Using branching-property preserving Prüfer Code to encode solutions for particle swarm optimisation

In the area of applied optimisation, heuristics are a popular means to address computational problems of high complexity. Modelling the problem and mapping all variations of its solution into a so-called solution space are integral parts of this process. Representing solutions as graphs is common and, for a special type of graph, Prüfer Code (PC) offers a computationally efficient mapping (algorithms of Θ(n)-complexity are known) to n-2 dimensional Euclidean space. However, this encoding does not preserve properties such as e.g. locality and therefore PC has been shown to be a bad choice for entire classes of problems. We argue that PC does allow the preservation of some properties (e.g. degree of branching and branching vertices) and that these are sufficiently relevant for certain types of problems to motivate encoding them in PC. We present our investigations and provide an example where PC has been shown to be a useful encoding.