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14.11.2016 | Ausgabe 4/2016 Open Access

Swarm Intelligence 4/2016

Searching for structural bias in particle swarm optimization and differential evolution algorithms

Swarm Intelligence > Ausgabe 4/2016
Adam P. Piotrowski, Jaroslaw J. Napiorkowski
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The online version of this article (doi:10.​1007/​s11721-016-0129-y) contains supplementary material, which is available to authorized users.


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.

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