Load pattern clustering using differential evolution with Pareto Tournament

Load Patterns (LPs) clustering has a broad range of applications, such as tariff formulation, power system planning, load forecasting, and so on. In this paper, we develop a multi-objective version of Differential Evolution (DE) using a Pareto Tournament (PT) selection to solve the LP clustering problem. Our automatic DE LP clustering (ADE-LPC) algorithm provides an entire Pareto front, and by incorporating a locus-based adjacency encoding, it inherent determines the number of clusters associated with the solutions during the optimization process. We analyze the results using two metrics for clustering, one based on compactness (the overall deviation (DEV)) and the other based on connectedness (connectivity (CONN)). These two metrics have complementary behavior and, in some cases, the correct clustering solution can be found in a trade-off between the two objectives. In addition, we compare our ADE-LPC algorithm against traditional clustering algorithms, such as k-means and single-linkage, and against two evolutionary algorithms, one based on ACO, and the well-known Non-dominated Sorted Genetic Algorithm II (NSGA-II). The results show that our ADE-LPC algorithm finds the best Pareto set, measure by the hypervolume, compared to the other algorithms.