Geodesic
Influence of a Neighborhood Shape on the Efficiency of Continuous Variable Neighborhood Search
Yugoslav journal of operations research, Tome 30 (2020) no. 1, p. 3 .

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The efficiency of a Variable neighborhood search metaheuristic for continuous global optimization problems greatly depends on geometric shape of neighborhood structures used by the algorithm. Among the neighborhoods defined by balls in $l_p$, $1 \le p \le \infty$ metric, we tested the $l_1$, $l_2$ and $l_{\infty}$ ball shape neighborhoods, for which there exist efficient algorithms for obtaining uniformly distributed points. On many challenging high-dimensional problems, our exhaustive testings showed that, popular and the easiest for implementation, $l_{\infty}$ ball shape of neighborhoods performed the worst, and much better efficiency was obtained with $l_1$ and $l_2$.
Classification : 90C59, 90C06, 90C30
Keywords: Global Optimization, Continuous Optimization, Metaheuristic Algorithms, Variable Neighborhood Search 
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     author = {Milan Dra\v{z}i\'c},
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Milan Dražić. Influence of a Neighborhood Shape on the Efficiency of Continuous Variable Neighborhood Search. Yugoslav journal of operations research, Tome 30 (2020) no. 1, p. 3 . http://geodesic.mathdoc.fr/item/YJOR_2020_30_1_a0/