Differential Evolution is a popular optimisation method with a small number of parameters. However, different hyper-parameters and Differential Evolution variants such as different mutation... Show moreDifferential Evolution is a popular optimisation method with a small number of parameters. However, different hyper-parameters and Differential Evolution variants such as different mutation operators and the F and Cr parameter may introduce structural bias. Structural bias is a form of bias where artefacts in the algorithm lead to a preference to particular regions in the search space regardless of the objective function. Many algorithm configurations suffer from structural bias, but it is very hard to automatically detect it and even harder to detect what kind of structural bias is involved and what component might be the cause of it. A comprehensive study of the occurrence and type of structural bias in Differential Evolution configurations has not yet been carried out till now. In this chapter, we systematically evaluate 10980 Differential Evolution configurations on structural bias with the open-source BIAS toolbox. Using this toolbox we identify which configurations cause bias and what type of bias it is. In addition, we analyse the results to make clear recommendations on which components and parameters can be used in Differential Evolution to ensure unbiased behaviour within reasonable computational budget. Show less
This paper investigates how often the popular configurations of Differential Evolution generate solutions outside the feasible domain. Following previous publications in the field, we argue that... Show moreThis paper investigates how often the popular configurations of Differential Evolution generate solutions outside the feasible domain. Following previous publications in the field, we argue that what the algorithm does with such solutions and how often this has to happen is important for the overall performance of the algorithm and interpretation of results. Significantly more solutions than what is usually assumed by practitioners have to undergo some sort of 'correction' to conform with the definition of the problem's search domain. A wide range of popular Differential Evolution configurations is considered in this study. Conclusions are made regarding the effect the Differential Evolution components and parameter settings have on the distribution of percentages of infeasible solutions generated in a series of independent runs. Results shown in this study suggest strong dependencies between percentages of generated infeasible solutions and every aspect mentioned above. Further investigation of the distribution of percentages of generated infeasible solutions is required. Show less
Structural Bias (SB) is an important type of algorithmic deficiency within iterative optimisation heuristics. However, methods for detecting structural bias have not yet fully matured, and recent... Show moreStructural Bias (SB) is an important type of algorithmic deficiency within iterative optimisation heuristics. However, methods for detecting structural bias have not yet fully matured, and recent studies have uncovered many interesting questions. One of these is the question of how structural bias can be related to anisotropy. Intuitively, an algorithm that is not isotropic would be considered structurally biased. However, there have been cases where algorithms appear to only show SB in some dimensions. As such, we investigate whether these algorithms actually exhibit anisotropy, and how this impacts the detection of SB. We find that anisotropy is very rare, and even in cases where it is present, there are clear tests for SB which do not rely on any assumptions of isotropy, so we can safely expand the suite of SB tests to encompass these kinds of deficiencies not found by the original tests.We propose several additional testing procedures for SB detection and aim to motivate further research into the creation of a robust portfolio of tests. This is crucial since no single test will be able to work effectively with all types of SB we identify. Show less
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... Show moreThis 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. Show less
