Graph Partitioning Using Genetic Algorithms

The eecient implementation of parallel processing ar-chitectures generally requires the solution of hard combi-natorial problems involving allocation and scheduling of tasks. Such problems can often be modelled with considerable accuracy as a graph partitioning problem|a problem well-known from complexity theory to be NP-hard, which implies that for practical purposes the global optimum will not be found by any exact algorithm, except for trivially small problems. Recently genetic algorithms (GAs) have been proposed as a means of nding good solutions to the graph partitioning problem. In this paper two methods of implementing GAs are explored. In the rst case, they are combined with a heuristic`greedy algorithm'. Unlike previous approaches the heuristic is directly linked to the re-combination operator and this leads to a new`heuristic neighbourhood search' operator. Comparisons with existing approaches for combining heuristics with genetic algorithms show that the direct approach leads to improved results. In addition the heuristic neighbourhood search operator gives rise to a more computationally ef-cient scheme. Secondly, an approach which uses a structural crossover operator is investigated. Again, improved versions of existing approaches are developed, and nally the two forms of operator are compared using a number of diierent graphs.