This paper presents a novel metaheuristic optimization algorithm inspired by the geometrical features of circles, called the circle search algorithm (CSA). The circle is the most well-known geometric object, with various features including diameter, center, perimeter, and tangent lines. The ratio between the radius and the tangent line segment is the orthogonal function of the angle opposite to the orthogonal radius. This angle plays an important role in the exploration and exploitation behavior of the CSA. To evaluate the robustness of the CSA in comparison to other algorithms, many independent experiments employing 23 famous functions and 3 real engineering problems were carried out. The statistical results revealed that the CSA succeeded in achieving the minimum fitness values for 21 out of the tested 23 functions, and the p-value was less than 0.05. The results evidence that the CSA converged to the minimum results faster than the comparative algorithms. Furthermore, high-dimensional functions were used to assess the CSA’s robustness, with statistical results revealing that the CSA is robust to high-dimensional problems. As a result, the proposed CSA is a promising algorithm that can be used to easily handle a wide range of optimization problems.

The integration of renewable energy resources and electric vehicle (EV) fleets with community microgrids (CMG) has increased fluctuations in net load. To address this and ensure safe operation, tapping into demand-side flexibility capacities in local electricity markets (LEM) is essential. Hence, this article presents a multilevel methodology for settling energy and flexibility markets among CMGs, utilizing the potential of Internet-of-Things-enabled appliances (IoT-EA), thermostatically-controlled loads (TCLs), and EVs in smart residential buildings (SRB) to enhance system performance. At level 1, SRBs are modeled using the virtual energy storage system (VESS) concept. Level 2 involves CMG scheduling, and at level 3, the distribution system operator settles the energy and flexibility markets using an adaptive alternating direction method of multipliers (ADMM) algorithm. Strong duality theory (SDT) and Karush-Kuhn-Tucker (KKT) conditions form a mathematical program with equilibrium constraints (MPEC) where market prices are variable for all participants. By unlocking the potential of SRBs, the proposed framework reduces flexibility market costs by 49.67%, network losses by 24.1%, and improves the voltage profile. The results confirm that the proposed market clearing mechanism ensures market efficiency and protects CMGs' privacy.