Robust Optimization Method for Mountain Railway Alignments Considering Preference Uncertainty for Costs and Seismic Risks
Taoran Song, Hao Pu, Paul Schonfeld, Jianping Hu, Jiangtao Liu
Abstract
Railways 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.