Estimating the number of basins of attraction of multi-objective combinatorial problems

Drugan, Mădălina M.

doi:10.1007/s10878-018-0357-8

Cited by 2 publications

(2 citation statements)

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“…The concept of attraction basins has been used in many fields, such as Economy [1][2][3], Mathematics [4][5][6], Biology [7][8][9], Physics [10][11][12], Computer Science [13][14][15], etc. Their definitions may vary in different degrees (even within the same field), although the underlying idea stays the same.…”

Section: Introductionmentioning

confidence: 99%

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Attraction Basins in Metaheuristics: A Systematic Mapping Study

2021

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Context: In this study, we report on a Systematic Mapping Study (SMS) for attraction basins in the domain of metaheuristics. Objective: To identify research trends, potential issues, and proposed solutions on attraction basins in the field of metaheuristics. Research goals were inspired by the previous paper, published in 2021, where attraction basins were used to measure exploration and exploitation. Method: We conducted the SMS in the following steps: Defining research questions, conducting the search in the ISI Web of Science and Scopus databases, full-text screening, iterative forward and backward snowballing (with ongoing full-text screening), classifying, and data extraction. Results: Attraction basins within discrete domains are understood far better than those within continuous domains. Attraction basins on dynamic problems have hardly been investigated. Multi-objective problems are investigated poorly in both domains, although slightly more often within a continuous domain. There is a lack of parallel and scalable algorithms to compute attraction basins and a general framework that would unite all different definitions/implementations used for attraction basins. Conclusions: Findings regarding attraction basins in the field of metaheuristics reveal that the concept alone is poorly exploited, as well as identify open issues where researchers may improve their research.

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Section: Introductionmentioning

confidence: 99%

“…Ref. [15]: "The basin of attraction of the Pareto local solution p, is the set of solutions for which B(p) = {s ∈ S | p ∈ maxPLS(s )}", where maxPLS is the maximal Pareto local search algorithm from [15].…”

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confidence: 99%