knitr::opts_chunk$set(collapse = T, comment = "#>", warning = FALSE, message = FALSE) options(tibble.print_min = 4L, tibble.print_max = 4L)

The **mcMST** package for the statistical programming language R contains methods for benchmark instance generation of multi-objective graph problems and methods for solving the multi-criteria spanning tree problem (mcMST).

Here we first generate a bi-criteria graph problem with n = 25 nodes. The first objective is the euclidean distance of node coordinates in [0, 10] x [0, 10] in the euclidean plane. The second objective follows a normal distribution with mean 5 and standard deviation 1.5. The instance generation process is modular and thus highly flexible (see the vignette on graph generation for details).

library(mcMST) library(gridExtra) set.seed(1) # reproducability g = mcGP(lower = 0, upper = 10) g = addCoordinates(g, n = 25, generator = coordUniform) g = addWeights(g, method = "euclidean") g = addWeights(g, method = "random", weight.fun = rnorm, mean = 5, sd = 1.5) print(g) plots = plot(g) plots$nrow = 1 do.call(grid.arrange, plots)

Next, we apply a (30 + 10) genetic algorithm based on the Pruefer-number encoding as proposed by Zhou & Gen to approximate the Pareto-front for `max.iter = 500`

generations.

res = mcMSTEmoaZhou(g, mu = 30L, lambda = 10L, max.iter = 500L) head(res$pareto.front, n = 5) ecr::plotFront(res$pareto.front)

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