考虑排放的交通分配模型及其算法研究
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摘要
交通拥堵和环境污染是城市现代“病”的重要方面,如何改善和调节交通拥堵和环境污染已经成为城市发展必须面对的难题。论文研究了考虑环境因素的机动车尾气排放对城市交通系统,特别是交通分配、出行行为等影响,建立了考虑排放的广义交通分配模型,考虑排放因素的降低拥堵和排放的路网双层规划模型,通过引入排放收费概念,采用排放收费来限制某些路段或区域的排放量,从而优化出行行为和出行方式,使得路网的总排放不超过某个给定的阈值,达到排放的“公平目标”。本文主要完成了以下的研究工作:
(1)在传统的静态交通分配模型的基础上,给出了排放约束下的多用户交通分配模型,在所定义的广义出行费用中明确考虑排放因素,排放因子模型选用TRANSYT 7-F模型,将变分不等式问题转换成等价的最优化问题,引入改进的投影算法,通过将变分不等式问题转换成一系列二次规划子问题求解,在给出的数值算例中明确考虑了两类对排放不同偏好的出行者,所得的弧流量及路径最优解收敛且均满足Wardrop平衡条件,计算结果显示改进的投影算法在求解广义均衡费用最优方面具有可行性。
另外,采用自适应的投影收缩算法求解与考虑排放的多用户交通分配模型等价的非线性互补问题,从而得到广义费用下的UE最优解,数值算例结果显示,与其他投影算法相比,SA-PC算法在求解广义均衡费用最优方面具有较高的效率。
(2)在Venigalla等人研究工作的基础上,分别采用基于路径的梯度投影算法(gradient projection,GP)和基于路径的非集计的单纯分解算法(disaggregated simplicial decomposition,DSD)来求解考虑不同发动机启动模式下,具有非可加路径费用的交通分配问题,在实例计算中比较了这两种算法的计算性能。从数值计算结果看,这两种基于路径的算法得出的数值最优解收敛速度比基于F-W的收敛速度要快,结果较为满意。
另外,随着路网拥挤程度的提高,DSD和GP算法的计算时间也会相应地增加,但DSD比GP的增加速度要快。这两种基于路径的算法在搜索时都只用到较少的最短路径,适用于中大规模网络,随着路网规模的扩大,其计算时间和收敛速度并不十分理想。
(3)讨论了一类考虑降低排放和拥堵的路网设计问题,在所建立的双层规划模型中,考虑了路网中因路段上的排队而导致的延迟,同时在模型中也考虑了路段的排放,通过采用道路收费以限制某些关键路段的排放,使其不超过一个预先给定的阈值,同时也降低了路段的拥堵,道路收费对于减轻政府财政压力,改善路网结构,更好地服务于出行者,从而提高他们的满意度具有现实意义。
模型的求解分别采用改进的粒子群算法和改进的量子进化算法求解上层规划问题并得到全局最优解,采用Frank-Wolfe算法求解下层规划问题。实例证明,上述算法对于求解考虑排放和拥堵的路网双层规划模型较为有效。
(4)引入排放收费的概念,选取了一个小型的路网算例对考虑降低排放和拥堵的路网设计问题进行了理论上的探讨,并采用一种新的仿生优化算法,即膜计算优化算法验证了模型的正确性和可行性。
Traffic congestion and environmental pollution are two important aspects of modern urban disease.Therefore,how to improve and rectify traffic congestion as well as environmental pollution becomes a difficult issue that urban development should face up to.In this dissertation,we discussed the vehicle emission effects on urban traffic system,especially on traffic assignment,travel behavior.We established a general traffic assignment model considering emission effects,and a road network bi-level model considering reducing congestion and emission simultaneously.We introduced emission pricing,which could be used to restrain emission amount on certain link or district,in order to optimize travel behavior and travel pattern.Our goal of using this concept is to guarantee the total emission inventory of certain road network not exceed a given threshold so that we can approach the so-called equity objective.We mainly do research as follows:
(1) On the basis of traditional traffic assignment model,we put forward a general,multi-class traffic assignment model considering emission effects.Emission factors were explicitly considered in our model,we used TRANSYT-7F model in emission factor model,then transferred variational inequality problem into optimization problem,introduced modified projection algorithm to solve it.By turning variatioal inequality problem into a series of quadratic programming sub-problem,and considering two classes of preferable emission sensitive travelers in the numerical examples,we found that the optimal link and path flow solution is convergent and meet Wardrop equilibrium conditions as well.The results also showed that modified projection algorithm can efficiently improve the solution process of general equilibrium problem and is feasible.In addition,we adopted a self-adaptive projection and contraction method to solve the multi-class traffic assignment model considering emission effects and its equivable nonlinear complementarity problem.By using SA-PC method,we got the user equilibrium solution of generalized travel cost function of above model.Numerical results showed that compared with other algorithms,the SA-PC method had higher solution efficiency while solving optimization problem with generalized travel cost function.
