Title :
Test problems and representations for graph evolution
Author :
Ashlock, Daniel ; Schonfeld, Justin ; Barlow, Lee-Ann ; Lee, Chi-Kwan
Author_Institution :
Dept. of Math. & Stat, Univ. of Guelph, Guelph, ON, Canada
Abstract :
Graph evolution - evolving a graph or network to fit specific criteria - is a recent enterprise because of the difficulty of representing a graph in an easily evolvable form. Simple, obvious representations such as adjacency matrices can prove to be very hard to evolve and some easy-to-evolve representations place severe limits on the space of graphs that is explored. This study fills in a gap in the literature by presenting two scalable families of benchmark functions. These functions are tested on a number of representations. The first family of benchmark functions is matching the eccentricity sequences of graphs, the second is locating graphs that are relatively easy to color non-optimally. One hundred examples of the eccentricity sequence matching problem are tested. The examples have a difficulty, measured in time to solution, that varies through four orders of magnitude, demonstrating that this test problem exhibits scalability even within a particular size of problem. The ordering by problem hardness, for different representations, varies significantly from representation to representation. For the difficult coloring problem, a parameter study is presented demonstrating that the problem exhibits very different results for different algorithm parameters, demonstrating its effectiveness as a benchmark problem.
Keywords :
computational complexity; graph colouring; algorithm parameters; benchmark functions; benchmark problem; coloring problem; eccentricity sequence matching problem; graph evolution representations; graphs location; problem hardness; scalability; test problems; Benchmark testing; Color; Evolutionary computation; Graph theory; Sociology; Statistics; Topology;
Conference_Titel :
Foundations of Computational Intelligence (FOCI), 2014 IEEE Symposium on
Conference_Location :
Orlando, FL
DOI :
10.1109/FOCI.2014.7007805