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Geometric crossover is a representation-independent generalization of traditional crossover for binary strings. It is defined in a simple geometric way by using the distance associated with the search space. Many interesting recombination operators for the most frequently used representations are geometric crossovers under some suitable distance. Showing that a given recombination operator is a geometric...
Using an exact coarse-grained formulation of the dynamics of a GA we investigate in the context of a tunable family of “modular” fitness landscapes under what circumstances one would expect recombination to be “useful”. We show that this depends not only on the fitness landscape and the state of the population but also on the particular crossover mask under consideration. We conclude that rather than...
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...
Evolutionary algorithms are randomized search heuristics that are often described as robust general purpose problem solvers. It is known, however, that the performance of an evolutionary algorithm may be very sensitive to the setting of some of its parameters. A different perspective is to investigate changes in the expected optimization time due to small changes in the fitness landscape. A class...
In this paper, the behavior of intermediate (μ/μI,λ)-ES with self-adaptation is considered for two classes of ridge functions: the sharp and the parabolic ridge. Using a step-by-step approach to describe the system’s dynamics, we will investigate the underlying causes for the different behaviors of the ES on these function types and the effects of intermediate recombination.
The infinite population model for the genetic algorithm, where the iteration of the genetic algorithm corresponds to an iteration of a map G, is a discrete dynamical system. The map G is a composition of a selection operator and a mixing operator, where the latter models the effects of both mutation and crossover. This paper shows that for a typical mixing operator, the fixed point set of G is finite...
In the case where the search space has a group structure, classical genetic operators (mutation and two-parent crossover) which respect the group action are completely characterized by formulas defining them in terms of the search space and its group operation. This provides a representation-free implementation for those operators, in the sense that the genotypic encoding of search space elements...
We show that a fitness function, when taken together with an algorithm, can be reformulated as a set of probability distributions. This set can, in some cases, be equivalently viewed as an information vector which gives ordering information about pairs of search points in the domain. Certain performance criteria definable over such an information vector can be learned by linear regression in such...
The effects of neutrality on evolutionary search are not fully understood. In this paper we make an effort to shed some light on how and why bit-wise neutrality – an important form of neutrality induced by a genotype-phenotype map where each phenotypic bit is obtained by transforming a group of genotypic bits via an encoding function – influences the behaviour of a mutation-based GA on functions of...
We propose a method to build discrete Markov chain models of continuous stochastic optimisers that can approximate them on arbitrary continuous problems to any precision. We discretise the objective function using a finite element method grid which produces corresponding distinct states in the search algorithm. Iterating the transition matrix gives precise information about the behaviour of the optimiser...
Barrier trees are a convenient way of representing the structure of complex combinatorial landscapes over graphs. Here we generalize the concept of barrier trees to landscapes defined over general multi-parent search operators based on a suitable notion of topological connectedness that depends explicitly on the search operator. We show that in the case of recombination spaces, path-connectedness...
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