Optimasi

library(mosaicCalc)

## Loading required package: mosaic

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## Attaching package: 'mosaic'

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## Loading required package: mosaicCore

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## Attaching package: 'mosaicCore'

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## The legacy packages maptools, rgdal, and rgeos, underpinning the sp package,
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## It may be desirable to make the sf package available;
## package maintainers should consider adding sf to Suggests:.

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Optimasi adalah proses mencari solusi optimal (minimum atau maksimum) dengan memperhatikan batasan yang ada. optimasi memaksimalkan atau meminimalkan beberapa fungsi relative terhadap beberapa set, sering mewakili berbagai pilihan yang tersedia dalam situasi tertentu. Fungsinya memungkinkan perbandingan pilihan yang berbeda untuk menentukan mana yang bias dijadikan pilihan yang terbaik.

3 Cari Metode atau algoritma yang sering digunakan pada Optimasi, berdasarkan: 1. Optimasi Satu Dimensi

f <- function(x) {sin(x) + sin(2 * x) + cos(3 * x)}
optimize(f, interval = c(0, 2 * pi))

## $minimum
## [1] 3.033129
## 
## $objective
## [1] -1.054505

2. Optimasi Multidimensi

f <- function(x) 2*(x[1]-1)^2+5*(x[2]-3)^2+10
optim(c(1,1),f)

## $par
## [1] 1.000168 3.000232
## 
## $value
## [1] 10
## 
## $counts
## function gradient 
##       75       NA 
## 
## $convergence
## [1] 0
## 
## $message
## NULL

3. Pemrograman Linier

library(lpSolve)
objective.in  <- c(25, 20)
const.mat     <- matrix(c(20, 12, 1/15, 1/15), nrow=2, byrow=TRUE)
const.rhs     <- c(1800, 8)
const.dir     <- c("<=", "<=")
optimum       <- lp(direction="max", objective.in, const.mat, const.dir, const.rhs)

# Optimal values of x1 and x2
optimum$solution

## [1] 45 75

#objective at minimum
optimum$objval

## [1] 2625