Spherical Distributions Used in Evolutionary Algorithms

Alexandru Agapie
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Alexandru Agapie: Department of Applied Mathematics, Faculty of Economic Cybernetics, Statistics and Informatics, Bucharest University of Economic Studies, Calea Dorobantilor 15-17, 010552 Bucharest, Romania

Mathematics, 2021, vol. 9, issue 23, 1-15

Abstract: Performance of evolutionary algorithms in real space is evaluated by local measures such as success probability and expected progress. In high-dimensional landscapes, most algorithms rely on the normal multi-variate, easy to assemble from independent, identically distributed components. This paper analyzes a different distribution, also spherical, yet with dependent components and compact support: uniform in the sphere. Under a simple setting of the parameters, two algorithms are compared on a quadratic fitness function. The success probability and the expected progress of the algorithm with uniform distribution are proved to dominate their normal mutation counterparts by order n ! ! .

Keywords: probabilistic optimization; spherical distribution; multi-variate calculus; hypergeometric functions; transition kernel (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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