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The Geometry of Evolutionary Algorithms: Unification and Theory-Laden Design

Alberto Moraglio
Post-doctoral Research Fellow in the School of Computer Science
University of Birmingham



The various flavours of traditional Evolutionary Algorithms (EAs) look very similar when cleared of algorithmically irrelevant differences such as domain of application and phenotype interpretation. Representation-independent algorithmic characteristics, like the selection scheme, can be freely exchanged between algorithms. Ultimately, EAs differences boil down to their solution representations and associated genetic operators

  • Are there common principles that explain how all EAs across representations work?
  • Can these principles be formalised in a rigorous theory?
  • Can this theory lead to the systematic design of provably good EAs for my favourite problem?

The aim of the tutorial is to introduce a formal, but intuitive, unified point of view on Evolutionary Algorithms across representations based on geometric ideas, which provides a possible answer to the above questions.

The geometric view has a number of interesting consequences for both theory and practice of which this tutorial will give a comprehensive overview. The tutorial is subdivided in five parts:

1. Geometric Interpretation of Search Operators: Basic notions of geometry on search spaces
    and geometric definitions of mutation and crossover.

 2. Unification of Evolutionary Algorithms: Formal unification of many existing search operators
     across representations.

3. Principled Design of Crossover Operators: Principled way of designing crossover operators for
    new representations.

4. Principled Generalization of Search Algorithms: Principled way of generalizing search
    algorithms from continuous to combinatorial spaces.

5. Unified Theory of Evolutionary Algorithms: Rigorous general theory of evolutionary algorithms
    across representations.


Alberto Moraglio is currently a Post-doctoral Research Fellow in the School of Computer Science at the University of Birmingham. He holds a PhD in Computer Science from the University of Essex and a Master (Laurea) in Computer Engineering from the Polytechnic University of Turin, Italy. Before the current appointment, he worked as a researcher for Hewlett-Packard Research Laboratories, as an Assistant Professor for the University of Coimbra, Portugal, and as post-doctoral research associate affiliated with the School of Computing and the Centre for Reasoning, University of Kent, UK.

He was chair of the European Conference on Genetic Programming 2012, and reconfirmed for 2013, and co-chair of the Theory track at GECCO 2013. He is member of IEEE CIS Task Force on Theoretical Foundations of Bio-Inspired Computation. He presented a tutorial on the Geometry of Evolutionary Algorithms at GECCO 2011 and GECCO 2012. He has 60+ peer-reviewed publications in journals and conference proceedings almost exclusively on the geometric view of Evolutionary Algorithms, which he has developed in his PhD study and post-doctoral research. His current research interest is on the theoretical foundations of Evolutionary Computation, and theory-laden design of search operators


The length of the tutorial:
two hours.


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