An Improved Whale Optimization Algorithm via Angle Penalized Distance for Automatic Train Operation.

This study proposes a novel effective improved whale optimization algorithm via angle penalized distance (IWOA-APD) for automatic train operation (ATO) to effectively improve the ATO quality. Specifically, aiming at the high-quality target speed curve of urban rail trains, a target speed curve multi-objective optimization model for ATO is established with energy saving, punctuality, accurate stopping, and comfort as the indexes; and the comprehensive evaluation strategy utilizing angle-penalized distance as the evaluation index is proposed to enhance the assessment's rationality and applicability. On this basis, the IWOA-APD is proposed using strategies of non-linear decreasing convergence factor, solutions of out-of-bounds eliminating via combination of reflection and refraction, mechanisms of genetic evolution with variable probability, and elite maintenance based on fusion distance and crowding degree distance. In addition, the detailed design scheme of IWOA-APD is given. The test results show that the proposed IWOA-APD achieves significant performance improvements compared to traditional MOWOA. In the optimization scenario from Lvshun New Port Station to Tieshan Town Station of Dalian urban rail transit line No.12, the IGD value shows a remarkable 69.1% reduction, while energy consumption decreases by 12.5%. The system achieves a 64.6% improvement in punctuality and a 76.5% enhancement in parking accuracy. Additionally, comfort level improves by 15.9%.