## 1 Introduction and State of Art
State of ArtIn recent years, the concerns of fossil fuel reduction and climate change, combined with the gradual decrease in costs of unconventional sources, are pushing the incorporation of renewable energy or other types of sources on isolated networks (PV, EV, Genset, BESS) or small grids that allow local energy transactions, as seen in LEM. Nevertheless, the changeable and undefined nature of renewable energy has created significant challenges for power networks because the power produced by renewable energy is not completely dispatchable and therefore cannot be controlled. For this reason, new approaches have developed to integrate large amounts of renewable energy in smart grids and local markets, leading them to operate in a more effective, efficient, economical, and sustainable direction [4; 12]. A local grid could include loads and distributed energy resources, storage, and controllable loads, and it should be managed in a controlled manner whether or not it is interconnected to the main power grid [12]. A local small grid could deliver auxiliary services to TSO or DSO could operate energy arbitrage (store energy when the price is low to sell it or use it when the price is high) and actively participate in energy markets, in addition to participating in the distribution systems with the sell or bid of additional or required energy. However, to ensure that these activities are achievable, a small grid has to optimize the utilization of its resources, pursuing economic profit. Due to the nature of renewable energy sources, load forecasting elements, and the energy market, the time horizon for the optimization and dispatch is the day-ahead. On the other hand, LEMs whose energy prices can vary hourly may require optimization with an equivalent time horizon. Thus, day-ahead and intra-day optimal load balances are the most important requirements in an LEM. The operation of LEMs is one of the main problems in recent years due to the increased number of agents in the grid. The growing interest in these systems has been the result of [13; 14], the integration of renewable sources, DGs price reduction, community self-resilience strategies, market flexibility, and dynamic loads, among other factors. LEM requires two main elements: a market controller that creates conditions and policies to carry out the local balance and maximize their economic gains [8], and an energy controller that distributes and schedules the available energy request and resources [8]. A good number of publications had been conducted in the area of autonomous generation and load control, including intermittent sources and demand response [15; 16; 17; 18; 19; 20; 21; 22; 23]; however, few have investigated the operation of autonomous market controllers [8]. Some efforts have focused on the theoretical assessment of optimal strategies. The solutions include the performance evaluation of real customer behavior, making the problem complex [24]. Since these types of problems are normally non-convex with a wide search space, they can become NP-hard problems [25]. This characteristic results in high computation time that limits the possibility of mathematical simplifications that allow finding points closer to the global optimal solution. Different alternatives have emerged to solve these problems. (a) Metaheuristic solutions search for problem optimization in efficient time; nevertheless, the formulation does not guarantee global optimal solutions. (b) Exhaustive searches guarantee feasible and global optimal solutions with the evaluation of various combinations of different decision variables. The last process can be cumbersome, making the problem unfeasible for applications that require responses in time frames of a day or hours. Metaheuristic algorithms are presented as possible strategies for optimal bidding in an LEM. Different computational strategies for optimal agents bidding are assessed in [6].