Accurate estimation of the state-of-charge is a crucial need for the battery, which is the most important power source in electric vehicles. To achieve better estimation result, an accurate battery model with optimum parameters is required. In this paper, a gradient-free optimization technique, namely tree seed algorithm (TSA), is utilized to identify specific parameters of the battery model. In order to strengthen the search ability of TSA and obtain more quality results, the original algorithm is improved. On one hand, the DE/rand/2/bin mechanism is employed to maintain the colony diversity, by generating mutant individuals in each time step. On the other hand, the control parameter in the algorithm is adaptively updated during the searching process, to achieve a better balance between the exploitation and exploration capabilities. The battery state-of-charge can be estimated simultaneously by regarding it as one of the parameters. Experiments under different dynamic profiles show that the proposed method can provide reliable and accurate estimation results. The performance of conventional algorithms, such as genetic algorithm and extended Kalman filter, are also compared to demonstrate the superiority of the proposed method in terms of accuracy and robustness.

When Simulated Annealing (SA) is applied to continuous optimization problems, the design of the neighborhood used in SA becomes important. Many experiments are necessary to determine an appropriate neighborhood range in each problem, because the neighborhood range corresponds to distance in Euclidean space and is decided arbitrarily. We propose Multi-point Simulated Annealing with Adaptive Neighborhood (MSA/AN) for continuous optimization problems, which determine the appropriate neighborhood range automatically. The proposed method provides a neighborhood range from the distance and the design variables of two search points, and generates candidate solutions using a probability distribution based on this distance in the neighborhood, and selects the next solutions from them based on the energy. In addition, a new acceptance judgment is proposed for multi-point SA based on the Metropolis criterion. The proposed method shows good performance in solving typical test problems.