Analytic Continued Fractions for Regression: A Memetic Algorithm Approach

Moscato, Pablo; Sun, Haoyuan; Haque, Mohammad Nazmul

doi:10.1016/j.eswa.2021.115018

Cited by 14 publications

(20 citation statements)

References 65 publications

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“…We used a method based on multivariate regression using an analytic continued fraction representation of our target function of interest [20][21][22][23][24] . We looked at approximating E(n) as follows:…”

Section: A First Approximation Using Continued Fraction Regressionmentioning

confidence: 99%

Continued fractions and the Thomson Problem

Moscato

Haque

Moscato

2022

Preprint

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We introduce new analytical approximations of the minimum electrostatic energy configuration of n electrons, E(n), when they are constrained to be on the surface of a unit sphere. Using 454 putative optimal configurations we searched for approximations of the form E(n) = (n2/2) e g(n) where g(n) was obtained via a memetic algorithm that searched for truncated analytic continued fractions finally obtaining one with Mean Squared Error equal to 4.5744×10^(-8). Using the Online Encyclopedia of Integer Sequences, we searched over 350,000 sequences and, for small values of n, we identified a strong correlation of the highest residual of our best approximations with the sequence of integers n defined by the condition that n2 +12 is a prime. We also observed an interesting correlation with the behaviour of the smallest angle α(n), measured in radians, subtended by the vectors associated with the nearest pair of electrons in the optimal configuration. When using both √n and α(n) as variables a very simple approximation formula for E(n) was obtained with MSE = 7.9963×10^(-8). When expanded as a power series in infinity, we observe that an unknown constant of an expansion as a function of n-1/2 of E(n) first proposed by Glasser and Every in 1992 as -1.1039, and later refined by Morris, Deaven and Ho as -1.104616 in 1996, may actually be very close to -1-π/30.

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Section: A First Approximation Using Continued Fraction Regressionmentioning

confidence: 99%

Continued fractions and the Thomson Problem

Moscato

Haque

Moscato

2022

Preprint

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“…Among these approaches, we mention the well-known genetic algorithms (GA) 17 and the memetic algorithms (MA). 18 This work proposes a new method called Evolutionary Iterated Local Search (EILS) to solve the APP. The proposed method explores the search space using several local searches, evolutionary operations of crossing and mutation and a new mechanism for choosing the starting solution to relaunch a new search cycle.…”

Section: Introductionmentioning

confidence: 99%

“…They use reproduction operators such as crossover and mutation for generating new improved individuals. Among these approaches, we mention the well‐known genetic algorithms (GA) 17 and the memetic algorithms (MA) 18 …”

Section: Introductionmentioning

confidence: 99%

Evolutionary Iterated Local Search meta‐heuristic for the antenna positioning problem in cellular networks

Benmezal

Benhamou²,

Boughaci

2021

Computational Intelligence

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Radio network planning is a core problem in cellular networks. It includes coverage, capacity and parameter planning. This paper investigates the Antenna Positioning Problem (APP) which is a main task in cellular networks planning. The aim is to find a trade‐off between maximizing coverage and minimizing costs. APP is the task of selecting a subset of potential locations where installing the base stations to cover the entire area. In theory, the APP is NP‐hard. To solve it in practice, we propose a new meta‐heuristic called Evolutionary Iterated Local Search that merges the local search method and some evolutionary operations of crossover and mutation. The proposed method is implemented and evaluated on realistic, synthetic and random instances of the problem of different sizes. The numerical results and the comparison with the state‐of‐the‐art show that the proposed method succeeds in finding good results for the considered problem.

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“…• We extend the continued fraction regression method presented in Moscato et al (2021) which represents mathematical expressions. We utilised two advantages of this method: feature subset selection and optimising the coefficients by means of an iterative approach.…”

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confidence: 99%

“…for non-linear regression problems (Moscato et al, 2021Sun & Moscato, 2019) and other machine learning problems (Moscato & Mathieson, 2019).…”

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confidence: 99%