Ant Lion Optimizer

Description

An algorithm built by Mirjalili (2015) inspired by the hunting behaviour of antlion whose making pit trap for ant prey in order to optimized real-valued objective function in continuous search space in a population-based manner.

Usage

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

Arguments

Details

The algorithm mimics the ALO hunting behaviour by simulating a stochastic search where ants move around randomly under the influence of selected antlions and an elite antlion.

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.

References

Mirjalili, S. (2015). The Ant Lion Optimizer. Advances in Engineering Software, 83, 80-98. https://doi.org/10.1016/j.advengsoft.2015.01.010.

Examples

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

# ALO optimization
set.seed(123)
result <- ALO(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
}

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

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
}

Combined Archimedes Optimization with Coot Bird Optimization

Description

A hybrid metaheuristic algorithm that combines Archimedes Optimization (AO) with Coot Bird Optimization (CBO) to optimized real-valued objective function in continuous search space.

Usage

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

Arguments

Details

This metaheuristic implement combination of all step of Archimedes Optimization with first step used after initialization is Coot Leader selection stage in CBO as early exploration step. The hybrid design enhances convergence and stability in optimization step so it can maximize the best parameter.

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.

Examples

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

# AOCBO optimization
set.seed(123)
result <- AOCBO(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
}

Coot Bird Optimization

Description

An algorithm built by Naruei & Keynia (2021) that mimics the regular-irregular movement behaviour of Coot birds. Its population divided by two groups as leaders to guide the process and coots to follow leaders and randomly explore search space. This movement use to optimized real-valued objective function in continuous search space.

Usage

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

Arguments

Details

This algorithms used movement such as: random movement, chain movement, adjusting the position based on the group leaders, and leader movement to emphasize the exploration and exploitation phase to get the best fitness.

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.

References

Naruei, I., & Keynia, F. (2021). A New Optimization Method Based on COOT Bird Natural Life Model. Expert Systems with Applications, 183. https://doi.org/10.1016/j.eswa.2021.115352

Examples

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

# CBO optimization
set.seed(123)
result <- CBO(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
}

Enhanced Harris Hawks Optimization with Coot Bird Optimization

Description

This function implements a hybrid metaheuristic optimization algorithm that combines Harris Hawks Optimization with leader selection of Coot Bird Optimization to optimized real-valued objective function in continuous search space in a population-based manner built by Cui et al. (2023).

Usage

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

Arguments

Details

This algorithm start by adding leadership mechanism of CBO into HHO process so it can make better foundation for the global search. Ensemble Mutation Strategy (EMS) to improve the exploration trend and population diversity also Refracted Opposition-Based Learning (ROBL) to update current optimal solution in the swarm added to enhanced the combination of HHO and CBO.

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.

References

Cui, H., Guo, Y., Xiao, Y., Wang, Y., Li, J., Zhang, Y., & Zhang, H. (2023). Enhanced Harris Hawks Optimization Integrated with Coot Bird Optimization for Solving Continuous Numerical Optimization Problems. CMES - Computer Modeling in Engineering and Sciences, 137(2), 1635–1675. https://doi.org/10.32604/cmes.2023.026019

Examples

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

# EHHOCBO optimization
set.seed(123)
result <- EHHOCBO(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
}

Grey Wolf Optimizer

Description

An algorithm built by Mirjalili et al. (2014) inspired by leadership hierarchy and hunting mechanism of grey wolves in nature to optimized real-valued objective function in continuous search space in a population-based manner.

Usage

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

Arguments

Details

This algorithm proposed social hierarchy on GWO to obtain the best fitness and get the best proposed hunting method to locate probable position of the pray. Adaptive values on alpha and A make it possible smooth transition between exploration and exploitation phase.

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.

References

Mirjalili, S., Mirjalili, S. M., & Lewis, A. (2014). Grey wolf optimizer. Advances in engineering software, 69, 46-61. https://doi.org/10.1016/j.advengsoft.2013.12.007

Examples

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

# GWO optimization
set.seed(123)
result <- GWO(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
}

Harris Hawks Optimization

Description

An algorithm built by Heidari et al. (2019) that inspired by the movement of Harris Hawks on cooperative hunting behaviour to optimized real-valued objective function in continous search space in a population-based manner.

