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### fixanddive.R

# Copyright 2024, Gurobi Optimization, LLC
#
# Implement a simple MIP heuristic.  Relax the model,
# sort variables based on fractionality, and fix the 25% of
# the fractional variables that are closest to integer variables.
# Repeat until either the relaxation is integer feasible or
# linearly infeasible.

library(Matrix)
library(gurobi)

args <- commandArgs(trailingOnly = TRUE)
if (length(args) < 1) {
stop('Usage: Rscript fixanddive.R filename\n')
}

cat('... done\n')

# Detect set of non-continous variables
numvars    <- ncol(model$A) intvars <- which(model$vtype != 'C')
numintvars <- length(intvars)
if (numintvars < 1) {
stop('All model\'s variables are continuous, nothing to do\n')
}

# create lb and ub if they do not exists, and set them to default values
if (!('lb' %in% model)) {
model$lb <- numeric(numvars) } if (!('ub' %in% model)) { model$ub <- Inf + numeric(numvars)
}

# set all variables to continuous
ovtype                 <- model$vtype model$vtype[1:numvars] <- 'C'

# parameters
params            <- list()
params$OutputFlag <- 0 result <- gurobi(model, params) # Perform multiple iterations. In each iteration, identify the first # quartile of integer variables that are closest to an integer value # in the relaxation, fix them to the nearest integer, and repeat. for (iter in 1:1000) { # See if status is optimal if (result$status != 'OPTIMAL') {
cat('Model status is', result$status,'\n') cat('Cannot keep fixing variables\n') break } # collect fractionality of integer variables fractional <- abs(result$x - floor(result$x+0.5)) fractional <- replace(fractional, fractional < 1e-5, 1) fractional <- replace(fractional, ovtype == 'C', 1) fractional <- replace(fractional, ovtype == 'S', 1) nfractional <- length(which(fractional<0.51)) cat('Iteration:', iter, 'Obj:', result$objval,
'Fractional:', nfractional, '\n')
if (nfractional == 0) {
cat('Found feasible solution - objective', result$objval, '\n') break } # order the set of fractional index select <- order(fractional, na.last = TRUE, decreasing = FALSE) # fix 25% of variables nfix <- as.integer(ceiling(nfractional / 4)) # cat('Will fix', nfix, 'variables, out of', numvars, '\n') if (nfix < 10) cat('Fixing ') else cat('Fixing',nfix,'variables, fractionality threshold:',fractional[select[nfix]],'\n') for (k in 1:nfix) { j <- select[k] val <- floor(result$x[j] + 0.5)
model$lb[j] <- val model$ub[j] <- val
if (nfix < 10)
cat(model$varname[j],'x*=',result$x[j],'to',val,' ')
}
if (nfix < 10)
cat('\n')

# reoptimize
result <- gurobi(model, params)
}

# Clear space
rm(model, params, result)


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