Result of optimization is random - r

Question

I have got a script which runs ARIMA, putting weights on errors. The script runs fine however each time is it run, even using the same series it outputs different forecasts. I have looked all through the code and can't find where the problem is. I would really appreciate it if someone could have a quick look and point out where i have gone wrong.
M<-matrix(c("08Q1", "08Q2", "08Q3", "08Q4", "09Q1", "09Q2", "09Q3", "09Q4", "10Q1", "10Q2", "10Q3", "10Q4", "11Q1", "11Q2", "11Q3", "11Q4", "12Q1", "12Q2", "12Q3", "12Q4", "13Q1", "13Q2", "13Q3", "13Q4", "14Q1", "14Q2", 79160.56, 91759.73, 91186.48, 106353.82, 70346.47, 80279.15, 82611.60, 131392.72, 93798.99, 105944.78, 103913.13, 154530.69, 110157.40, 117416.09, 127423.42, 156752.00,120097.81, 121307.75, 115021.12, 150657.83, 113711.53, 115353.14, 112701.98, 154319.18,116803.54, 118352.54),ncol=2,byrow=FALSE)
deltaT<-1/4
horiz<-4
startY<-c(8,1)
aslog<-"y"
Nu<-M[,length(M[1,])]
Nu<-as.numeric(Nu)
Nu<-ts(Nu,deltat=deltaT,start=startY)
Mdates<-as.character(M[,1])
if(aslog=="y")
{N<-log(Nu)} else
{N<-Nu}
library(forecast)
library(tseries)
max.sdiff <- 3
arima.force.seasonality <- "n"
fweight <- function(x)
{
PatX <- 0.5+x
return(PatX)
}
integ1 <- integrate(fweight, lower = 0.00, upper = 1)
valinteg <- 2*integ1$value
integvals <- rep(0, length.out = length(N))
for (i in 1:length(N))
{
integi <- integrate(fweight, lower = (i-1)/length(N), upper= i/length(N))
integvals[i] <- 2*integi$value
}
kpssW <- kpss.test(N, null="Level")
ppW <- tryCatch({ppW <- pp.test(N, alternative = "stationary")}, error = function(ppW) {ppW <- list(error = "TRUE", p.value = 0.99)})
adfW <- adf.test(N, alternative = "stationary", k = trunc((length(N)-1)^(1/3)))
if(kpssW$p.value < 0.05 | ppW$p.value > 0.05 | adfW$p.value > 0.05) {ndiffsW = 1} else {ndiffsW = 0}
aaw <- auto.arima(N, max.D= max.sdiff, d=ndiffsW, seasonal=TRUE,
allowdrift=FALSE, stepwise=FALSE, trace=TRUE, seasonal.test="ch")
orderWA <- c(aaw$arma[1], aaw$arma[6] , aaw$arma[2])
orderWS <- c(aaw$arma[3], aaw$arma[7] , aaw$arma[4])
if(sum(aaw$arma[1:2])==0) {orderWA[1] <- 1} else {NULL}
if(arima.force.seasonality == "y") {if(sum(aaw$arma[3:4])==0) {orderWS[1] <- 1} else {NULL}} else {NULL}
stAW <- Arima(N, order= orderWA, seasonal=list(order=orderWS), method="ML")
parSW <- stAW$coef
WMAEOPT <- function(parSW)
{
ArimaW <- Arima(N, order = orderWA, seasonal=list(order=orderWS),
include.drift=FALSE, method = "ML", fixed = c(parSW))
errAR <- c(abs(resid(ArimaW)))
WMAE <- t(errAR) %*% integvals
return(WMAE)
}
OPTWMAE <- optim(parSW, WMAEOPT, method="SANN", control = list(fnscale= 1, maxit = 5000))
parS3 <- OPTWMAE$par
ArimaW1 <- Arima(N, order = orderWA, seasonal=list(order=orderWS),
include.drift=FALSE, method = "ML", fixed = c(parS3))
fArimaW1 <- forecast(ArimaW1, h=8, simulate= TRUE, fan=TRUE)
if (aslog == "y") {fArimaWF <- exp(fArimaW1$mean[1:horiz])} else {fArimaWF <- fArimaW1$mean[1:horiz]}
plot(fArimaW1, main = "ARIMA Forecast", sub="blue=fitted, red=actual") # ylim=c(17, 20)
lines(N, col="red", lwd=2)
lines(ts(append(fitted(ArimaW1), fArimaW1$mean[1]), deltat=deltaT, start = startY),
col= "blue", lwd = 2) # makes the graph look nicer
if (aslog == "y") {ArimaALT <- exp(fArimaW1$mean[1:horiz])} else {ArimaALT <- fArimaW1$mean[1:horiz]}
start(fArimaW1$mean) -> startF
ArimaALTf <- ts(prettyNum(ArimaALT, big.interval = 3L, big.mark = ","), deltat = deltaT , start= startF)
View(ArimaALTf, title = "ARIMA forecast")
summary(ArimaW1)
Edit
I have just found where it goes wrong. But i dont understand why.
OPTWMAE <- optim(parSW, WMAEOPT, method="SANN", control = list(fnscale= 1, maxit = 5000))
This is where it gives different values
Thank-you for your time

Answer 1

From help("optim") (emphasis by me):
Method "SANN" is by default a variant of simulated annealing given in
Belisle (1992). Simulated-annealing belongs to the class of stochastic
global optimization methods.
Use set.seed to get reproducible results.