R/SA.R

In LHD: Latin Hypercube Designs (LHDs)

#' Simulated Annealing for LHD
#'
#' \code{SA} returns a \code{n} by \code{k} LHD matrix generated by simulated annealing algorithm (SA)
#'
#' @param n A positive integer, which stands for the number of rows (or run size).
#' @param k A positive integer, which stands for the number of columns (or factor size).
#' @param N A positive integer, which stands for the number of iterations. The default is set to be 10. A large value of \code{N} will result a high CPU time, and it is recommended to be no greater than 500.
#' @param T0 A positive number, which stands for the user-defined initial temperature. The default is set to be 10.
#' @param rate A positive percentage, which stands for temperature decrease rate, and it should be in (0,1). For example, rate=0.25 means the temperature decreases by 25\% each time. The default is set to be 10\%.
#' @param Tmin A positive number, which stands for the minimium temperature allowed. When current temperature becomes smaller or equal to \code{Tmin}, the stopping criterion for current loop is met. The default is set to be 1.
#' @param Imax A positive integer, which stands for the maximum perturbations the algorithm will try without improvements before temperature is reduced. The default is set to be 5. For the computation complexity consideration, \code{Imax} is recommended to be smaller or equal to 5.
#' @param OC An optimality criterion. The default setting is "phi_p", and it could be one of the following: "phi_p", "AvgAbsCor", "MaxAbsCor", "MaxProCriterion".
#' @param p A positive integer, which is the parameter in the phi_p formula, and \code{p} is prefered to be large. The default is set to be 15.
#' @param q The default is set to be 1, and it could be either 1 or 2. If \code{q} is 1, \code{dij} is the Manhattan (rectangular) distance. If \code{q} is 2, \code{dij} is the Euclidean distance.
#' @param maxtime A positive number, which indicates the expected maximum CPU time given by user, and it is measured by minutes. For example, maxtime=3.5 indicates the CPU time will be no greater than three and half minutes. The default is set to be 5.
#'
#' @return If all inputs are logical, then the output will be a \code{n} by \code{k} LHD.
#'
#' @references Morris, M.D., and Mitchell, T.J. (1995) Exploratory designs for computer experiments. \emph{Journal of Statistical Planning and Inference}, \strong{43}, 381-402.
#'
#' @examples
#' #generate a 5 by 3 maximin distance LHD with the default setting
#' try=SA(n=5,k=3)
#' try
#' phi_p(try)   #calculate the phi_p of "try".
#'
#' #Another example
#' #generate a 8 by 4 nearly orthogonal LHD
#' try2=SA(n=8,k=4,OC="AvgAbsCor")
#' try2
#' AvgAbsCor(try2)  #calculate the average absolute correlation.
#'
#' @export

SA=function(n,k,N=10,T0=10,rate=0.1,Tmin=1,Imax=5,OC="phi_p",p=15,q=1,maxtime=5){
  #n and k are the rs and fa.
  #N: maximum number of iterations.
  #T0: initial temperature
  #rate: temperature decrease rate. 0<rate<1
  #Tmin: minumum temperature for each itertaion,TPmin > 0
  #Imax:# of perturbations the algorithm will try without improvements before Temperature is reduced
  #OC: optimality criterion, the default is "phi_p", along with default p and q

  maxtime=maxtime*60  #convert minutes to seconds
  timeALL=NULL        #record all cpu time

  C=1  #step 1: counter index

  X=rLHD(n=n,k=k)   #step 2

  Xbest=X;TP=T0;Flag=1

  if(OC=="phi_p"){

    progressbar = utils::txtProgressBar(min = 0, max = N, style = 3)

    while (C<=N) {

      time0=Sys.time()

      while(Flag==1 & TP>Tmin){
        Flag=0;I=1

        while (I<=Imax) {
          rcol=sample(1:k,1)   #step 3:Randomly choose a column
          Xnew=exchange(X=X,j=rcol)  #step 4:Exchange two randomly elements within the column "rcol"

          a=phi_p(X=Xnew,p=p,q=q)       #step 5 begins here
          b=phi_p(X=X,p=p,q=q)
          if (a<b){X=Xnew;Flag=1}
          if (a>=b){
            prob=exp((b-a)/TP)
            draw=sample(c(0,1),1,prob=c(1-prob,prob))    #draw==1 means replace
            if(draw==1){X=Xnew;Flag=1}
          }                         #step 5 ends here

          c=phi_p(X=Xbest,p=p,q=q)
          if (a<c){Xbest=Xnew;I=1}
          if (a>=c){I=I+1}

        }

        TP=TP*(1-rate)
      }

      time1=Sys.time()
      timediff=time1-time0
      timeALL=c(timeALL,timediff)

      ##########progress bar codes
      utils::setTxtProgressBar(progressbar, C)
      ##########

      if(as.numeric(sum(timeALL)+timediff)<=maxtime){C=C+1}
      if(as.numeric(sum(timeALL)+timediff)>maxtime){C=N+1}
      TP=T0;Flag=1
    }


