Differentielle Evolution (DE) is a powerful, population-based Optimierungsalgorithmus that is particularly effective for solving complex, nonlinear, and multi-dimensional problems. It belongs to the family of evolutionary algorithms, which are inspired by the process of natural selection.
The core idea behind Differential Evolution is to evolve a population of candidate solutions over a series of iterations, known as generations. Each individual in the population represents a potential solution to the Optimierungsproblem. DE operates by combining existing solutions to generate new candidate solutions, which are then evaluated based on a predefined objective function.
Der Algorithmus folgt diesen Hauptschritten:
- Initialisierung: A population of candidate solutions is randomly generated within the defined search space.
- Mutation: For each candidate solution, a new solution is created by adding a scaled difference between two randomly selected members of the population to a third member.
- Kreuzung: The mutated solution is combined with the original candidate solution to create a trial solution. This is typically done using a crossover probability die bestimmt, wie viel der neuen Lösung mit der ursprünglichen vermischt wird.
- Auswahl: The trial solution is compared to the original candidate solution. If the trial solution has a better fitness Wert, ersetzt es die ursprüngliche Lösung in der Population.
Dieser Zyklus aus Mutation, Kreuzung und Selektion wird fortgesetzt, bis ein Abbruchkriterium erfüllt ist, beispielsweise eine maximale Anzahl an Generationen oder ein akzeptabler Fehlerwert.
Differential Evolution is known for its simplicity and effectiveness, making it a popular choice in various fields, including engineering, economics, and maschinellem Lernen, for optimizing functions that may be difficult to solve using traditional methods.