Usage

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

Arguments

Details

There are two phase of Harris Hawks hunting, namely exploration and exploitation that will be modelized to find optimization result. The movement used in this algorithms such as: exploration phase; transition between exploitation and exploration phase; and exploitation phase that has 4 different strategies based on E and r (soft besiege, hard besiege, soft besiege with progressive rapid, and hard besiege with progressive rapid).

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.

References

Heidari, A. A., Mirjalili, S., Faris, H., Aljarah, I., Mafarja, M., & Chen, H. (2019). Harris hawks optimization: Algorithm and applications. Future generation computer systems, 97, 849-872. https://doi.org/10.1016/j.future.2019.02.028

Examples

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

# HHO optimization
set.seed(123)
result <- HHO(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
}

Perform Random Walk Around Antlion

Description

Function simulates random walk of an ant within the boundaries influenced by an antlion's position.

Usage

Random_walk_around_antlion(dim, Max_iter, lb, ub, antlion, current_iter)

Arguments

Value

A numeric matrix of shape (N, dim) representing the position of the ant in each step of the random walk.

Note

This function used inside ALO function to update the position of ants.

Roulette Wheel Selection

Description

Function used to select an individual index based on fitness-proportional selection (inverse fitness weight).

Usage

RouletteWheelSelection(weights)

Arguments

Value

An integer representing the selected index.

Note

This function used inside ALO function to probabilistically select antlions for guiding ants.

Denormalize

Description

Convert normalized data back to original scale using given min and max.

Usage

denormalize(x, min, max)

Arguments

Value

A numeric vector already converted to original scale.

Examples

# Example of the original data
original_data <- c(10, 20, 30, 40, 50)

# Data being normalized
normalized_data <- (original_data - min(original_data)) /
                   (max(original_data) - min(original_data))

# Denormalization function use to change value to the original
denormalize(normalized_data, min(original_data), max(original_data))

Default Bounds Initialization for SVR Optimization

Description

This function return the default value of lower and upper bounds also the dimension for SVR optimization. The three dimensions represent as the parameter that need to be optimized in SVR with exact range of bound. Three dimension and the range represent as: Cost (C): 2^0 to 2^10; Gamma: 2^(-8) to 2^0; Epsilon: 2^(-8) to 2^0.

Usage

get_default_bounds()

Value

A list containing:

lb

A numeric vector of lower bounds.

ub

A numeric vector of upper bounds.

dim

An integer representing the number of dimensions, 3.

Note

The bounds for parameters search space is based on previous research with range: Cost=[2^0,2^10], Gamma=[2^(-8),2^0], dan Epsilon=[2^(-8),2^0]

References

Liu, H.-H., Chang, L.-C., Li, C.-W., & Yang, C.-H. (2018). Particle Swarm Optimization-Based Support Vector Regression for Tourist Arrivals Forecasting. Computational Intelligence and Neuroscience, 2018, 1–13. https://doi.org/10.1155/2018/6076475.

Examples

bounds <- get_default_bounds()
bounds$lb  # Lower bounds
bounds$ub  # Upper bounds
bounds$dim # Number of parameters

Initialize Position on Ant Lion Optimizer

Description

This function generates the initial position of antlions and ants within the defined upper and lower bound in every dimension.

Usage

initALO(N, dim, ub, lb)

Arguments

Value

A numeric matrix of shape (N, dim) representing initialized positions.

Note

This function used inside ALO function for initialization process.

Initialize Position on Enhanced Harris Hawks Optimization with Coot Bird Optimization

Description

This function generates the initial position of all agents (X) within the defined upper and lower bound in every dimension.

Usage

initEHHOCBO(N, dim, ub, lb)

Arguments

Value

A numeric matrix of shape (N, dim) representing initialized positions.

Note

This function used inside EHHOCBO function for initialization process.

Initialize Position on Grey Wolf Optimizer

Description

This function generates the initial position of gray wolf within the defined upper and lower bound in every dimension.

Usage

initGWO(N, dim, ub, lb)

Arguments

Value

A numeric matrix of shape (N, dim) representing initialized positions.

Note

This function used inside GWO function for initialization process.

Initialize Position on Harris Hawks Optimization

Description

This function generates the initial position of Harris Hawk agents within the defined upper and lower bound in every dimension.

Usage

initHHO(N, dim, ub, lb)

Arguments

Value

A numeric matrix of shape (N, dim) representing initialized positions.

Note

This function used inside HHO function for initialization process.

Levy Flight Generator

Description

Generates a random step vector based on Lévy flight distribution, used in the exploitation phase of HHO that used as combined in EHHOCBO.

