Can Compact Optimisation Algorithms Be Structurally Biased

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 an (existing) visual and an (updated) statistical (Anderson-Darling) test. 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 the cBFO algorithm, regardless of the choice of strategy of dealing with infeasible solutions, and cPSO with mirror strategy. 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.