Theoretical formulation and analysis of the deterministic dendritic cell algorithm
As one of the emerging algorithms in the eld of Articial Immune Systems(AIS), the Dendritic Cell Algorithm (DCA) has been successfully applied to a number of challenging real-world problems. However, one criticism is the lack of a formal denition, which could result in ambiguity for understanding th...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
2013
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| Online Access: | http://eprints.nottingham.ac.uk/2071/ http://eprints.nottingham.ac.uk/2071/ http://eprints.nottingham.ac.uk/2071/ http://eprints.nottingham.ac.uk/2071/1/Theoretical_Formulation_%26_Anaylsis_of_the_Deterministic_Dendritic_Cell_Algorithm.Biosystems_111%282%29.2013.pdf |
| Summary: | As one of the emerging algorithms in the eld of Articial Immune Systems(AIS), the Dendritic Cell Algorithm (DCA) has been successfully applied to a number of challenging real-world problems. However, one criticism is the lack of a formal denition, which could result in ambiguity for understanding the algorithm. Moreover, previous investigations have mainly focused on its empirical aspects. Therefore, it is necessary to provide a formal def-
inition of the algorithm, as well as to perform runtime analyses to reveal its theoretical aspects. In this paper, we dene the deterministic version of the DCA, named the dDCA, using set theory and mathematical functions.
Runtime analyses of the standard algorithm and the one with additional segmentation are performed. Our analysis suggests that the standard dDCA has a runtime complexity of O(n2) for the worst-case scenario, where n is the
number of input data instances. The introduction of segmentation changes the algorithm's worst case runtime complexity to O(max(nN; nz)), for DC population size N with size of each segment z. Finally, two runtime variables
of the algorithm are formulated based on the input data, to understand its runtime behaviour as guidelines for further development. |
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