AO: Archimedes Optimization

In metaSVR: Support Vector Regression with Metaheuristic Algorithms Optimization

Archimedes Optimization

Description

An algorithm built by Hashim et al. (2021) use buoyancy law and fluid dynamics behavior in Archimedes principle to optimized real-valued objective function in continuous search space in a population-based manner.

Usage

AO(N, Max_iter, lb, ub, dim, fobj)

Arguments

N	An integer indicate population size.
Max_iter	An integer indicate maximum number of iterations.
lb	A numeric vector that show lower bounds of the search space. One value per dimension.
ub	A numeric vector that show upper bounds of the search space. One value per dimension.
dim	An integer show the number of dimension (parameters) of the problem to optimize. It indicate the number of parameters to be optimized.
fobj	An objective function used to be minimized. It is return single numeric value that show evaluation matrix result in every iteration. It used to calculate the best fitness in every iteration.

Details

This algorithm uses population-based search to conduct physical law such as volume, density difference, and acceleration in every iteration. It balancing the exploration and exploitation phase by using Transfer Function (TF) as a shifting indicates.

The algorithm performs until maximum iteration reached or convergence condition when the difference in objective values for ten consecutive times is less than 10^-5.

Value

A list containing:

best_fitness

The best (minimum) fitness value found.

best_position

The parameter vector (position) corresponding to the best fitness.

jml_iter

The number of iterations executed.

param

Matrix of best parameters found across every iterations (dim × iter).

param_list

Vector of best fitness values at each iteration.

Note

The input vectors 'lb' and 'ub' must have the same length as the number of dimensions 'dim'.

This optimization function used inside svrHybrid function.

Constant of C3 = 1 and C4 = 2 used in basic standard optimization function.

References

Hashim, F. A., Hussain, K., Houssein, E. H., Mabrouk, M. S., & Al-Atabany, W. (2021). Archimedes Optimization Algorithm: A New Metaheuristic Algorithm for Solving Optimization Problems. Applied Intelligence, 51(3), 1531–1551. https://doi.org/10.1007/s10489-020-01893-z

Examples

{
sphere_fn <- function(x) sum(x^2) # simple function for objective function

# AO optimization
set.seed(123)
result <- AO(N = 20, Max_iter = 50, lb = c(-5,-5,-5), ub = c(5,5,5), dim = 3, fobj = sphere_fn)

# View best fitness and position found
result$best_fitness
result$best_position
}

metaSVR documentation built on Aug. 21, 2025, 5:58 p.m.