Multi-objective Parallel Feasible Direction Algorithm for Hypergraph Partitioning Problem with Rank-Two Semidefinite Programming Relaxation

This research introduces an innovative and high-performance multi-objective parallel feasible direction approach for hypergraph partitioning, utilizing rank-two semidefinite programming relaxation frameworks. The algorithm generates high-quality initial partitions through strategies such as recursive bisection, and multi-domain adjustment. These partitions are further optimized using multi-partition synchronized parallel clustering optimization algorithms and embedded into a multilevel framework as initial partitions. The numerical results demonstrate superior performance in both solution quality and computational efficiency across diverse test cases. Our method achieves approximately 5% average improvement in bipartitioning quality, with up to 44.4% enhancement over K-SpecPart on instances like ibm06. The algorithm also shows better scalability than KaHyPar, with slower runtime growth as partition count increases. Parameter sensitivity analysis confirms consistent performance across different configurations, highlighting remarkable robustness. Additionally, ablation studies validate the effectiveness of each component of the proposed method. In summary, the presented algorithm effectively balances partitioning quality with computational efficiency, offering a competitive solution for large-scale hypergraph partitioning.