Can Compact Optimisation Algorithms Be Structurally Biased?

Preprints.org

Abstract

In the field of stochastic optimisation, the so-called structural bias constitutes an undesired behaviour of an algorithm that is unable to explore the search space to a uniform extent. In this paper, we investigate whether algorithms from a subclass of estimation of distribution algorithms, the compact algorithms, exhibit structural bias. Our approach, justified in our earlier publications, is based on conducting experiments on a test function whose values are uniformly distributed in its domain. For the experiment, 81 combinations of compact algorithms and strategies of dealing with infeasible solutions have been selected as test cases. We have applied two approaches for determining the presence and severity of structural bias, namely a visual and a statistical (Anderson-Darling) tests. Our results suggest that compact algorithms are more immune to structural bias than their counterparts maintaining explicit populations. Both tests indicate that strong structural bias is found only in one of the algorithms (cBFO) regardless of the choice of strategy of dealing with infeasible solutions and cPSO mirror. For other test cases, statistical and visual tests disagree on some cases classified as having mild or strong structural bias: the former one tends to make harsher decisions, thus needing further investigation.

Authors 4

1. Anna V. Kononova Aachen Leiden Institute of Advanced Computer Science

   Leiden University

   Affiliation as printed

   Leiden Institute of Advanced Computer Science (LIACS) , Leiden University , The Netherlands

   Leiden Institute of Advanced Computer Science (LIACS), Leiden University, The Netherlands

2. Fabio Caraffini corresponding

   De Montfort University

   Affiliation as printed

   Institute of Artificial Intelligence , De Montfort University , UK

   Institute of Artificial Intelligence, De Montfort University, UK

3. Hao Wang

   Sorbonne Université · LIP6

   Affiliation as printed

   LIP6 , Sorbonne Université Paris , France

   LIP6, Sorbonne Université Paris, France

4. Thomas Bäck Aachen Leiden Institute of Advanced Computer Science

   Leiden University

   Affiliation as printed

   Leiden Institute of Advanced Computer Science (LIACS) , Leiden University , The Netherlands

   Leiden Institute of Advanced Computer Science (LIACS), Leiden University, The Netherlands