Improved Neighbourhood Search-Based Methods for Graph Layout

Graph drawing, or the automatic layout of graphs, is a challenging problem. There are several search-based methods for graph drawing that are based on optimising a fitness function which is formed from a weighted sum of multiple criteria. This thesis proposes a new neighbourhood search-based method that uses a tabu search coupled with path relinking in order to optimise such fitness functions for general graph layouts with undirected straight lines. None of these methods have been previously used in general multi-criteria graph drawing. Tabu search uses a memory list to speed up searching by avoiding previously tested solutions, while the path relinking method generates new solutions by exploring paths that connect high quality solutions. We use path relinking periodically within the tabu search procedure to speed up the identification of good solutions.

We have evaluated our new method against the commonly used neighbourhood search optimisation techniques: hill climbing and simulated annealing. Our evaluation examines the quality of the graph layout (fitness function's value) and the speed of the layout in terms of the number of the evaluated solutions required to draw a graph. We also examine the relative scalability of our method. Our experimental results were applied to both random graphs and a real-world dataset. We show that our method outperforms both hill climbing and simulated annealing by producing a better layout in a lower number of evaluated solutions. In addition, we demonstrate that our method has greater scalability as it can lay out larger graphs than the state-of-the-art neighbourhood search-based methods. Finally, we show that similar results can be produced in a real world setting by testing our method against a standard public graph dataset.