This article tackles the Distribution Network Expansion Planning (DNEP) problem that has to be solved by distribution network operators to decide which, where, and/or when enhancements to electricity networks should be introduced to satisfy the future power demands. Because of many real-world details involved, the structure of the problem is not exploited easily using mathematical programming techniques, for which reason we consider solving this problem with evolutionary algorithms (EAs). We compare three types of EAs for optimizing expansion plans: the classic genetic algorithm (GA), the estimation-of-distribution algorithm (EDA), and the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA). Not fully knowing the structure of the problem, we study the effect of linkage learning through the use of three linkage models: univariate, marginal product, and linkage tree. We furthermore experiment with the impact of incorporating different levels of problem-specific knowledge in the variation operators. Experiments show that the use of problem-specific variation operators is far more important for the classic GA to find high-quality solutions. In all EAs, the marginal product model and its linkage learning procedure have difficulty in capturing and exploiting the DNEP problem structure. GOMEA, especially when combined with the linkage tree structure, is found to have the most robust performance by far, even when an out-of-the-box variant is used that does not exploit problem-specific knowledge. Based on experiments, we suggest that when selecting optimization algorithms for power system expansion planning problems, EAs that have the ability to effectively model and efficiently exploit problem structures, such as GOMEA, should be given priority, especially in the case of black-box or grey-box optimization.