PB-MNSGA-II algorithm and its application for multi-objective optimization design of under-vehicle equipment

Structural damage caused to under-vehicle equipment under adverse working conditions affects the safe operation of high-speed electric multiple units (EMUs). To address the low optimization efficiency and take into account vibration fatigue in traditional under-vehicle equipment design, herein, a multi-objective optimization design method (PB-MNSGA-II) that combines particle swarm optimization-back propagation (PSO-BP) neural network and modified non-dominated sorting Genetic Algorithm II (MNSGA-II) was proposed. It can help engineers choose better equipment component thickness and achieve efficient and accurate design. First, MNSGA-II, the core content of PB-MNSGA-II, was proposed, which improved four aspects of NSGA-II: Latin hypercube sampling population initialization, adaptive crossover and mutation probability, mutation interference of Levy flight strategy, and optimal elite strategy. Then, zero-ductility transition (ZDT) series functions were employed to test MNSGA-II, thereby verifying its convergence and computational efficiency. Subsequently, utilizing the frame structure of the traction transformer (TTR) as an illustrative example, the PB-MNSGA-II approach was employed to enable multi-objective optimization. During this optimization process, the focus was on random vibration fatigue damage, thus enhancing the rationality of the optimization outcomes. After structural optimization, the mass of the TTR decreased by 20.1 kg, and the maximum vibration fatigue damage value decreased from 1.09 to 0.808, verifying the effectiveness and feasibility of the proposed method. The findings of this study provide important insights for the multi-objective optimization design of under-vehicle equipment under complex operating conditions.