Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
Arc crossing minimization in hierarchical digraphs with tabu search
Computers and Operations Research
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Visualization and Navigation in Information Visualization: A Survey
IEEE Transactions on Visualization and Computer Graphics
Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms
Proceedings of the 6th International Conference on Genetic Algorithms
A Contribution to the Study of the Fitness Landscape for a Graph Drawing Problem
Proceedings of the EvoWorkshops on Applications of Evolutionary Computing
Minimizing crossings in hierarchical digraphs with a hybridized genetic algorithm
Journal of Heuristics
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Minimizing arc crossings for drawing acyclic digraphs is a well-known NP-complete problem for which several local-search approaches based on local transformations (switching, median, ...) have been proposed. Their adaptations have been recently included in different metaheuristics. As an attempt to better understand the dynamics of the search processes, we study the fitness landscapes associated with these transformations. We first resort to a set of multi-start descents to sample the search space for three hundred medium-sized graphs. Then, we investigate complete fitness landscapes for a set of 1875 smaller graphs, this aims at showing some instance characteristics that influence search strategies. The underlying idea is to consider a fitness landscape as a graph whose vertices are drawings and arcs representing a transformation of a drawing into another. We confirm that the properties of basins of attraction closely depend on the instances. Also, we show that the probability of being stuck on a local optimum is linked to the specific shapes of the basins of attraction of global optima which may be very different from the regular image of the continuous case generally used as a reference.