode
- 1.Prepare the inputs and state needed for Particle Swarm Optimization.
- 2.Apply the swarm population step while the stopping condition has not been met.
- 3.Update intermediate state and discard invalid candidates.
- 4.Return best candidate.
Canonical Example
- Input
- Particle Swarm Optimization input with a small representative case
- Output
- Best candidate
- Explanation
- Particle Swarm Optimization applies swarm population to produce best candidate.
Implementation Notes
- Track both best-so-far and current candidate state.
- Keep the swarm population step separate enough to test independently.
Common Pitfalls
- Stopping too early can make a poor local result look like convergence.
- Forgetting to check edge cases can make Particle Swarm Optimization look correct on only ideal inputs.
Interactive Mechanism Walkthrough
Iterative Convergence & State TrajectoryPlot candidate points, objective values, and improvement steps across iterations.
Step 1 of 4: Prepare the inputs and state needed for Particle Swarm Optimization.
optimization-mechanismNotes
Particle Swarm Optimization should be used with the assumptions and tradeoffs of population-Based Optimization in mind.
Sources (1)
What each reference supports for this entry.
Explore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageConceptual neighborDifferential Evolution
Both evolve a population of candidate solutions in continuous spaces.
Alternative toGenetic Algorithm
Both are population-based optimization methods.
Related Algorithms
Tags
OptimizationPopulation BasedMetaheuristicStochastic