title: Toward Large-Scale Continuous EDA: A Random Matrix Theory Perspective.
abstract: Estimations of distribution algorithms (EDAs) are a major branch of evolutionary algorithms (EA) with some unique advantages in principle. They are able to take advantage of correlation structure to drive the search more efficiently, and they are able to provide insights about the structure of the search space. However, model building in high dimensions is extremely challenging, and as a result existing EDAs may become less attractive in large-scale problems because of the associated large computational requirements. Large-scale continuous global optimisation is key to many modern-day real-world problems. Scaling up EAs to large-scale problems has become one of the biggest challenges of the field. This paper pins down some fundamental roots of the problem and makes a start at developing a new and generic framework to yield effective and efficient EDA-type algorithms for large-scale continuous global optimisation problems. Our concept is to introduce an ensemble of random projections to low dimensions of the set of fittest search points as a basis for developing a new and generic divide-and-conquer methodology. Our ideas are rooted in the theory of random projections developed in theoretical computer science, and in developing and analysing our framework we exploit some recent results in nonasymptotic random matrix theory.
authors.affiliation: School of Computer Science, University of Birmingham, Edgbaston, B15 2TT, Birmingham, UK A.Kaban@cs.bham.ac.uk.
authors.forename: A
authors.initials: A
authors.lastname: Kabán
authors.affiliation: Department of Computer Science, Chiang Mai University, Muang, Chiang Mai 50200, Thailand Jakramate.B@cmu.ac.th.
authors.forename: J
authors.initials: J
authors.lastname: Bootkrajang
authors.affiliation: Department of Statistics, University of Waikato, Private Bag 3105, Hamilton 3240, New Zealand BobD@waikato.ac.nz.
authors.forename: R J
authors.initials: RJ
authors.lastname: Durrant
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical
keywords: Large-scale optimisation; estimation of distribution algorithms; random matrix theory; random projections