ARTICLE | doi:10.20944/preprints202004.0403.v1
Subject: Mathematics & Computer Science, Numerical Analysis & Optimization Keywords: structural bias; compact algorithm; continuous optimisation; estimation of distribution algorithm; infeasible solution
Online: 23 April 2020 (04:49:23 CEST)
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.
ARTICLE | doi:10.20944/preprints202002.0277.v1
Subject: Mathematics & Computer Science, Numerical Analysis & Optimization Keywords: structural bias; algorithmic design; hypothesis testing; single solution methods; constraint handling
Online: 19 February 2020 (11:37:08 CET)
This paper investigates whether optimisation methods with the population made up of one solution can suffer from structural bias just like their multisolution variants. Following recent results highlighting the importance of choice of strategy for handling solutions generated outside the domain, a selection of single solution methods are considered in conjunction with several such strategies. Obtained results are tested for the presence of structural bias by means of a traditional approach from literature and a newly proposed here statistical approach. These two tests are demonstrated to be not fully consistent. All tested methods are found to be structurally biased with at least one of the tested strategies. Confirming results for multisolution methods, it is such strategy that is shown to control the emergence of structural bias in single solution methods. Some of the tested methods exhibit a kind of structural bias that has not been observed before.