## 1 Introduction
For cobalt-based LiBs, this is generally set at 4.2 V. In this method, when the cut-off voltage is reached during charging, the current is reduced, and the charging continues until the cut-off voltage is reached again. This process is repeated until a predefined number of stages is completed, making the implementation straightforward. Each CC stage can be executed in various configurations, including four stages [18; 19; 20], five stages [21; 22; 23; 24; 25; 26; 27; 28; 29], and ten stages [30], to evaluate the life and performance of the LiB. However, dividing the charging process into five stages has been reported to be optimal in terms of computational efficiency and performance [23]. The MSCC charging strategy has been shown to improve CE, shorten charging time, enhance charge and discharge capacities, reduce temperature rise, and extend the lifespan of LiBs compared to the traditional CC-CV method. Additionally, the cut-off voltage-based criterion is simpler and easier to implement than other SOC-based methods. The performance indicators of the MSCC charging method, including total charging capacity, charging time, and CE, depend on the selection of current values for each stage. Thus, it is crucial to adopt an efficient method to determine the optimal charging pattern (OCP) to enhance the performance of the MSCC charging method. While mathematical techniques such as the Taguchi method [21; 24] and Bayesian optimization [26] have been employed to identify the optimal OCP, these methods necessitate experimental verification of candidate charging patterns, which can be time-consuming and significantly increase the time and cost associated with finding the optimal solution. In [21], a Thevenin equivalent circuit model (ECM) was implemented, which does not require extensive experimentation and time cost for lithium-ion batteries. In this study, the OCP was derived by differentiating a charging time equation consisting of mathematically derived current and voltage variables. This approach allows for easy implementation without using the CV mode to charge the battery to its maximum capacity. However, it is important to note that this method is primarily optimized, neglecting various performance indicators such as temperature rise and charging loss. Metaheuristic optimization algorithms (MOAs) simulate the movements of plants and animals in search of food or survival, as well as the physical chaos phenomena of nature. They have been widely applied to optimization problems due to their advantages, including few parameters, ease of implementation, and the ability to achieve a balance between exploration and exploitation during the optimization process. To explore the OCP in the MSCC method, the particle swarm optimization (PSO) algorithm [31] was utilizedin [18; 23; 28], the grey wolf optimization (GWO) algorithm [32] was employed in [27], and the jellyfish search algorithm (JSA) [33] was applied in [28]. Furthermore, charging time (CT) and charging loss were selected as objective functions for each optimization of the performance indicators of the MSCC charging method [27; 28]. However, CT, which is a key objective of OCP, and the charging loss indicator have an indirect relationship, complicating the optimization process. Additionally, calculating the charging loss during the optimization is complex. To implement an accurate ECM, electrochemical impedance spectroscopy (EIS) is conducted to derive the internal resistance, polarization resistance, polarization capacity, and time constant values of the model. Since the cycler experimental equipment for battery charging and discharging only measures the charging voltage, current, and temperature, a separate and costly potentiostat equipment is required to perform EIS analysis on the LiBs. Based on the aforementioned background, this study adopted the ECM of lithium-ion batteries with the Dandelion optimizer (DO) algorithm [34], a type of MOA. The OCP of the MSCC charging method simultaneously considers the performance indices of charging time and charging temperature.