基于群体的算法中的结构偏差
Structural bias in population-based algorithms
摘要：
在科学的各个领域都有大量的最优化问题。自20世纪50年代以来，科学家们已经开发出了不断多样化的黑盒优化算法家族，旨在解决任何优化问题，只需要通过特定于问题的适应度函数计算候选解决方案的质量。对于这样的算法是成功的，至少需要三个属性：一个有效的知情抽样策略，指导新的候选人的基础上的适应性和位置的先前访问的候选人的生成;机制，以确保效率，使相同的候选人不会被重复访问;没有结构性偏差，如果存在结构性偏差，则会使算法倾向于将其搜索限制在解空间的某些区域。前两个属性已经被广泛研究，但第三个很少被理解。在这篇文章中，我们提供了理论和实证分析，有助于理解结构性偏见。在实值搜索空间中证明了种群方差动力学的一个定理。这揭示了结构性偏差如何随着时间的推移表现为人口的不均匀聚集。理论预测，结构性偏差会随着人口规模和问题难度的增加而加剧。这些预测揭示了结构性偏差的两个以前未被认识到的方面。相应地，人口规模的增加虽然表面上促进了多样性，但会放大任何固有的结构性偏差，并且结构性偏差的影响在面临困难问题时更加明显。我们的理论结果还表明，两种常用的方法，以加强探索，增加人口规模和增加搜索运营商的破坏性，有相当不同的影响结构性偏差。
英文摘要：
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.
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