Memetic Algorithm with Hungarian Matching Based Crossover and Diversity Preservation

The Graph Partitioning Problem (GPP) is a well-known NP-hard combinatorial problem that involves the finding of a partition of vertexes that minimizes the number of cut edges while fulfilling a set of constraints. This paper presents a newly designed optimizer for the GPP: the Memetic Algorithm with Hungarian Matching Based Crossover and Diversity Preservation (MAHMBCDP). MAHMBCDP is a population-based scheme that incorporates an explicit mechanism to control the diversity with the aim of making a proper use of resources when dealing with long-term executions. Among the novelties of our proposal, the design of a crossover operator that is based on the Hungarian Algorithm to calculate a maximum matching is particularly important. Experimental validation with a set of well-known instances of the graph partitioning archive shows the proper performance of our proposal. In fact, new best-known solutions could be attained in ten test cases.