# The Link and Node Biased Encoding Revisited: Bias and Adjustment of Parameters

## Abstract

When using genetic and evolutionary algorithms (GEAs) for the optimal communication spanning tree problem, the design of a suitable tree network encoding is crucial for finding good solutions. The link and node biased (LNB) encoding represents the structure of a tree network using a weighted vector and allows the GEA to distinguish between the importance of the nodes and links in the network. This paper investigates whether the encoding is unbiased in the sense that all trees are equally represented, and how the parameters of the encoding influence the bias. If the optimal solution is underrepresented in the population, a reduction in the GEA performance is unavoidable. The investigation reveals that the commonly used simpler version of the encoding is biased towards star networks, and that the initial population is dominated by only a few individuals. The more costly link-and-node-biased encoding uses not only a node-specific bias, but also a link-specific bias. Similarly to the node-biased encoding, the link-and-node-biased encoding is also biased towards star networks, especially when using a low weighting for the link-specific bias. The results show that by increasing the link-specific bias, that the overall bias of the encoding is reduced. If researchers want to use the LNB encoding, and they are interested in having an unbiased representation, they should use higher values for the weight of the link-specific bias. Nevertheless, they should also be aware of the limitations of the LNB encoding when using it for encoding tree problems. The encoding could be a good choice for the optimal communication spanning tree problem as the optimal solutions tend to be more star-like. However, for general tree problems the encoding should be used carefully.

## Keywords

Genetic Algorithm Span Tree Minimum Span Tree Tree Network Span Tree Problem## Preview

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