The Algebraic Differential Evolution (ADE) is a recently proposed combinatorial evolutionary scheme which mimics the behaviour of the classical Differential Evolution (DE) in discrete search spaces which can be represented as finitely generated groups. ADE has been successfully applied to both permutation and binary optimization problems. However, in the previous works, the relationship between ADE and the classical continuous DE has been only intuitively sketched without any theoretical or experimental proof. Here, we fill this gap by providing both theoretical and experimental justifications proving that ADE is a full-fledged generalization of DE which works across different search spaces. First, we formally prove that there exists a concrete implementation of ADE’s algebraic operations converging to the classical vector operations of DE, then we propose a real-vector implementation of ADE and we experimentally prove that its behaviour is statistically equivalent to DE. As conclusion, we also pave the way for further applications of the original DE idea to mixed discrete/continuous search spaces.

Is Algebraic Differential Evolution Really a Differential Evolution Scheme?

Santucci, Valentino
2021

Abstract

The Algebraic Differential Evolution (ADE) is a recently proposed combinatorial evolutionary scheme which mimics the behaviour of the classical Differential Evolution (DE) in discrete search spaces which can be represented as finitely generated groups. ADE has been successfully applied to both permutation and binary optimization problems. However, in the previous works, the relationship between ADE and the classical continuous DE has been only intuitively sketched without any theoretical or experimental proof. Here, we fill this gap by providing both theoretical and experimental justifications proving that ADE is a full-fledged generalization of DE which works across different search spaces. First, we formally prove that there exists a concrete implementation of ADE’s algebraic operations converging to the classical vector operations of DE, then we propose a real-vector implementation of ADE and we experimentally prove that its behaviour is statistically equivalent to DE. As conclusion, we also pave the way for further applications of the original DE idea to mixed discrete/continuous search spaces.
978-1-7281-8393-0
978-1-7281-8392-3
Differential Evolution, Algebraic Differential Evolution, Search spaces, Theoretical analysis
File in questo prodotto:
File Dimensione Formato  
002-CEC2021-155.pdf

non disponibili

Descrizione: Versione editoriale
Tipologia: Versione Editoriale (PDF)
Licenza: NON PUBBLICO - Accesso chiuso
Dimensione 498.43 kB
Formato Adobe PDF
498.43 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
_IEEE_CEC_2021____Continuous_ADE.pdf

accesso aperto

Descrizione: Preprint
Tipologia: Documento in Pre-print
Licenza: Creative commons
Dimensione 468.85 kB
Formato Adobe PDF
468.85 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12071/26265
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
social impact