## 1 Introduction and State of Art  
These days, there are multiples changes in the structure of transmission and distribution of electric energy that allows the integration of new technologies notions in generation, storage, electric mobility [1, 2], and energy metering [3]. As a result of these system changes, electricity dependence and energy transactions have increased. The Local Energy Markets (LEM) is an opportunity for small grid actors to actively take part in the bidding process. LEM allows local transactions that empower consumers, producers, and prosumers in the goal of creating energy balances [4]. LEM are defined locally in terms of residential customers close enough in the same geographical and social area. However, the larger the number of actors, the harder the synchronization, control, and optimal market operation. To replicate and achieve optimal local energy market responses, it is necessary to guarantee coordination among the different market participants and appropriate tools for proper decision making [4, 5]. The CEC (Congress on Evolutionary Computation) and GECCO (Genetic and Evolutionary Computation Conference) 2021 competition on \"Evolutionary Computation in the Energy Domain: Smart Grid Applications\" called for participants to develop metaheuristic optimization solutions for LEMs operation under complex conditions such as those that include trading energy in an LM (Local Market) [6]. Considering several explicit mathematical formulations, these problems cannot be solved efficiently due to the complex nature of LEM models. Heuristic and metaheuristic algorithms have been shown to be a reliable option in problems that include energy transactions [7]. An example of this is the different set of evolutionary algorithms explored for the solution of a bi-level energy market problem of nine participants in [6; 7]. Track 1 of a 2021 competition includes a complex bi-level market problem with nine different participants. The upper-level agents try to maximize their profits, depending on the solution of the lower level problem. This interdependency between decisions makes the problem not an easy task [6; 8]. Therefore, the complexity of this problem with the high number of variables is adequate for the application of different heuristics-based algorithms and special computational structures [6]. More complex computational architectures had been required for the development of electrical networks, control strategies, and optimal decisions. In order, to obtain optimal and feasible solutions in recent times for the planning and operation of complex systems with a high number of devices, one of the proposed architectures is the use of Parallel Computing (PC). PC allows the execution of tasks in parallel, thus avoiding the long processing times required in the execution of activities sequentially [9]. In this work, a parallel architecture is used to reach a global optimum in a bi-level local market with different agents using brute force [10; 11]. In this way, not only a complex optimization problem is solved, but it is also possible to measure the performance of different metaheuristic algorithms. The remainder of this document includes the following: Section 1--a summary of the state-of-the-art for different approaches in terms of metaheuristic algorithm for SMGs operation planning and PC power system applications. The next section is a presentation of a test case. Section 3 is a presentation of the HyDE-DF (hybrid-adaptive differential evolution with a decay function), HHO (Harris Hawks Optimization), WOA (whale optimization algorithm), and DEEPSO (Differential Evolutionary Particle Swarm Optimization) algorithms. Section 4 presents the algorithm for PC; then, it presents the evaluation of a metaheuristic algorithm using PC global optimal. Finally, the last section shows the conclusion of the work.