Metaheuristic search algorithms in real-time charge scheduling optimisation: A suite of benchmark problems and research on stability-analysis

The most important challenges in the optimization of real-time charging scheduling (CS) problems are (i) the need to model CS problems with a large number of decision variables for precise control, (ii) the increase in computational complexity with the high penetration of electric vehicles, and (iii) the lack of research on the stability and computation time of optimization algorithms on CS problems. In this paper, we design a real-time model and introduce the CS Benchmark Problems (CSBP) suite of twelve problems of four different types. Furthermore, a driver satisfaction model is introduced for the first time to analyse the impact of the results on user satisfaction. Best known solutions for all problems in CSBP are presented for the first time in this study. According to the statistical analysis results, the three competitive algorithms among 66 competitors in the optimization of CSs are LSHADE-CnEpSin, LSHADE-SPACMA and LRFDB-COA. Stability and computational complexity analyses revealed that LSHADE-SPACMA is the most successful algorithm for problems where consumers outnumber prosumer and LRFDB-COA is the most successful algorithm for problems where consumers equal or exceed prosumer. When the performance of the algorithms is evaluated regardless of the problem type, LSHADE-Spacma is the most stable algorithm with an overall success rate of 100 % on CSs. In addition, the average peak load shaving for the best known solutions of the algorithms with the highest success rate for each problem is calculated to be 94.84 %, and the average satisfaction score for all drivers is calculated to be 0.81.