Towards LargeScale ContinuousEDA: A RandomMatrix Theory Perspective

Abstract

Estimation of distribution algorithms (EDA) 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 highdimensionsisextremelychallengingandasaresultexistingEDAsmaylosetheir strengthsinlargescale problems. 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 challengesof thefield. 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 introduceanensembleofrandomprojectionstolowdimensionsofthesetoffittestsearch points as a basis for developing a new and generic divide-and-conquer methodology. Ourideasarerootedinthetheoryofrandomprojectionsdevelopedintheoreticalcomputerscience,andindevelopingandanalysingourframeworkweexploitsomerecent resultsin non-asymptoticrandommatrixtheory