Geometric Crossovers for Multiway Graph Partitioning
Authors
Abstract
Geometric crossover is a representation-independent generalization of the traditionalcrossover defined using the distance of the solution space. By choosing a distance firmly
rooted in the syntax of the solution representation as a basis for geometric crossover,
one can design new crossovers for any representation. Using a distance tailored to the
problem at hand, the formal definition of geometric crossover allows us to design new
problem-specific crossovers that embed problem-knowledge in the search.
The standard encoding for multiway graph partitioning is highly redundant: each
solution has a number of representations, one for each way of labeling the represented
partition. Traditional crossover does not perform well on redundant encodings.
We propose a new geometric crossover for graph partitioning based on a
labelingindependent distance that filters out the redundancy of the encoding. A
correlation analysis of the fitness landscape based on this distance shows that it is
well suited to graph partitioning.
A second difficulty with designing a crossover for multiway graph partitioning is that of
feasibility: in general recombining feasible partitions does not lead to feasible
offspring partitions. We design a new geometric crossover for permutations with
repetitions that naturally suits partition problems and we test it on the graph
partitioning problem. We then combine it with the labeling-independent crossover and
obtain a much superior geometric crossover inheriting both advantages.