  Challenging optimisation problems are abundant in all areas of science. Since
the 1950s, scientists have developed ever-diversifying families of black box
optimisation algorithms designed to address any optimisation problem, requiring
only that quality of a candidate solution is calculated via a fitness function
specific to the problem. For such algorithms to be successful, at least three
properties are required: an effective informed sampling strategy, that guides
generation of new candidates on the basis of fitnesses and locations of
previously visited candidates; mechanisms to ensure efficiency, so that same
candidates are not repeatedly visited; absence of structural bias, which, if
present, would predispose the algorithm towards limiting its search to some
regions of solution space. The first two of these properties have been
extensively investigated, however the third is little understood. In this
article we provide theoretical and empirical analyses that contribute to the
understanding of structural bias. We prove a theorem concerning dynamics of
population variance in the case of real-valued search spaces. This reveals how
structural bias can manifest as non-uniform clustering of population over time.
Theory predicts that structural bias is exacerbated with increasing population
size and problem difficulty. These predictions reveal two previously
unrecognised aspects of structural bias. Respectively, increasing population
size, though ostensibly promoting diversity, will magnify any inherent
structural bias, and effects of structural bias are more apparent when faced
with difficult problems. Our theoretical result also suggests that two commonly
used approaches to enhancing exploration, increasing population size and
increasing disruptiveness of search operators, have quite distinct implications
in terms of structural bias.
