Demand-side management in the smart grid often consists of optimizing energy-related objective functions, with respect to variables, in the presence of constraints expressing electrical consumption habits. These functions are often related to the user’s electricity invoice (cost) or to the peak energy consumption (peak-to-average energy ratio), which can cause electrical network failure on a large scale. However, the growth in energy demand, especially in emerging countries, is causing a serious energy crisis. This is why several studies focus on these optimization approaches. To our knowledge, no article aims to collect and analyze the results of research on peak-to-average energy consumption ratio and cost optimization using a systematic reproducible method. Our goal is to fill this gap by presenting a systematic mapping study on the subject, spanning the last decade (2013–2022). The methodology used first consisted of searching digital libraries according to a specific search string (104 relevant studies out of 684). The next step relied on an analysis of the works (classified using 13 criteria) according to 5 research questions linked to algorithmic trends, energy source, building type, optimization objectives and pricing schemes. Some main results are the predominance of the genetic algorithms heuristics, an insufficient focus on renewable energy and storage systems, a bias in favor of residential buildings and a preference for real-time pricing schemes. The main conclusions are related to the promising hybridization between the genetic algorithms and swarm optimization approaches, as well as a greater integration of user preferences in the optimization. Moreover, there is a need for accurate renewable and storage models, as well as for broadening the optimization scope to other objectives such as CO₂ emissions or communications load.