Try our new documentation site (beta).
Filter Content By
Version
Text Search
${sidebar_list_label} - Back
Filter by Language
multiobj.R
# Copyright 2018, Gurobi Optimization, LLC # # Want to cover three different sets but subject to a common budget of # elements allowed to be used. However, the sets have different priorities to # be covered; and we tackle this by using multi-objective optimization. library(Matrix) library(gurobi) # define primitive data groundSetSize <- 20 nSubSets <- 4 Budget <- 12 Set <- list( c( 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ), c( 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1 ), c( 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0 ), c( 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0 ) ) SetObjPriority <- c(3, 2, 2, 1) SetObjWeight <- c(1.0, 0.25, 1.25, 1.0) # Initialize model model <- list() model$modelsense <- 'max' model$modelname <- 'multiobj' # Set variables, all of them are binary, with 0,1 bounds. model$vtype <- 'B' model$lb <- 0 model$ub <- 1 model$varnames <- paste(rep('El', groundSetSize), 1:groundSetSize, sep='') # Build constraint matrix model$A <- spMatrix(1, groundSetSize, i = rep(1,groundSetSize), j = 1:groundSetSize, x = rep(1,groundSetSize)) model$rhs <- c(Budget) model$sense <- c('<') model$constrnames <- c('Budget') # Set multi-objectives model$multiobj <- list() for (m in 1:nSubSets) { model$multiobj[[m]] <- list() model$multiobj[[m]]$objn <- Set[[m]] model$multiobj[[m]]$priority <- SetObjPriority[m] model$multiobj[[m]]$weight <- SetObjWeight[m] model$multiobj[[m]]$abstol <- m model$multiobj[[m]]$reltol <- 0.01 model$multiobj[[m]]$name <- sprintf('Set%d', m) model$multiobj[[m]]$con <- 0.0 } # Save model gurobi_write(model,'multiobj_R.lp') # Set parameters params <- list() params$PoolSolutions <- 100 # Optimize result <- gurobi(model, params) # Capture solution information if (result$status != 'OPTIMAL') { cat('Optimization finished with status', result$status, '\n') stop('Stop now\n') } # Print best solution cat('Selected elements in best solution:\n') for (e in 1:groundSetSize) { if(result$x[e] < 0.9) next cat(' El',e,sep='') } cat('\n') # Iterate over the best 10 solutions if ('pool' %in% names(result)) { solcount <- length(result$pool) cat('Number of solutions found:', solcount, '\n') if (solcount > 10) { solcount <- 10 } cat('Objective values for first', solcount, 'solutions:\n') for (k in 1:solcount) { cat('Solution', k, 'has objective:', result$pool[[k]]$objval[1], '\n') } } else { solcount <- 1 cat('Number of solutions found:', solcount, '\n') cat('Solution 1 has objective:', result$objval, '\n') } # Clean up rm(model, params, result)