Description Usage Arguments Details Value References See Also Examples

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`

.

1 2 3 |

`FUN` |
an objective function or cost function, |

`optimType` |
a string value that represent the type of optimization.
There are two option for this arguments: |

`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 ( |

`gravitationalConst` |
a numeric to determine gravitational constant while
calculating total force. The default value is |

`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. |

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.

`Vector [v1, v2, ..., vn]`

where `n`

is number variable
and `vn`

is value of `n-th`

variable.

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

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)
``` |

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