A Multi-Parent Edge Assembly Crossover Driven Hybrid Genetic Algorithm for the Hamiltonian \textit{p}-Median Problem
Junkai Huang, Pengfei He, Jin-Kao Hao, Xin Yao
原文摘要
The Hamiltonian \textit{p}-median problem seeks to partition the vertices of a graph into exactly $p$ disjoint cycles while minimizing their total cost. This paper presents a hybrid genetic algorithm incorporating a multi-parent edge assembly crossover operator. The crossover combines a base solution with multiple donor solutions in a single recombination operation, thereby expanding the space of available edge exchanges. It uses virtual copies of the base solution to establish edge balance, together with an auxiliary directed graph and a budgeted search to construct valid AB-cycles. Extensive experiments on 215 benchmark instances across four sets show that the proposed algorithm improves the best-known solution values for 34 instances and matches those for another 168. Additional experiments indicate that a moderate number of parents provides beneficial diversity, whereas excessive parent counts, particularly when $p$ is large, lead to excessive population dispersion and hinder convergence.
cs.NE