arXiv subjects

Arnaud Berny

Publications and source records attributed to Arnaud Berny.

3 recordsLinked to original sources

arXiv2023

An information-theoretic evolutionary algorithm

We propose a novel evolutionary algorithm on bit vectors which derives from the principles of information theory. The information-theoretic evolutionary algorithm (it-EA) iteratively updates a search distribution with two parameters, the center, that is the bit vector at which standard bit mutation is applied, and the mutation rate. The mutation rate is updated by means of information-geometric optimization and the center is updated by means of a maximum likelihood principle. Standard elitist and non elitist updates of the center are also considered. Experiments illustrate the dynamics of the mutation rate and the influence of hyperparameters. In an empirical runtime analysis, on OneMax and LeadingOnes, the elitist and non elitist it-EAs obtain promising results.

cs.NE↗

arXiv2021

Linear representation of categorical values

We propose a binary representation of categorical values using a linear map. This linear representation preserves the neighborhood structure of categorical values. In the context of evolutionary algorithms, it means that every categorical value can be reached in a single mutation. The linear representation is embedded into standard metaheuristics, applied to the problem of Sudoku puzzles, and compared to the more traditional direct binary encoding. It shows promising results in fixed-budget experiments and empirical cumulative distribution functions with high dimension instances, and also in fixed-target experiments with small dimension instances.

cs.NE↗

arXiv2021

Affine OneMax

A new class of test functions for black box optimization is introduced. Affine OneMax (AOM) functions are defined as compositions of OneMax and invertible affine maps on bit vectors. The black box complexity of the class is upper bounded by a polynomial of large degree in the dimension. The proof relies on discrete Fourier analysis and the Kushilevitz-Mansour algorithm. Tunable complexity is achieved by expressing invertible linear maps as finite products of transvections. The black box complexity of sub-classes of AOM functions is studied. Finally, experimental results are given to illustrate the performance of search algorithms on AOM functions.

cs.NE↗