A Contribution to the Study of the Fitness Landscape for a Graph Drawing Problem
These past few years genetic algorithms and stochastic hill-climbing have received a growing interest for different graph drawing problems. This paper deals with the layered drawing of directed graphs which is known to be an NP-complete problem for the arc-crossing minimization criterium. Before setting out a (n+1)th comparison between meta-heuristics, we here prefer to study the characteristics of the arc-crossings landscape for three local transformations (greedy switching, barycenter, median) adapted from the Sugiyama heuristic and we propose a descriptive analysis of the landscape for two graph families. First, all the possible layouts of 2021 small graphs are generated and the optima (number, type, height, attracting sets) are precisely defined. Then, a second family of 305 larger graphs (up to 90 vertices) is examined with one thousand hill-climbers. This study highlights the diversity of the encountered configurations and gives leads for the choice of efficient heuristics.
KeywordsGenetic Algorithm Global Optimum Local Optimum Fitness Landscape Hill Climbing
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