Overview
Differential Evolution mutates candidates with scaled vector differences, crosses them with current candidates, and keeps the better result.
CoreSource checked
Differential Evolution
Optimizes continuous parameters by combining differences between population members.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Optimization
- Difficulty
- Intermediate
- Family
- Evolutionary Optimization
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 5
- Code example
- Ready
- Visualization
- Ready
Core Concepts
vector differencepopulation mutationcrossoverselection
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(population)
Average
O(iterations * population * cost)
Worst
O(iterations * population * cost)
Space
O(population)
When to Use
- Use when tuning model parameters needs vector difference.
- Use when the input matches the assumptions behind evolutionary 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
- Optimizes continuous parameters by combining differences between population members
- Uses vector difference and population mutation 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)
Mutation vector
v = xa + F · (xb − xc)
v = x_a + F * (x_b - x_c)Creates a trial direction from differences between existing candidates.
Pseudocode
- 1.Prepare the inputs and state needed for Differential Evolution.
- 2.Apply the vector difference step while the stopping condition has not been met.
- 3.Update intermediate state and discard invalid candidates.
- 4.Return best candidate.
Canonical Example
- Input
- Differential Evolution input with a small representative case
- Output
- Best candidate
- Explanation
- Differential Evolution applies vector difference to produce best candidate.
Implementation Notes
- Track both best-so-far and current candidate state.
- Keep the vector difference 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 Differential Evolution 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 Differential Evolution.
optimization-mechanismNotes
Differential Evolution should be used with the assumptions and tradeoffs of evolutionary Optimization in mind.
Sources (1)
What each reference supports for this entry.
Storn and Price 1997
PaperFoundational paper for differential evolution over continuous spaces.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageConceptual neighborGenetic Algorithm
Differential evolution shares mutation and selection ideas with evolutionary algorithms.
Alternative toParticle Swarm Optimization
Both are derivative-free population optimizers for continuous spaces.
Related Algorithms
Tags
OptimizationPopulation BasedEvolution StrategyStochastic