Challenging optimisation problems are abundant in all areas of science and industry. Since the 1950s, scientists have responded to this by developing everdiversifying families of 'black box' optimisation algorithms. The latter are designed to be able to address any optimisation problem, requiring only that the quality of any candidate solution can be calculated via a 'fitness function' specific to the problem. For such algorithms to be successful, at least three properties are required: (i) an effective informed sampling strategy, that guides the generation of new candidates on the basis of the fitnesses and locations of previously visited candidates; (ii) mechanisms to ensure efficiency, so that (for example) the same candidates are not repeatedly visited; (iii) the absence of structural bias, which, if present, would predispose the algorithm towards limiting its search to specific regions of the solution space. The first two of these properties have been extensively investigated, however the third is little understood and rarely explored. In this article we provide theoretical and empirical analyses that contribute to the understanding of structural bias. In particular, we state and prove a theorem concerning the dynamics of population variance in the case of real-valued search spaces and a 'flat' fitness landscape. This reveals how structural bias can arise and manifest as non-uniform clustering of the population over time. Critically, theory predicts that structural bias is exacerbated with (independently) increasing population size, and increasing problem difficulty. These predictions, supported by our empirical analyses, reveal two previously unrecognised aspects of structural bias that would seem vital for algorithm designers and practitioners. Respectively, (i) increasing the population size, though ostensibly promoting diversity, will magnify any inherent structural bias, and (ii) the effects of structural bias are more apparent when faced with (many classes of) 'difficult' problems. Our theoretical result also

This paper thoroughly investigates a range of popular DE configurations to identify components responsible for the emergence of structural bias -recently identified tendency of the algorithm to prefer some regions of the search space for reasons directly unrelated to the objective function values. Such tendency was already studied in GA and PSO where a connection was established between the strength of structural bias and population sizes and potential weaknesses of these algorithms was highlighted. For DE, this study goes further and extends the range of aspects that can contribute to presence of structural bias by including algorithmic component which is usually overlooked -constraint handling technique. A wide range of DE configurations were subjected to the protocol for testing for bias. Results suggest that triggering mechanism for the bias in DE differs to the one previously found for GA and PSO -no clear dependency on population size exists. Setting of DE parameters is based on a separate study which on its own leads to interesting directions of new research. Overall, DE turned out to be robust against structural bias -only DE/current-to-best/1/bin is clearly biased but this effect is mitigated by the use of penalty constraint handling technique.

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