Towards a Geometric Unification of Evolutionary Algorithms

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  author =       "Alberto Moraglio",
  title =        "Towards a Geometric Unification of Evolutionary
  school =       "Department of Computer Science, University of Essex",
  year =         "2007",
  address =      "UK",
  month =        nov,
  keywords =     "genetic algorithms, genetic programming",
  URL =          "",
  URL =          "",
  size =         "392 pages",
  abstract =     "Evolutionary algorithms are successful and widespread
                 general problem solving methods that mimic in a
                 simplified manner biological evolution. Whereas most of
                 evolutionary algorithms share the same basic
                 algorithmic structure, they differ in the solution
                 representation - the genotype - and in the search
                 operators employed - mutation and crossover - that are
                 representation specific. In the research community
                 there is a strong feeling that the evolutionary
                 computation field needs unification and systematisation
                 in a rational framework to survive its own exceptional
                 growth of the last two decades. The lack of a common
                 formal framework encompassing all solution
                 representations have prevented EC researchers to build
                 a truly general theory of evolutionary algorithms, as
                 well as to develop a formal theory of search operators
                 design for new representations and problems.

                 In this thesis, we propose a general geometric
                 framework that addresses these two important problems.
                 The unification is made possible by surprisingly simple
                 representation-independent geometric definitions of
                 crossover and mutation using the notion of distance
                 associated with the search space. This novel way of
                 looking at genetic operators allows us to rethink
                 various familiar aspects of evolutionary algorithms in
                 a very general setting, simplifying and clarifying
                 their relations. We show that many important genetic
                 operators for the most frequently used representations
                 fit this framework. This makes this framework highly
                 relevant because it unifies pre-existing evolutionary
                 algorithms. The abstract definitions of mutation and
                 crossover can be used as formal recipes to build new
                 mutations and crossovers for virtually any new solution
                 representations and problems. We designed and tested
                 new operators on a number of problems obtaining very
                 good experimental results. The same abstract
                 definitions of mutation and crossover can be used to
                 build a truly general representation-independent theory
                 of evolutionary algorithms. We started building such a
                 theory and showed that all evolutionary algorithms with
                 geometric crossover does the same type of search,
                 convex search. This is a general and important result
                 because it shows that a non-trivial
                 representation-independent theory of evolutionary
                 algorithms is possible.",
  notes =        "Some chapters on GP trees",

Genetic Programming entries for Alberto Moraglio