Metaheuristics: searching between exploration and exploitation
The core ideas behind GA and Differential Evolution, with a link to dynamic optimization.
Learning goal
Understand the solution space, objective function, population search, and the exploration-exploitation trade-off.
Prerequisites
- Optimization basics
- Basic probability
The solution space
Every allowed combination of decision variables is a candidate solution. The search tries to find points with better objective values.
Genetic Algorithm
A GA maintains several candidates at once. Selection, crossover, and mutation change the population while evaluation measures quality.
- selection: choose parents
- crossover: combine information
- mutation: introduce variation
- evaluation: measure quality
Differential Evolution
DE uses differences between population members to create a new vector, providing directional information in the search space.
The trial vector is then compared with the target and the better candidate survives.
Connection to dynamic optimization
In Event-Driven Metaheuristic Optimization the problem itself changes over time. The question becomes whether a previous optimizer state can be adapted after a change instead of restarting from scratch.
Exercises
- Define a two-variable objective.
- Compute a DE mutant vector from three vectors.
- Explain why warm-start should be evaluated with benchmarks rather than treated as universally better.
Related project
Event-Driven Metaheuristic Optimization
A real project using GA and DE for dynamic optimization and comparing restart with warm-start.
Open sourceRelated solutions
Have a difficult optimization search space?
We can characterize the model first and then choose a suitable method.