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https://github.com/jakobbossek/mcmst
Algorithms to solve the multi-criteria minimum spanning tree problem (mcMST) in R
https://github.com/jakobbossek/mcmst
cran evolutionary-algorithms mcmst minimum-spanning-trees multi-objective-optimization r spanningtrees
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Algorithms to solve the multi-criteria minimum spanning tree problem (mcMST) in R
- Host: GitHub
- URL: https://github.com/jakobbossek/mcmst
- Owner: jakobbossek
- License: other
- Created: 2017-07-04T11:51:54.000Z (over 7 years ago)
- Default Branch: master
- Last Pushed: 2023-03-13T18:52:00.000Z (over 1 year ago)
- Last Synced: 2024-09-23T01:58:54.024Z (about 2 months ago)
- Topics: cran, evolutionary-algorithms, mcmst, minimum-spanning-trees, multi-objective-optimization, r, spanningtrees
- Language: R
- Homepage:
- Size: 2.02 MB
- Stars: 4
- Watchers: 2
- Forks: 2
- Open Issues: 14
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# mcMST: A Toolbox for the Multi-Criteria Minimum Spanning Tree Problem
[](https://doi.org/10.21105/joss.00374)
[](https://cran.r-project.org/package=mcMST)
[](https://cran.r-project.org/package=mcMST)
[](https://cran.r-project.org/package=mcMST)
[](https://github.com/jakobbossek/mcMST/actions)
[](https://coveralls.io/github/jakobbossek/mcMST?branch=master)
## Introduction
It is well known, that the single-objective spanning tree problem (MST) is solvable in polynomial time, e.g., by the Prim's algorithm. However, in real-world applications, e.g., in network design, often multiple conflicting objectives have to be considered simultaneously. The multi-criteria version of the MST is NP-hard. The **mcMST** package for the [R](https://www.r-project.org) programming language contains several methods for solving the multi-criteria spanning tree problem (mcMST).
Key features of the **mcMST** package are:
* A multi-objective version of Prim's algorithm.
* Evolutionary multi-objective algorithms (based on the Prüfer-encoding or direct edge list representation) with several mutation operators.
* A modular approach for benchmark problem generation (**outsourced to R package [grapherator](https://github.com/jakobbossek/grapherator)**.)
## Example
Here we first generate a bi-criteria graph problem with n = 25 nodes with [grapherator](https://github.com/jakobbossek/grapherator). The first objective is the Euclidean distance of node coordinates in the euclidean plane [0, 10] x [0, 10]. The second objective follows a normal distribution (N(5, 1.5)).
```r
library(grapherator)
set.seed(1)
g = graph(lower = 0, upper = 100)
g = addNodes(g, n = 25, generator = addNodesUniform)
g = addEdges(g, generator = addEdgesDelauney)
g = addWeights(g, generator = addWeightsDistance, method = "euclidean")
g = addWeights(g, generator = addWeightsRandom, method = rnorm, mean = 5, sd = 1.5)
print(g)
```
Next, we apply the multi-objective evolutionary algorithm proposed by Bossek & Grimme with population size `mu = 10` and number of offspring `lambda = 10` for `max.iter = 100` generations.
```r
library(ggplot2)
res = mcMSTEmoaBG(g, mu = 30L, max.iter = 300L)
ecr::plotFront(res$pareto.front)
```
See the package vignettes for more details.
## Installation Instructions
Install the [CRAN](https://cran.r-project.org) release version via:
```r
install.packages("mcMST")
```
If you are interested in trying out and playing around with the current development version use the [devtools](https://github.com/r-lib/devtools) package and install directly from GitHub:
```r
install.packages("devtools", dependencies = TRUE)
devtools::install_github("jakobbossek/mcMST")
```
## Contributing to mcMST
If you encounter problems using this software, e.g., bugs or insufficient/misleading documentation, or you simply have a question, feel free to open an issue in the [issue tracker](https://github.com/jakobbossek/mcMST/issues).
In order to reproduce potential problems, please provide a minimal and reproducible code example.
Contributions to this software package are welcome via [pull requests](https://help.github.com/articles/about-pull-requests/) and will be merged at the sole discretion of the author.
## Publications
The following publications are strongly related to the package.
Bossek, J., & Grimme, C. (2017). A Pareto-Beneficial Sub-Tree Mutation for the Multi-Criteria Minimum Spanning Tree Problem. In Proceedings of the IEEE Symposium Series on Computational Intelligence, Honolulu, Hawai.
Bossek, J. (2017). mcMST: A Toolbox for the Multi-Criteria Minimum Spanning Tree Problem. The Journal of Open Source Software, 2017.
## Related work
The following packages provide methods to solve the __single-objective__ MST problem:
* [vegan: Community Ecology Package](https://cran.r-project.org/package=vegan)
* [igraph: Network Analysis and Visualization](https://cran.r-project.org/package=igraph)
Several packages implement methods to solve multi-criteria optimization problems in general:
* [ecr: Evolutionary Computation in R](https://cran.r-project.org/package=ecr)
* [mopsocd: Multi-Objective Particle Swarm Optimization with Crowding Distance](https://cran.r-project.org/package=mopsocd)
* [moko: Multi-Objective Kriging Optimization](https://cran.r-project.org/package=moko)
* [mco: Multiple Criteria Optimization Algorithms and Related Functions](https://cran.r-project.org/package=mco)