An integrated multi-objective optimization method with application to train crashworthiness design

The collision performance of crashworthy structures can be improved using the optimization design. However, conflicting objective functions and the non-uniqueness of solutions hinder the Pareto optimum selection. This study constructs a hybrid optimization approach (TA-FBGV) integrating the multi-objective optimization and the multiple criteria decision-making (MCDM). TA-FBGV combines the two-phase differential evolution (ToPDE) method, indicator-based multi-objective evolutionary algorithm (AR-MOEA), fuzzy best worst (F-BW) strategy, grey relational analysis (GRA), and VIsekriterijumsko KOmpromisno Rangiranje (VIKOR) integrating method (G-VIKOR) to address difficulties of the Pareto optimum selection. The ToPDE method is employed to generate uniform samples. AR-MOEA is used to produce Pareto optimal solutions. Weighting values of competing objectives are calculated through the F-BW strategy. G-VIKOR is applied to choose the final Pareto optimum from the Pareto front. Subsequently, the multi-objective optimization of the train underframe structure is performed using TA-FBGV. The results show that the Pareto optimum obtained by G-VIKOR is a good compromising solution which locates near the knee point provided by the minimum distance selection method (TMDSM). This implies that the G-VIKOR approach can achieve a good trade-off among conflictive objectives. Compared with the initial model, although the energy absorption of the Pareto optimum is decreased, the initial peak crushing force and structural mass are reduced. Optimization results indicate that the TA-FBGV approach is efficient to select the Pareto optimum for the structure optimization design.