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.

We describe a parameter-free estimation-of-distribution algorithm (EDA) called the adapted maximum-likelihood Gaussian model iterated density-estimation evolutionary algorithm (AMaLGaM-ID A, or AMaLGaM for short) for numerical optimization. AMaLGaM is benchmarked within the 2009 black box optimization benchmarking (BBOB) framework and compared to a variant with incremental model building (iAMaLGaM). We study the implications of factorizing the covariance matrix in the Gaussian distribution, to use only a few or no covariances. Further, AMaLGaM and iAMaLGaM are also evaluated on the noisy BBOB problems and we assess how well multiple evaluations per solution can average out noise. Experimental evidence suggests that parameter-free AMaLGaM can solve a wide range of problems efficiently with perceived polynomial scalability, including multimodal problems, obtaining the best or near-best results among all algorithms tested in 2009 on functions such as the step-ellipsoid and Katsuuras, but failing to locate the optimum within the time limit on skew Rastrigin-Bueche separable and Lunacek bi-Rastrigin in higher dimensions. AMaLGaM is found to be more robust to noise than iAMaLGaM due to the larger required population size. Using few or no covariances hinders the EDA from dealing with rotations of the search space. Finally, the use of noise averaging is found to be less efficient than the direct application of the EDA unless the noise is uniformly distributed. AMaLGaM was among the best performing algorithms submitted to the BBOB workshop in 2009.