# SCA: Optimization using Sine Cosine Algorithm In metaheuristicOpt: Metaheuristic for Optimization

## Description

This is the internal function that implements Sine Cosine Algorithm. It is used to solve continuous optimization tasks. Users do not need to call it directly, but just use metaOpt.

## Usage

 1 2 SCA(FUN, optimType = "MIN", numVar, numPopulation = 40, maxIter = 500, rangeVar) 

## Arguments

 FUN an objective function or cost function, optimType a string value that represent the type of optimization. There are two option for this arguments: "MIN" and "MAX". The default value is "MIN", which the function will do minimization. Otherwise, you can use "MAX" for maximization problem. The default value is "MIN". numVar a positive integer to determine the number variables. numPopulation a positive integer to determine the number populations. The default value is 40. maxIter a positive integer to determine the maximum number of iterations. The default value is 500. rangeVar a matrix (2 \times n) containing the range of variables, where n is the number of variables, and first and second rows are the lower bound (minimum) and upper bound (maximum) values, respectively. If all variable have equal upper bound, you can define rangeVar as matrix (2 \times 1).

## Details

This algorithm was proposed by (Mirjalili, 2016). The SCA creates multiple initial random candidate solutions and requires them to fluctuate outwards or towards the best solution using a mathematical model based on sine and cosine functions. Several random and adaptive variables also are integrated to this algorithm to emphasize exploration and exploitation of the search space in different milestones of optimization.

In order to find the optimal solution, the algorithm follow the following steps.

• Initialization: Initialize the first population of candidate solution randomly, calculate the fitness of candidate solution and find the best candidate.

• Update Candidate Position: Update the position with the equation that represent the behaviour of sine and cosine function.

• Update the best candidate if there are candidate solution with better fitness.

• Check termination criteria, if termination criterion is satisfied, return the best candidate as the optimal solution for given problem. Otherwise, back to Update Candidate Position steps.

## Value

Vector [v1, v2, ..., vn] where n is number variable and vn is value of n-th variable.

## References

Seyedali Mirjalili, SCA: A Sine Cosine Algorithm for solving optimization problems, Knowledge-Based Systems, Volume 96, 2016, Pages 120-133, ISSN 0950-7051, https://doi.org/10.1016/j.knosys.2015.12.022

metaOpt
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ################################## ## Optimizing the step function # define step function as objective function step <- function(x){ result <- sum(abs((x+0.5))^2) return(result) } ## Define parameter numVar <- 5 rangeVar <- matrix(c(-100,100), nrow=2) ## calculate the optimum solution using Sine Cosine Algorithm resultSCA <- SCA(step, optimType="MIN", numVar, numPopulation=20, maxIter=100, rangeVar) ## calculate the optimum value using step function optimum.value <- step(resultSCA)