During the last two decades, a large number of metaheuristics have been proposed, leading to various studies that call for a deeper insight into the behaviour, efficiency and effectiveness of such methods. Among numerous concerns that are briefly reviewed in this paper, the presence of a structural bias (i.e. the tendency, not justified by the fitness landscape, to visit some regions of the search space more frequently than other regions) has recently been detected in simple versions of the genetic algorithm and particle swarm optimization. As of today, it remains unclear how frequently such a behaviour occurs in population-based swarm intelligence and evolutionary computation methods, and to what extent structural bias affects their performance. The present study focuses on the search for structural bias in various variants of particle swarm optimization and differential evolution algorithms, as well as in the traditional direct search methods proposed by Nelder–Mead and Rosenbrock half a century ago. We found that these historical direct search methods are structurally unbiased. However, most tested new metaheuristics are structurally biased, and at least some presence of structural bias can be observed in almost all their variants. The presence of structural bias seems to be stronger in particle swarm optimization algorithms than in differential evolution algorithms. The relationships between the strength of the structural bias and the dimensionality of the search space, the number of allowed function calls and the population size are complex and hard to generalize. For 14 algorithms tested on the CEC2011 real-world problems and the CEC2014 artificial benchmarks, no clear relationship between the strength of the structural bias and the performance of the algorithm was found. However, at least for artificial benchmarks, such old and structurally unbiased methods like Nelder–Mead algorithm performed relatively well. This is a warning that the presence of structural bias in novel metaheuristics may hamper their search abilities.

中文翻译：

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在粒子群优化和微分进化算法中寻找结构偏差

在过去的二十年中，已经提出了大量的元启发式方法，导致了各种各样的研究，需要对这种方法的行为，效率和有效性有更深入的了解。在本文简要回顾的众多问题中，最近已在简单版本中检测到存在结构性偏见（即，没有被适应性景观证明是合理的趋势，比其他区域更频繁地访问搜索空间的某些区域）遗传算法和粒子群优化算法。直到今天，仍不清楚这种行为在基于群体的群体智能和进化计算方法中多久发生一次，以及结构性偏差在多大程度上影响其性能。本研究的重点是寻找粒子群优化和差分进化算法的各种变体以及半个世纪前由Nelder-Mead和Rosenbrock提出的传统直接搜索方法中的结构偏差。我们发现这些历史直接搜索方法在结构上没有偏见。但是，大多数经过测试的新元启发法在结构上都有偏见，并且几乎在所有它们的变体中都可以观察到至少一些结构偏见的存在。在粒子群优化算法中，结构偏差的存在似乎比在差分进化算法中更强。结构偏差的强度与搜索空间的维数，允许的函数调用数和总体大小之间的关系非常复杂，很难一概而论。对于在CEC2011实际问题和CEC2014人工基准上测试的14种算法，没有发现结构偏倚的强度与算法性能之间的明确关系。但是，至少对于人工基准测试，诸如Nelder-Mead算法之类的古老且无结构偏差的方法表现相对较好。这是一种警告，即新颖的元启发法中存在结构性偏见可能会妨碍其搜索能力。