# GBS: Optimization using Gravitational Based Search Algorithm. In metaheuristicOpt: Metaheuristic for Optimization

## Description

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

## Usage

 1 2 3 GBS(FUN, optimType = "MIN", numVar, numPopulation = 40, maxIter = 500, rangeVar, gravitationalConst = max(rangeVar), kbest = 0.1) 

## 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). gravitationalConst a numeric to determine gravitational constant while calculating total force. The default value is max(rangeVar). kbest a positive numeric between 0 and 1 to determine fraction of population with best fitness which will affect every candidate solution in population. The default value is 0.1.

## Details

This algorithm was proposed by (Rashedi, 2009). GBS use newton law of universal gravitation and second law of motion to optimize. Every candidate solution in population consider having mass and it move using newton law of universal gravitation and second law of motion.

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

• initialize population randomly.

• calculate gravitational mass of every candidate solution in population.

• calculate total force of every candidate solution in population using newton law of universal gravitation.

• calculate acceleration of every candidate solution in population using newton second law of motion.

• update velocity of every candidate solution in population based on its acceleration.

• move every candidate solution in population based on its velocity.

• If a termination criterion (a maximum number of iterations or a sufficiently good fitness) is met, exit the loop, else back to calculate gravitational mass.

## Value

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

## References

Rashedi, E., Nezamabadi-Pour, H., & Saryazdi, S. (2009). GSA: a gravitational search algorithm. Information sciences, 179(13), 2232-2248.

metaOpt
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 ################################## ## Optimizing the schewefel's problem 2.22 function # define schewefel's problem 2.22 function as objective function schewefels2.22 <- function(x){ return(sum(abs(x)+prod(abs(x)))) } ## Define parameter numVar <- 5 rangeVar <- matrix(c(-10,10), nrow=2) ## calculate the optimum solution using Gravitational Based Search resultGBS <- GBS(schewefels2.22, optimType="MIN", numVar, numPopulation=20, maxIter=100, rangeVar) ## calculate the optimum value using schewefel's problem 2.22 function optimum.value <- schewefels2.22(resultGBS)