管理工程学报2026，Vol.40Issue(1)：274-286,13.DOI:10.13587/j.cnki.jieem.2026.01.019
考虑碳排放的交通流分配与交通系统最优模型及算法研究
Emission based traffic assignment problem and system optimization problem:Models and algorithms
摘要
Abstract
In the era of sustainable development,the study of traffic assignment with consideration of vehicle emissions has attracted great attention,as the emissions of carbon dioxide and carbon monoxide are harmful to human health as well as the environment.To control the emissions of traffic vehicles,extensive research is needed on Traffic Assignment Problem(TAP)and System Optimization Problem(SOP)that take pollution emissions into account.In Classical Traffic Assignment and System Optimization Problems,the traffic cost function of the arc is assumed to be a positive and monotonically increasing function,so the problems involved are convex optimization problems with traffic network constraints.However,the situation is quite different for Environmental Traffic Assignment Problem(ETAP)and Environmental System Optimization Problem(ESOP)that consider emissions.According to the emission equation,the emission cost on the arc is non-monotonic,resulting in non-convex optimization problems with traffic network constraints.Some studies on(ETAP)and(ESOP)adopt a time limiting strategy to ensure that the pollution cost is monotonous.However,this strategy is practically hard to be implemented and controlled.This paper adopts constrained non-convex optimization method to solve(ETAP)and(ESOP),which ensures convergence to the equilibrium point of the problems with complexity analysis results. In Section 1,the operating time function and emission function of the environmental traffic network are analyzed and a conclusion is drawn after calculations that the emission function on the arc is a weakly convex function with respect to the arc flow.In Section 2,the Environmental Traffic Assignment Problem(ETAP)is first introduced.Then,based on the understanding from the first section that(ETAP)is a difficult non-convex constrained optimization problem for traffic networks,non-convex constrained optimization generalized Lagrangian primal/dual algorithm is proposed to solve this problem after analyzing the problem structure of(ETAP)and the properties of relevant functions since(ETAP)meets all assumptions of this algorithm and delivers good convergence and complexity results.In the last part of Section 3.2,Algorithm 2 is proposed to solve the corresponding(ETAP)which makes its iterative sub-problems easy to solve.In Section 3.3,the Environmental System Optimization Problem(ESOP)is introduced,which is also a difficult non-convex constrained optimization problem.It is analyzed that Algorithm 1 can be used to solve(ESOP),therefore Algorithm 3 is constructed to further solve(ESOP). In Sections 4.1～4.2,calculation and analysis was made to the(ETAP)and(ESOP)of a simple network with two arcs.The above case analysis of a simple traffic network with two arcs also reveals that(ETAP)has a stable region for the local equilibrium point and the algorithm quickly converges to this point when the starting point lies within this region.However,the algorithm will not converge to one local equilibrium point unless this point is taken as the initial point.The(ESOP)of this simple traffic network has only one stable global minimum point,and the algorithm quickly converges to this system optimization point regardless of the starting point selection.In section 4.3,the(ETAP)and(ESOP)networks proposed by Nguyen and Dupuis is computed and analyzed.The computational analysis shows that algorithm 2 and algorithm 3 have good convergence and complexity analysis results,and can effectively solve(ETAP)and(ESOP).In section 5,it is concluded that the algorithm also indicates that Algorithm 2 may converge to different equilibrium points of(ETAP)for different starting points.Therefore,the stability analysis of equilibrium points is meaningful.For(ESOP),Algorithm 3 may also converge to different local minima for different starting points.It is also worth discussing how to distinguish its convergence point as the global minimum.If emission costs is incorporated into the constraints of(TAP)and(SOP),it becomes an(ETAP)with non-convex constraints.How to solve this(ETAP)with non-convex constraints and conduct further study on emission pricing mechanism will then become a critical research direction and will be addressed in another paper.关键词
环境交通分配问题/环境交通系统最优问题/非凸约束最优化算法Key words
Environmental traffic assignment problem/Environmental system optimization/Non-convex constrained optimization algorithm分类
管理科学引用本文复制引用
姚明山,赵磊,朱道立..考虑碳排放的交通流分配与交通系统最优模型及算法研究[J].管理工程学报,2026,40(1):274-286,13.基金项目
国家自然科学基金(71871140、72293582) The National Natural Science Foundation of China(71871140,72293582) （71871140、72293582）