Usage

levyEHHOCBO(dim)

Arguments

Value

A numeric vector of length dim representing the Lévy flight step.

Note

This function used inside EHHOCBO function to generate random Levy Flight vector.

Levy Flight Generator

Description

Generates a random step vector based on Lévy flight distribution, used in the exploitation phase of the HHO algorithm.

Usage

levyHHO(dim)

Arguments

Value

A numeric vector of length dim representing the Lévy flight step.

Note

This function used inside HHO function to generate random Levy Flight vector.

Calculate Loss Based on Selected Objective Function

Description

Compute the loss between predictive and actual values using a selected objective function. Supported objecive functions used in this functions are: "SMAPE', "MAPE", "RMSE", and "MAE".

Usage

loss_calculate(preds, actuals, objective)

Arguments

Value

A numeric value that represent the computed loss.

Examples

preds <- c(80, 120, 180)
actuals <- c(95, 115, 177)
loss_calculate(preds, actuals, "RMSE")

Mean Absolute Error

Description

Calculate the RMSE value between predicted and actual values.

Usage

mae(preds, actuals)

Arguments

Value

MAE value.

Examples

preds <- c(80, 120, 180)
actuals <- c(95, 115, 177)
mae(preds, actuals)

Mean Absolute Percentage Error

Description

Calculate the MAPE value between predicted and actual values. Can't be used if the actual values contain 0 value.

Usage

mape(preds, actuals)

Arguments

Value

MAPE value (percentage).

Examples

preds <- c(80, 120, 180)
actuals <- c(95, 115, 177)
mape(preds, actuals)

Normalize

Description

Normalize data using min-max scale.

Usage

normalize(x)

Arguments

Value

A numeric vector scaled between 0 and 1.

Examples

# Normalize example use:
data <- c(10, 20, 30, 40, 50)
normalize(data)

Root Mean Squared Error

Description

Calculate the RMSE value between predicted and actual values.

Usage

rmse(preds, actuals)

Arguments

Value

RMSE value.

Examples

preds <- c(80, 120, 180)
actuals <- c(95, 115, 177)
rmse(preds, actuals)

Symmetric Mean Absolute Percentage Error

Description

Calculate the SMAPE value between predicted and actual values.

Usage

smape(preds, actuals)

Arguments

Value

SMAPE value (percentage).

Examples

preds <- c(80, 120, 180)
actuals <- c(95, 115, 177)
smape(preds, actuals)

SVR with Metaheuristic Algorithms Optimization

Description

Trains a Support vector Regression Model by optimizing its parameter (Cost, Gamma, and Epsilon) using Metaheuristic Algorithms such as: Archimedes Optimization (AO), Coot Bird Optimization (CBO), Combined Archimedes Optimization with Coot Bird Optimization (AOCBO), Harris Hawks Optimization (HHO), Grey Wolf Optimizer (GWO), Ant Lion Optimization (ALO), and Enhanced Harris Hawks Optimization with Coot Bird Optimization (EHHOCBO).

Usage

svrHybrid(
  x_train,
  y_train,
  x_test,
  y_test,
  kernel = "radial",
  optimizer = "AO",
  objective = "RMSE",
  is.y.normalize = FALSE,
  min.y = min.y,
  max.y = max.y,
  max_iter = 100,
  N = 30,
  seed = 123,
  degree = 3,
  coef0 = 0,
  nu = 0.5,
  class.weights = NULL,
  cachesize = 40,
  tolerance = 0.001,
  scale = TRUE,
  shrinking = TRUE,
  cross = 0,
  probability = FALSE,
  fitted = TRUE,
  subset,
  na.action = na.omit
)

Arguments

Value

A list containing:

best_params

A list with the best values for 'cost', 'gamma', and 'epsilon'.

total_iter

Total number of iterations run by the optimizer.

model

The final trained SVR model (using 'e1071::svm').

time

Total training time in HMS format.

Examples

{
set.seed(1)
x <- matrix(rnorm(100), ncol = 2)
y <- x[,1] * 3 + rnorm(50)
model <- svrHybrid(x_train = x[1:40,], y_train = y[1:40],
                   x_test = x[41:50,], y_test = y[41:50],
                   kernel = "radial", optimizer = "AO",
                   objective = "RMSE", is.y.normalize = FALSE)
# To
model$best_params
}