Alignment Optimization Theory And Application Of Urban Rail Transit

The alignment scheme is the essential information for the survey,geological exploration,and design of other professions in a rail transit project.It determines the distribution and scale of major structures,influences the investment and construction period,formulates a part of essential data for the operation period.In the procedure of manual alignment design,an alignment engineer concludes a recommended alignment scheme only by comparison of limited schemes,which misses better alignment schemes easily because of the subjectivity and inadequate experience in alignment design.The application of optimization theory in alignment optimization could compensate for the defect of manual alignment design,improve the quality and efficiency of alignment design,reduce the investment,decrease the expense for operation.However,the first approach based on derivation is a local optimization method that needs an initial feasible solution.The second approach based on path searching simplifies geography greatly,and the fitting alignment may not satisfy all geometry constraints.The third approach based on computational intelligence is inefficiency,and the related literature usually misses the analysis of variable size,it could not optimize an alignment in large-scale geography.Therefore,this paper focuses on interval alignment optimization theory and application of urban rail transit,i.e.searching the optimal horizontal alignment and vertical alignment connecting two fixed stations in a given geographical feasible zone.The proposed alignment optimization models related to the various assignment of alignment design should be solved by a kind of computational intelligence method.They could optimize an alignment in a large geographical feasible zone,and deal with the alignment optimization even the distribution of horizontal points of intersection and vertical points of gradient change are not known.The main contents are listed as follows:(1)Analyzing the basic model of alignment optimization,unifying the selection,coding,distribution,and geometry constraints of variables,thus the iteration process links with the practical alignment optimization through a unified interface.This paper proposes three kinds of optimization structures based on the requirement of alignment design in various circumstances,i.e.single-level optimization with a single objective,bi-level optimization with a single objective,and bi-level optimization with multi-objective.The process of the differential evolution(DE)algorithm is analyzed as the model solution.To improve the optimization efficiency,this paper suggests four methods,i.e.improving the algorithm,setting suitable terminal conditions,reducing the feasible region of variables,decreasing the size of valid variables.To deal with the defect in finding the optimal solution under a rigorously geographical environment,this paper put forward three methods i.e.optimizing with seed,setting passing point,setting corridor constraints.(2)Studying the interactive design with two dimensional(2D)and three dimensional(3D)manners for mass integration of geographic information and alignment spatial analysis.This paper set up a 3D scene integrating terrain and geographic feature affecting alignment scheme based on two open-source kits named osg Earth and QT.The scene could model 3D geographic features dynamically and transfer status between 2D and 3D smoothly.The proposed method of interactive design not only supports the plan and profile alignment design in a traditional2 D manner but also describes the alignment scheme by real spatial alignment and light 3D models of subgrade,bridge,and tunnel.This paper also studies the mapping relation between alignment and geographical environment through which the right-of-way cost and special cost of construction are expressed for various structures.It is the basic technology for the spatial analysis of alignment optimization.(3)Based on the structure of single-level optimization with a single objective,optimizing the horizontal alignment in shield interval of urban rail transit with the minimization of investment,and optimizing the vertical alignment in shield interval of urban rail transit with the minimization of energy consumption in operation period.For the single horizontal alignment optimization in planning phase,this paper improves the Rapidly-exploring Random Tree-connect(RRT-connect)algorithm to search the path with minimum cost,fits the path to be an initial horizontal alignment,and optimize the initial horizontal alignment by DE algorithm;For the double horizontal alignment optimization in implementation phase,it is suggested determining valid variables on the left line based on the given alignment,and selecting the optimization strategies among direct optimization,optimization with seed and optimization through two stages;For the vertical alignment optimization considering minimization of energy consumption,this paper analyzes the objectives for traction-idling-braking operation manner and traction-cruise-braking operation manner,calculates the train resistance through integral method,put forward the optimization strategy combing initial alignment search and deep optimization in order to improve the efficiency and determine the suitable amount and distribution of vertical points of gradient change.The analysis of single-level optimization with a single objective indicates that alignment optimization needs multi-stage.(4)Based on the structure of bi-level optimization with a single objective,optimizing the horizontal alignment and vertical alignment simultaneously with the minimization of investment,when the geographical environment,horizontal alignment,and vertical alignment correlated strongly in suburban rail transit.The upper-level deals with horizontal alignment optimization,and each horizontal alignment satisfying geometry constraints invokes once vertical alignment optimization at the lower level.The optimal vertical alignment taking minimum investment is transferred to the corresponding horizontal alignment to promote the optimization of horizontal alignment.The solution strategy consists of multi-stage,i.e.corridor alignment generation,initial alignment generation,and optimal alignment generation.The strategy not only makes sure the necessary optimization efficiency but also determines the suitable amounts and distributions of horizontal points of intersection and vertical points of gradient change gradually.The bi-level optimization with a single objective coincides with manual alignment design in general geography,while the solution with multi-stage coincides with the manual procedure.(5)Based on the structure of bi-level optimization with multi-objective,optimizing the horizontal alignment and vertical alignment simultaneously in the ecologically sensitive region considering the minimization of investment and ecological protection for mountain rail transit.This paper analyzes the ecological protection measures and its limitation,sets up a bi-level alignment optimization model with multi-objective for an interval of mountain rail transit in the national natural reserve at Wolong Sichuan.The structure of bi-level optimization with multi-objective is an extension of the structure of bi-level optimization with a single objective.The horizontal alignment optimization at the upper-level covers the minimization of investment,drainage in tunnel construction,and noise from operating trains.The solution based on decomposition could maintain the diversity of the optimal solution set naturally.The vertical alignment optimization at lower-level only considers the minimization of investment.The solution based on the adaptive DE algorithm adjusts the essential parameters according to the iteration process,which improves the efficiency drastically.According to sensitivity analysis on the number of horizontal points of intersection and vertical points of gradient change,the optimization strategy with multi-stage could find the optimal solution in a larger scale.