Moving Clusters within a Memetic Algorithm for Graph Partitioning

Abstract

Most memetic algorithms (MAs) for graph partitioning reduce the cut size of partitions using iterative improvement. But this local process considers one vertex at a time and fails to move clusters between subsets when the movement of any single vertex increases cut size, even though moving the whole cluster would reduce it. A new heuristic identifies clusters from the population of locally optimized random partitions that must anyway be created to seed the MA, and as the MA runs it makes beneficial cluster moves. Results on standard benchmark graphs show significant reductions in cut size, in some cases improving on the best result in the literature.

Optimization by Simulated Catalytic Reaction: Application to Graph Bisection

“…In this study, a very simple clustering method [22] was used to find clusters that require large energy for movement. However, an improvement in its performance can be expected when more advanced clustering methods [7,21,24,25,26,27,28,29,30,31] are applied.…”

“…At present, designing approximate or heuristic algorithms that solve the problem is the only solution. There are also various meta-heuristic approaches to solving the graph bisection, including genetic algorithms [5,6,7] and tabu search [8,9]. Kim et al [10] present a survey of techniques using genetic algorithms.…”

“…This paper does not focus on suggesting a clustering method with superior performance. Hwang and Kim [7] and Yoon and Kim [21] described recent clustering methodologies. Instead, the simple clustering method proposed by Kim [22] is used in this paper.…”

Recent Progress on Graph Partitioning Problems Using Evolutionary Computation

“…The Fiduccia-Mattheyses algorithm [4] was used for local optimization and operators were revised to apply QEA. Hwang et al [5] demonstrated heuristic distinguishing clusters in the population of locally optimized random partitions. This becomes the seed of the memetic algorithm (MA), and once MA is executed, beneficial cluster moves can be performed.…”