Optimasi Grafis 1

library(mosaicCalc)

## Loading required package: mosaic

## Registered S3 method overwritten by 'mosaic':
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##   fortify.SpatialPolygonsDataFrame ggplot2

## 
## The 'mosaic' package masks several functions from core packages in order to add 
## additional features.  The original behavior of these functions should not be affected by this.

## 
## Attaching package: 'mosaic'

## The following objects are masked from 'package:dplyr':
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##     count, do, tally

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## The following objects are masked from 'package:stats':
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##     binom.test, cor, cor.test, cov, fivenum, IQR, median, prop.test,
##     quantile, sd, t.test, var

## The following objects are masked from 'package:base':
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##     max, mean, min, prod, range, sample, sum

## 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,
## which was just loaded, will retire in October 2023.
## Please refer to R-spatial evolution reports for details, especially
## https://r-spatial.org/r/2023/05/15/evolution4.html.
## It may be desirable to make the sf package available;
## package maintainers should consider adding sf to Suggests:.
## The sp package is now running under evolution status 2
##      (status 2 uses the sf package in place of rgdal)

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## Attaching package: 'mosaicCalc'

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##     D

library(mosaic)

Optimasi adalah suatu teknik untuk mmencari masukan yang menghasilkan keluaran terbesar. Optimasi menggunakan model matematika yang ketat untuk menemukan solusi paling efisien terhadap masalah yang diberikan. Terkait fungsi, maksimalisasi adalah proses menemukan masukan ke fungsi yang menghasilkan keluaran lebih besar daripada masukan terdekat lainnya.

Minimisasi mengacu pada teknik yang sama, tetapi garis vertikal digambar pada titik terdalam di setiap “lembah” grafik fungsi. Nilai masukan yang terletak di salah satu lembah tersebut disebut argmin .

Optimasi adalah istilah umum yang mencakup maksimum dan minimum. Seperti dalam fungsi ini:

f(x) = sin 2x + cos(x) + sin(4x)

f <- function(x) sin (2*x) + cos(x) + sin(x)
curve(f, from = -2, to = 2* pi)

optimize(f, interval = c(0, 2*pi)) #minimum lokal

## $minimum
## [1] 2.717545
## 
## $objective
## [1] -1.25

optimize(f, interval = c(3, -1*pi)) #minimum global

## $minimum
## [1] -1.146753
## 
## $objective
## [1] -1.25

optimize(f, interval = c(1, 2*pi), maximum = T) #maksimum lokal

## $maximum
## [1] 3.926992
## 
## $objective
## [1] -0.4142136

optimize(f, interval = c(6, 1), maximum = T) #maksimum global

## $maximum
## [1] 3.926973
## 
## $objective
## [1] -0.4142136