AbstractRailways are vital infrastructures whose design is complex and time-consuming. In addition to multiple conflicting objectives and highly-constrained search spaces, their design also faces great uncertainties. The aim of this study is to optimize railway alignments considering decision-makers’ preference uncertainty for multiple objectives, which can influence the alignment determination macroscopically and fundamentally. First, a multiobjective model is built by integrating costs (including construction and operation costs) and seismic risks (including direct and indirect losses) for mountain railway optimization. To solve this model, a particle swarm algorithm is improved by incorporating a multicriteria tournament decision (MTD). Then, a robust optimization MTD (RO-MTD) method is developed to find cost-risk tradeoffs by addressing the uncertainty of decision-makers’ preferences. The major steps of the RO-MTD include (1) treating uncertain preferences as variables, (2) sampling the uncertain space of preferences, (3) analyzing all possible preference scenarios, and (4) integrating those analyses to achieve a robust evaluation. Finally, the preceding approaches are applied to a complicated real-world case. By comparing the RO-MTD and MTD as well as the computer-generated alignment and the best manually-designed one, the effectiveness of the proposed method is confirmed.

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