Abstract
This paper presents a new way of measuring complexity in variable-size-chromosome-based evolutionary algorithms. Dealing with complexity is particularly useful when considering bloat in Genetic Programming. Instead of analyzing size growth, we focus on the time required for individuals’ fitness evaluations, which correlates with size. This way, we consider time and space as two sides of a single coin when devising a more natural method for fighting bloat. We thus view the problem from a perspective that departs from traditional methods applied in Genetic Programming. We have analyzed first the behavior of individuals across generations, taking into account their fitness evaluation times, thus providing clues about the general practice of the evolutionary process when modern parallel and distributed computers are used to run the algorithm. This new perspective allows us to understand that new methods for bloat control can be derived. Moreover, we develop from this framework a first proposal to show the usefulness of the idea: to group individuals in classes according to computing time required for evaluation, automatically accomplished by parallel and distributed systems without any change in the underlying algorithm, when they are only allowed to breed within their classes. Experimental data confirms the strength of the approach: using computing time as a measure of individuals’ complexity allows control of the natural size growth of genetic programming individuals while preserving the quality of solutions in both the parallel and sequential versions of the algorithm.
Highlights
Genetic Programming (GP) became popular from the mid-nineties onwards, after Koza published his first book on the topic [1]
We show how this new relationship could benefit EAs with chromosomes of variable size, enabling the development of new kinds of bloat-control mechanisms that can naturally benefit from the underlying parallel processors that are present in modern computer systems, including handheld devices, desktop systems, and large computer systems
(2) we show that the approach leads to a new kind of straightforward bloat control mechanism, and (3) we present the first such implementation based on fitness evaluation time, tested in both sequential and parallel executions of the algorithm
Summary
Genetic Programming (GP) became popular from the mid-nineties onwards, after Koza published his first book on the topic [1]. This machine learning technique has widely demonstrated capabilities for addressing hard, real-world problems, and in the case of tree-based GP, a challenge remains: the bloat phenomenon, see [2]–[4]. The associate editor coordinating the review of this manuscript and approving it for publication was Nuno Garcia. According to [5], fitness improvement correlates with the inherent bloating behavior present in any evolutionary approach using variable-size chromosomes. Many authors have addressed this problem from different perspectives, no perfect solution exists, and there is still room for improvement
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