A Combined Evolutionary Search and Multilevel Optimisation Approach to Graph-Partitioning

Hybrid Metaheuristics for the Graph Partitioning Problem

“…Strict aggregation (SAG) [11,23,28,44], also called edge contraction or matching of vertices, is employed by most multilevel partitioning algorithms. The idea of the SAG is to form a new vertex v ∈ V i+1 of a coarser graph G i+1 by merging a subset of vertices V c i ⊂ V i of G i that (usually) have a strong local coupling (i.e., connectivity).…”

“…Two main SAG schemes have been proposed for coarsening graphs. The first scheme is based on finding an independent subset of edges (matching) Γ ⊂ E i , and then collapsing the two vertices of each edge in Γ to form a new vertex of a coarsened graph G = (V i+1 , E i+1 ) [11,27,28,44]. Any vertex that is not part of Γ is simply copied over to G i+1 .…”

“…A popular approach for generating high quality graph partitions, proposed by Soper et al [44], is a combination of an evolutionary search algorithm and a multilevel partitioner.…”

“…In ITS [9], this is done by performing (most of the time) moves with only border (critical) vertices according to a selection strategy. A similar idea is also used in [44], where a smaller bias is assigned to vertices that appear as border vertices in one or more parent partitions, which results higher probability that these vertices will remain border in successive generations. In [11], besides the ITS, the BBC crossover also limits the region of explored search space by preserving vertex groupings that are common to a number of population individuals.…”

“…Column 'ρ f dc ' shows the correlation coefficients with respect to fitness and distance. KL tioning archive (used for performance evaluation in [9,11,44]), based on a sample of local optima obtained after 1500 independent runs of the ITS [9]. While Merz and Freisleben use the Hamming distance, Benlic and Hao use the set-theoretic distance to perform the landscape analysis.…”