How randomized search heuristics find maximum cliques in planar graphs

Surprisingly, general search heuristics often solve combinatorial problems quite sufficiently, although they do not outperform specialized algorithms. Here, the behavior of simple randomized optimizers on the maximum clique problem on planar graphs is investigated rigorously. The focus is on the worst-, average-, and semi-average-case behaviors. In semi-random planar graph models an adversary is allowed to modify moderately a random planar graph, where a graph is chosen uniformly at random among all planar graphs. With regard to the heuristics particular interest is given to the influences of the following four popular strategies to overcome local optima: local- vs. global-search, single- vs. multi-start, small vs. large population, and elitism vs. non-elitism selection. Finally, the black-box complexities of the planar graph models are analyzed. Categories and Subject Descriptors F.2 [Theory of Computation]: Analysis of Algorithms and Problem Complexity; G.2 [Mathematics of Computing...

• Type: Conference
• Year: 2006
• Where: GECCO
• Authors: Tobias Storch
• Keywords: GECCO 2006, Optimization, Planar Graph, Planar Graph Models, Semi-random Planar Graph