A weighted coding in a genetic algorithm for the degree-constrained minimum spanning tree problem

Abstract

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 identifies degree-constrained minimum spanning trees that are on average shorter than those found by several competing algorithms.

New genetic algorithm approach for the min-degree constrained minimum spanning tree

“…The second was suggested by Raidl and Julstrom [18] who used a completely different representation based on the vector of node weights introduced by Palmer and Kershenbaum [19]. In the following, we describe three different encodings of candidate spanning tree structures with two original representations.…”

“…The authors of [18] suggest the use of a vector based on the weights of the nodes since it can influence the performance of Kruskal's algorithm. The vector is initialised randomly with weights w i , ∀i ∈ V .…”

Chaotic Particle Swarm Optimization for Dynamic Routing and Wavelength Assignment in All-Optical WDM networks

“…This guiding information is used to generate a path from an arbitrary chromosome. In [25] a 'weighted encoding scheme' is used for chromosome representation in GA, whereas in [22], a cost-priority based encoding scheme is used for representing a particle in PSO. In this paper, for simplicity, a priority based encoding scheme is used.…”

Swarm intelligence based Dynamic Routing and Wavelength Assignment for wavelength constrained all-optical networks

“…This guiding information is used to generate a path from an arbitrary chromosome. In [17] a 'weighted encoding scheme' is used for chromosome representation in GA, whereas in [14], a cost-priority based encoding scheme is used for representing a particle in PSO.…”