R/distsumlpmin.R

In orloca: Operations Research LOCational Analysis Models

#' distsumlpmin at orloca package
#'
#' \code{distsumlpmin} is the \code{distsummin} function for the norm (\eqn{l_p}).
#' This function returns the solution of the minimization problem.
#' Mainly for internal use.
#'
#' @name distsumlpmin
#' @aliases distsumlpmin distsumlpmin,loca.p-method
#' @keywords internal classes optimize
#' @inherit distsummin  
setGeneric("distsumlpmin",
           function (o, x=0, y=0, p=2, max.iter=100, eps=1.e-3, verbose=FALSE, algorithm="Weiszfeld", ...) standardGeneric("distsumlpmin")
)

# Optimization by ucminf function from ucminf package
distsumlpminucminf.loca.p <- function (o, x=0, y=0, p=2, max.iter=100, eps=1.e-3, verbose=FALSE)
   {
     zdistsum <- function(xx) distsumlp(o, xx[1], xx[2], p=p)
     sol <- ucminf(par = c(x, y), fn = zdistsum, control=list(maxeval=max.iter, trace=verbose))
     if (verbose) cat(gettext(sol$message));
     return(sol$par)
   }

#' @export
setMethod("distsumlpmin", "loca.p",
          function (o, x=0, y=0, p=2, max.iter=100, eps=1.e-3, verbose=FALSE, algorithm="Weiszfeld", ...) {
              algorithm <- match.arg(algorithm, c('Weiszfeld', 'gradient', 'ucminf', 'Nelder-Mead', 'BFGS', 'CG', 'L-BFGS-B', 'SANN'))
              if (p>=1) {
                  if (algorithm=="gradient") distsumlpmingradient.loca.p(o, x, y, p, max.iter, eps, verbose)
                  else if (algorithm=="Weiszfeld") distsumlpminWeiszfeld.loca.p(o, x, y, p, max.iter, eps, verbose, ...)
                  else if (algorithm=="ucminf") distsumlpminucminf.loca.p(o, x, y, p, max.iter, eps, verbose)
                  else {
                      zdistsummin <- function(x) distsumlp(o, x[1], x[2], p=p)
                      par <- c(sum(o@x*o@w)/sum(o@w), sum(o@y*o@w)/sum(o@w))
                      optim(par, zdistsummin, method=algorithm, control=list(maxit=max.iter))$par
                  }
              } else stop(paste(p, gettext("is not a valid value for p, use 1 <= p")))
          }
          )

## Gradient Method
distsumlpmingradient.loca.p <- function (o, x=0, y=0, p=2, max.iter=100, eps=1.e-3, verbose=FALSE)
   {
   lambda = 1;
   eps2 <- eps^2
   u<-c(x,y)
   z <- distsumlp(o, u[1], u[2], p)
   for (i in 0:max.iter)
      {
      if (verbose) cat(paste(gettext("Iter"), ".", i, ": (", u[1], ",", u[2], ") ", z, "\n", sep=""))
      g <- distsumlpgra(o, u[1], u[2], p)
      mg <- sum(g^2)
      if (is.na(mg))
         {
         # A demand point stop rule
         g <- distsumlpgra(o, u[1], u[2], p, partial=T)
         q <- p/(p-1)
         mg <- sum(abs(g)^q)^(1/q)
         ii <- which.min((o@x-u[1])^2+(o@y-u[2])^2)
         if (mg < sum(o@w[ii]))
        	  {
        	  if(verbose) cat(gettext("Optimality condition reached at demand point."));
        	  break
        	  }
         }
      else if (mg<eps2)
         {
         if(verbose) cat(gettext("Optimality condition reached."));   
         break;
         }
      nu <- u - lambda*g
      nz <- distsumlp(o, nu[1], nu[2], p)
      if (nz < z)
         {
         u<-nu
         z<-nz
         lambda <- lambda*2.2
         }
      else
         {
         lambda <- lambda/2
         }
      }
   if (verbose && i == max.iter) cat(gettext("Maximun number of iteration reached"));
   u
   }


## Weiszfeld Method
distsumlpminWeiszfeld.loca.p <- function (o, x=0, y=0, p=2, max.iter=100, eps=1.e-3, verbose=FALSE, csmooth=.5)
   {
   # Check smooth value
   if (!identical(csmooth >= 0 && csmooth < 1, TRUE))
     {
       warning(paste(gettext("Value for smooth parameter non valid:"), smooth, gettext("Reseting to its default value.")))
       csmooth <- .5
     }
   eps2 <- eps^2
   u<-c(x,y)
   # Begin iterations in non smooth mode
   .smooth = 0
   i.i = 0
   i.s = round(max.iter*.5)
   for (j in 1:2)
     {
   for (i in i.i:i.s)
      {
      if (verbose) cat(paste(gettext("Iter"), ". ", i, ": (", u[1], ",", u[2], ") ", distsumlp(o, u[1], u[2], p), "\n", sep=""))
      # Compute the distances to demand points in l2 norm
      n <- (abs(u[1]-o@x)^p+abs(u[2]-o@y)^p)^(1/p)
      # Check for demand point proximities
      ii <- (n > eps)
      # Compute the numerator of iteration
      n <- o@w*(abs(u[1]-o@x)^p+abs(u[2]-o@y)^p)^(1/p-1)
      # Compute the gradient
      g <- c(sum(sign(u[1]-o@x[ii])*abs(u[1]-o@x[ii])^(p-1)*n[ii]), sum(sign(u[2]-o@y[ii])*abs(u[2]-o@y[ii])^(p-1)*n[ii]))
      mg <- sum(g^2)
      # Check stop rule
      if (all(ii))
         {
         # A demand point stop rule
         q <- p/(p-1)
         mg <- sum(abs(g)^q)^(1/q)
         if (mg < sum(o@w[!ii]) || mg < eps2)
           {
           if(verbose) cat(gettext("Optimality condition reached at demand point."));
           break
           }
         }
      # Generic stop rule
      else if (mg<eps2)
        {
        if(verbose) cat(gettext("Optimality condition reached."));
        break;
        }
      dx <- n*abs(u[1]-o@x)^(p-2)
      nx <- dx*o@x
      dy <- n*abs(u[2]-o@y)^(p-2)
      ny <- dy*o@y
      u <- .smooth * u + (1-.smooth) * c(sum(nx[ii])/sum(dx[ii]), sum(ny[ii])/sum(dy[ii]))
      }
      # Check if optimality condition had been reached
      if (i != i.s) break
      # Changing to smooth version
      .smooth = csmooth
      if (j == 1) warning(gettext("The algorithm seems converges very slowly. Trying now with the smooth version."))
   i.i = i.s
   i.s = max.iter

 }
   if (i == max.iter) warning.max.iter(max.iter)
   u
   }