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Metaheuristics: searching between exploration and exploitation

The core ideas behind GA and Differential Evolution, with a link to dynamic optimization.

Optimization & MetaheuristicsIntermediate

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.

Optimal solution
x^*\in\arg\min_{x\in\Omega}f(x)

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.

DE mutation
v=xr1+F(xr2−xr3)

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 source

Have a difficult optimization search space?

We can characterize the model first and then choose a suitable method.