Railway Alignment Optimization Under Uncertainty With a Minimax Robust Method

Railway alignment optimization is difficult due to theoretically infinite possible alternatives, multiple conflicting and hard-to-quantify objectives, as well as large-scale and highly constrained search spaces. Besides these factors, this problem includes great uncertainties, which weaken solution robustness. However, no proactive robust approach has been developed for explicit uncertainty analysis within alignment optimization. In this article, a novel minimax approach is proposed for railway alignment optimization. First, a minimax robust optimization (RO) model is developed. In it, the comprehensive alignment cost is defined as the raw objective function, and a minimax cost evaluation is constructed as the expected objective function. Multiple design constraints are also specified and categorized into hard and soft ones for robust assessments. Afterward, a previous particle swarm optimization (PSO) algorithm is modified into an RO–PSO algorithm by improving the search process with an RO procedure whose major steps include the determination of disturbance spaces, generation of alignment counterparts and implementation of minimax analysis. Finally, the model and algorithm are applied to a complex, real-world mountain railway case. The effectiveness of the proposed approach is verified through a comparison of the resulting cost and degree of robustness (DoR) among the best alignments generated by the previous PSO and the RO–PSO. The search performance of the RO–PSO is further tested by varying an important parameter, i.e., the number of alignment counterparts. The outcomes indicate that the DoR performance of the RO–PSO can be improved as the counterparts increase, but the performance will finally converge to a certain degree.