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

The coding by which chromosomes represent candidate solutions 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...

• Type: Conference
• Year: 2000
• Where: SAC
• Authors: Günther R. Raidl, Bryant A. Julstrom
• Keywords: Applied Computing, Genetic Algorithm, Minimum Spanning Trees, SAC 2000, Spanning Trees