Firefly algorithm: Difference between revisions

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The main update formula for any pair of two fireflies <math>\mathbf{x}_i </math> and <math>\mathbf{x}_j </math> is

:: <math display="block">\mathbf{x}_i^{t+1}=\mathbf{x}_i^t + \beta \exp[-\gamma r_{ij}^2] (\mathbf{x}_j^t - \mathbf{x}_i^t) +\alpha_t \boldsymbol{\epsilon}_t </math>

where <math>\alpha_t </math> is a parameter controlling the step size, while <math>\boldsymbol{\epsilon}_t </math> is a vector drawn from a Gaussian or other

distribution.zae

It can be shown that the limiting case <math>\gamma \rightarrow 0 </math> corresponds to the standard [[Particleparticle Swarmswarm Optimizationoptimization]] (PSO). In fact, if the inner loop (for j) is removed and the brightness <math>I_j</math> is replaced by the current global best <math>g^*</math>, then FA essentially becomes the standard PSO.

== Criticism ==

Nature-inspired [[metaheuristic]]s in general have attracted [[List of metaphor-inspired metaheuristics#Criticism of the metaphor methodology|criticism in the research community]] for hiding their lack of novelty behind metaphors. The firefly algorithm has been criticized as differing from the well-established [[particle swarm optimization]] only in a negligible way.<ref>{{cite journal|first1=Omid N.|last1=Almasi| first2=Modjtaba|last2= Rouhani|year=2016|title=A new fuzzy membership assignment and model selection approach based on dynamic class centers for fuzzy SVM family using the firefly algorithm|journal=Turkish Journal of Electrical Engineering & Computer Sciences|volume=4| pages=1–19|doi=10.3906/elk-1310-253|quote= Practical application of FA on UCI datasets.|doi-access=free}}</ref><ref>{{cite book|first=Michael A.|last=Lones|title=Proceedings of the Companion Publication of the 2014 Annual Conference on Genetic and Evolutionary Computation |chapter=Metaheuristics in nature-inspired algorithms |year=2014|pages=1419–1422|chapter-url=http://www.macs.hw.ac.uk/~ml355/common/papers/lones-gecco2014-metaheuristics.pdf|doi=10.1145/2598394.2609841|quote=FA, on the other hand, has little to distinguish it from PSO, with the inverse-square law having a similar effect to crowding and fitness sharing in EAs, and the use of multi-swarms in PSO.|isbn=9781450328814|citeseerx=10.1.1.699.1825|s2cid=14997975 }}</ref><ref>{{cite journal|first=Dennis|last=Weyland|year=2015|title=A critical analysis of the harmony search algorithm—How not to solve sudoku|journal=Operations Research Perspectives|volume=2|pages=97–105|doi=10.1016/j.orp.2015.04.001|quote=For example, the differences between the particle swarm optimization metaheuristic and "novel" metaheuristics like the firefly algorithm, the fruit fly optimization algorithm, the fish swarm optimization algorithm or the cat swarm optimization algorithm seem negligible.|doi-access=free|hdl=10419/178253|hdl-access=free}}</ref>

==See also==