FIMP-HGA: A Novel Approach to Addressing the Partitioning Min-Max Weighted Matching Problem
arxiv(2024)
摘要
The Partitioning Min-Max Weighted Matching (PMMWM) problem, being a practical
NP-hard problem, integrates the task of partitioning the vertices of a
bipartite graph into disjoint sets of limited size with the classical
Maximum-Weight Perfect Matching (MPWM) problem. Initially introduced in 2015,
the state-of-the-art method for addressing PMMWM is the MP_LS. In
this paper, we present a novel approach, the Fast Iterative Match-Partition
Hybrid Genetic Algorithm (FIMP-HGA), for addressing PMMWM. Similar to
MP_LS, FIMP-HGA divides the solving into match and partition stages,
iteratively refining the solution. In the match stage, we propose the KM-M
algorithm, which reduces matching complexity through incremental adjustments,
significantly enhancing runtime efficiency. For the partition stage, we
introduce a Hybrid Genetic Algorithm (HGA) incorporating an elite strategy and
design a Greedy Partition Crossover (GPX) operator alongside a Multilevel Local
Search (MLS) to optimize individuals in the population. Population
initialization employs various methods, including the multi-way Karmarkar-Karp
(KK) algorithm, ensuring both quality and diversity. At each iteration, the
bipartite graph is adjusted based on the current solution, aiming for
continuous improvement. To conduct comprehensive experiments, we develop a new
instance generation method compatible with existing approaches, resulting in
four benchmark groups. Extensive experiments evaluate various algorithm
modules, accurately assessing each module's impact on improvement. Evaluation
results on our benchmarks demonstrate that the proposed FIMP-HGA significantly
enhances solution quality compared to MP_LS, meanwhile reducing
runtime by 3 to 20 times.
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