A Study On Energy-efficient Timetabling In Subway Systems Using A Sparse Optimization Approach

With the rapid development of the industry and population in cities,the metro railways have been playing a more and more important role in urban economic and social development due to its high transport capacity and low pollution.Although the subway system has the mechanism of energy regeneration,its net energy consumption still has a huge magnitude.Therefore,the effective energy management for the metro system is of great importance.In this thesis,we aim to maximize the utilization of the regenerative braking energy for energy-efficient timetabling.The main work includes the following three parts.Firstly,the cardinality function(also known as the l0-norm)and the square of the Euclidean norm are introduced as the objective function,with those basic constraints for eligible timetabling.The resulting optimization is generally NP-hard due to the involved l0-norm.Thus,a weighted l1-norm is adopted to get a convex relaxation counterpart.Duality analysis and optimality conditions are discussed for the relaxation problem,which provide theoretical preparation for the algorithm design in the sequel.Secondly,a two-stage alternating direction method of multipliers is designed to efficiently solve the convex realxation model.The global convergence is also shown for such a numerical iterative algorithm.Finally,the resulting approach is applied to Beijing Metro Yizhuang Line with different instances of service for case study.Comparison with other methods are also conducted which illustrate the effectiveness of our proposed sparse optimization model in terms of the energy saving rate,and the efficiency of our numerical optimization algorithm in terms of computational time.