Geometric differential evolution for combinatorial and programs spaces

A. Moraglio, J. Togelius, S. Silva

    Research output: Contribution to journalArticlepeer-review


    Geometric differential evolution (GDE) is a recently introduced formal generalization of traditional differential evolution (DE) that can be used to derive specific differential evolution algorithms for both continuous and combinatorial spaces retaining the same geometric interpretation of the dynamics of the DE search across representations. In this article, we first review the theory behind the GDE algorithm, then, we use this framework to formally derive specific GDE for search spaces associated with binary strings, permutations, vectors of permutations and genetic programs. The resulting algorithms are representation-specific differential evolution algorithms searching the target spaces by acting directly on their underlying representations.We present experimental results for each of the new algorithms on a number of well-known problems comprising NK-landscapes, TSP, and Sudoku, for binary strings, permutations, and vectors of permutations.We also present results for the regression, artificial ant, parity, and multiplexer problems within the genetic programming domain. Experiments show that overall the new DE algorithms are competitive with well-tuned standard search algorithms.

    Original languageEnglish (US)
    Pages (from-to)591-624
    Number of pages34
    JournalEvolutionary Computation
    Issue number4
    StatePublished - Nov 2013


    • Combinatorial spaces
    • Differential evolution
    • Genetic programming
    • Principled design of search operators
    • Representations
    • Theory

    ASJC Scopus subject areas

    • Computational Mathematics


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