arXiv subjects

Keki Burjorjee

Publications and source records attributed to Keki Burjorjee.

3 recordsLinked to original sources

arXiv2009

Towards a Sound Theory of Adaptation for the Simple Genetic Algorithm

The pace of progress in the fields of Evolutionary Computation and Machine Learning is currently limited -- in the former field, by the improbability of making advantageous extensions to evolutionary algorithms when their capacity for adaptation is poorly understood, and in the latter by the difficulty of finding effective semi-principled reductions of hard real-world problems to relatively simple optimization problems. In this paper we explain why a theory which can accurately explain the simple genetic algorithm's remarkable capacity for adaptation has the potential to address both these limitations. We describe what we believe to be the impediments -- historic and analytic -- to the discovery of such a theory and highlight the negative role that the building block hypothesis (BBH) has played. We argue based on experimental results that a fundamental limitation which is widely believed to constrain the SGA's adaptive ability (and is strongly implied by the BBH) is in fact illusionary and does not exist. The SGA therefore turns out to be more powerful than it is currently thought to be. We give conditions under which it becomes feasible to numerically approximate and study the multivariate marginals of the search distribution of an infinite population SGA over multiple generations even when its genomes are long, and explain why this analysis is relevant to the riddle of the SGA's remarkable adaptive abilities.

cs.NE↗

arXiv2008

The Fundamental Problem with the Building Block Hypothesis

Skepticism of the building block hypothesis (BBH) has previously been expressed on account of the weak theoretical foundations of this hypothesis and the anomalies in the empirical record of the simple genetic algorithm. In this paper we hone in on a more fundamental cause for skepticism--the extraordinary strength of some of the assumptions that undergird the BBH. Specifically, we focus on assumptions made about the distribution of fitness over the genome set, and argue that these assumptions are unacceptably strong. As most of these assumptions have been embraced by the designers of so-called "competent" genetic algorithms, our critique is relevant to an appraisal of such algorithms as well.

cs.NE↗

arXiv2007

Sufficient Conditions for Coarse-Graining Evolutionary Dynamics

It is commonly assumed that the ability to track the frequencies of a set of schemata in the evolving population of an infinite population genetic algorithm (IPGA) under different fitness functions will advance efforts to obtain a theory of adaptation for the simple GA. Unfortunately, for IPGAs with long genomes and non-trivial fitness functions there do not currently exist theoretical results that allow such a study. We develop a simple framework for analyzing the dynamics of an infinite population evolutionary algorithm (IPEA). This framework derives its simplicity from its abstract nature. In particular we make no commitment to the data-structure of the genomes, the kind of variation performed, or the number of parents involved in a variation operation. We use this framework to derive abstract conditions under which the dynamics of an IPEA can be coarse-grained. We then use this result to derive concrete conditions under which it becomes computationally feasible to closely approximate the frequencies of a family of schemata of relatively low order over multiple generations, even when the bitstsrings in the evolving population of the IPGA are long.

cs.NE↗