  }

  if(OC=="AvgAbsCor"){

    progressbar = utils::txtProgressBar(min = 0, max = N, style = 3)

    while (C<=N) {

      time0=Sys.time()

      while(Flag==1 & TP>Tmin){
        Flag=0;I=1

        while (I<=Imax) {
          rcol=sample(1:k,1)   #step 3:Randomly choose a column
          Xnew=exchange(X=X,j=rcol)  #step 4:Exchange two randomly elements within the column "rcol"

          a=AvgAbsCor(X=Xnew)       #step 5 begins here
          b=AvgAbsCor(X=X)
          if (a<b){X=Xnew;Flag=1}
          if (a>=b){
            prob=exp((b-a)/TP)
            draw=sample(c(0,1),1,prob=c(1-prob,prob))    #draw==1 means replace
            if(draw==1){X=Xnew;Flag=1}
          }                         #step 5 ends here

          c=AvgAbsCor(X=Xbest)
          if (a<c){Xbest=Xnew;I=1}
          if (a>=c){I=I+1}

        }

        TP=TP*(1-rate)
      }

      time1=Sys.time()
      timediff=time1-time0
      timeALL=c(timeALL,timediff)

      ##########progress bar codes
      utils::setTxtProgressBar(progressbar, C)
      ##########

      if(as.numeric(sum(timeALL)+timediff)<=maxtime){C=C+1}
      if(as.numeric(sum(timeALL)+timediff)>maxtime){C=N+1}
      TP=T0;Flag=1
    }


  }

  if(OC=="MaxAbsCor"){

    progressbar = utils::txtProgressBar(min = 0, max = N, style = 3)

    while (C<=N) {

      time0=Sys.time()

      while(Flag==1 & TP>Tmin){
        Flag=0;I=1

        while (I<=Imax) {
          rcol=sample(1:k,1)   #step 3:Randomly choose a column
          Xnew=exchange(X=X,j=rcol)  #step 4:Exchange two randomly elements within the column "rcol"

          a=MaxAbsCor(X=Xnew)       #step 5 begins here
          b=MaxAbsCor(X=X)
          if (a<b){X=Xnew;Flag=1}
          if (a>=b){
            prob=exp((b-a)/TP)
            draw=sample(c(0,1),1,prob=c(1-prob,prob))    #draw==1 means replace
            if(draw==1){X=Xnew;Flag=1}
          }                         #step 5 ends here

          c=MaxAbsCor(X=Xbest)
          if (a<c){Xbest=Xnew;I=1}
          if (a>=c){I=I+1}

        }

        TP=TP*(1-rate)
      }

      time1=Sys.time()
      timediff=time1-time0
      timeALL=c(timeALL,timediff)

      ##########progress bar codes
      utils::setTxtProgressBar(progressbar, C)
      ##########

      if(as.numeric(sum(timeALL)+timediff)<=maxtime){C=C+1}
      if(as.numeric(sum(timeALL)+timediff)>maxtime){C=N+1}
      TP=T0;Flag=1
    }


  }

  if(OC=="MaxProCriterion"){

    progressbar = utils::txtProgressBar(min = 0, max = N, style = 3)

    while (C<=N) {

      time0=Sys.time()

      while(Flag==1 & TP>Tmin){
        Flag=0;I=1

        while (I<=Imax) {
          rcol=sample(1:k,1)   #step 3:Randomly choose a column
          Xnew=exchange(X=X,j=rcol)  #step 4:Exchange two randomly elements within the column "rcol"

          a=MaxProCriterion(X=Xnew)       #step 5 begins here
          b=MaxProCriterion(X=X)
          if (a<b){X=Xnew;Flag=1}
          if (a>=b){
            prob=exp((b-a)/TP)
            draw=sample(c(0,1),1,prob=c(1-prob,prob))    #draw==1 means replace
            if(draw==1){X=Xnew;Flag=1}
          }                         #step 5 ends here

          c=MaxProCriterion(X=Xbest)
          if (a<c){Xbest=Xnew;I=1}
          if (a>=c){I=I+1}

        }

        TP=TP*(1-rate)
      }

      time1=Sys.time()
      timediff=time1-time0
      timeALL=c(timeALL,timediff)

      ##########progress bar codes
      utils::setTxtProgressBar(progressbar, C)
      ##########

      if(as.numeric(sum(timeALL)+timediff)<=maxtime){C=C+1}
      if(as.numeric(sum(timeALL)+timediff)>maxtime){C=N+1}
      TP=T0;Flag=1
    }


  }

  avgtime=round(mean(timeALL),2)
  iterations=length(timeALL)

  close(progressbar)
  print(paste0("average CPU time per iteration is: ", avgtime, " seconds"))
  print(paste0("the number of iterations completed is: ", iterations))
  print(paste0("the elements in design matrix is scaled to be 1 to ", n))

  Xbest
}