## A Weighted Coding in a Genetic Algorithm for the Degree-Constrained Minimum Spanning Tree Problem (2000)

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Citations: | 18 - 4 self |

### BibTeX

@MISC{Raidl00aweighted,

author = {Günther R. Raidl},

title = {A Weighted Coding in a Genetic Algorithm for the Degree-Constrained Minimum Spanning Tree Problem},

year = {2000}

}

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### Abstract

is a fundamental design choice in a genetic algorithm. This paper describes a novel coding of spanning trees in a genetic algorithm for the degree-constrained minimum spanning tree problem. For a connected, weighted graph, this problem seeks to identify the shortest spanning tree whose degree does not exceed an upper bound k 2. In the coding, chromosomes are strings of numerical weights associated with the target graph's vertices. The weights temporarily bias the graph's edge costs, and an extension of Prim's algorithm, applied to the biased costs, identifies the feasible spanning tree a chromosome represents. This decoding algorithm enforces the degree constraint, so that all chromosomes represent valid solutions and there is no need to discard, repair, or penalize invalid chromosomes. On a set of hard graphs whose unconstrained minimum spanning trees are of high degree, a genetic algorithm that uses this coding identifies degree-constrained minimum spanning trees that are on average shorter than those found by several competing algorithms.