(2) On the basis of Venigalla's work,we adopted two path-based algorithms, namely,gradient projection algorithm and disaggregated simplicial decomposition algorithm to solve nonadditive path cost traffic assignment problem under different engine operating modes.We compared the above two algorithms in a network example which showed that compared with the traditional Frank-Wolfe algorithm, the two path-based algorithms had a more quicker convergency while getting optimal solution,and it can obtain a satisfying solution in most cases.Additionally, with the increasing of road network congestion,the computation times of DSD and GP algorithm will also increased,however,DSD is more quicker than GP.Due to these two algorithms only used fewer shortest path while searching optimal solution, it can be applied to medium and larger size network.The compution time and convergent speed are not ideal with the increasing of network scale.
(3) We discussed a road network design problem considering lessening emission and congestion simultaneously.In the bi-level programming model we established,vehicle delay on road links due to queuing was considered,and the emissions on road links were also considered at the same time.We introduced road pricing to restrict road link emissions especially on some key links,to guarantee the total emission inventory of road network not exceed a given threshold.Also,we count on it can lessen the congestion of road network.Road pricing had proved to be a great meaning of decreasing financial pressure of government,improving road network structure,providing travelers better services and eventually increasing their satisfactory degree.We used a modified particle wwarm optimization algorithm and an improved quantum evolutionary algorithm to solve the upper level problem of the above bi-level programming model respectively.As for lower level problem,we adopt Frank-Wolfe algorithm to solve it.Numerical results showed that both algorithms had an efficient solution while solving the bi-level programming model considering lessening emission and congestion.
(4) We firstly introduced the concept of emission pricing,and then selected a small scale road network to analysize the road network design problem considering lessening emission and congestion from both theoretical and practical point of view. We adopt a newly bionic optimization algorithm,that is,quantum evolutionary algorithm to validate the correctness and feasibility of our model.
(1)在传统的静态交通分配模型的基础上,给出了排放约束下的多用户交通分配模型,在所定义的广义出行费用中明确考虑排放因素,排放因子模型选用TRANSYT 7-F模型,将变分不等式问题转换成等价的最优化问题,引入改进的投影算法,通过将变分不等式问题转换成一系列二次规划子问题求解,在给出的数值算例中明确考虑了两类对排放不同偏好的出行者,所得的弧流量及路径最优解收敛且均满足Wardrop平衡条件,计算结果显示改进的投影算法在求解广义均衡费用最优方面具有可行性。
另外,采用自适应的投影收缩算法求解与考虑排放的多用户交通分配模型等价的非线性互补问题,从而得到广义费用下的UE最优解,数值算例结果显示,与其他投影算法相比,SA-PC算法在求解广义均衡费用最优方面具有较高的效率。
(2)在Venigalla等人研究工作的基础上,分别采用基于路径的梯度投影算法(gradient projection,GP)和基于路径的非集计的单纯分解算法(disaggregated simplicial decomposition,DSD)来求解考虑不同发动机启动模式下,具有非可加路径费用的交通分配问题,在实例计算中比较了这两种算法的计算性能。从数值计算结果看,这两种基于路径的算法得出的数值最优解收敛速度比基于F-W的收敛速度要快,结果较为满意。
另外,随着路网拥挤程度的提高,DSD和GP算法的计算时间也会相应地增加,但DSD比GP的增加速度要快。这两种基于路径的算法在搜索时都只用到较少的最短路径,适用于中大规模网络,随着路网规模的扩大,其计算时间和收敛速度并不十分理想。
(3)讨论了一类考虑降低排放和拥堵的路网设计问题,在所建立的双层规划模型中,考虑了路网中因路段上的排队而导致的延迟,同时在模型中也考虑了路段的排放,通过采用道路收费以限制某些关键路段的排放,使其不超过一个预先给定的阈值,同时也降低了路段的拥堵,道路收费对于减轻政府财政压力,改善路网结构,更好地服务于出行者,从而提高他们的满意度具有现实意义。
模型的求解分别采用改进的粒子群算法和改进的量子进化算法求解上层规划问题并得到全局最优解,采用Frank-Wolfe算法求解下层规划问题。实例证明,上述算法对于求解考虑排放和拥堵的路网双层规划模型较为有效。
(4)引入排放收费的概念,选取了一个小型的路网算例对考虑降低排放和拥堵的路网设计问题进行了理论上的探讨,并采用一种新的仿生优化算法,即膜计算优化算法验证了模型的正确性和可行性。
Traffic congestion and environmental pollution are two important aspects of modern urban disease.Therefore,how to improve and rectify traffic congestion as well as environmental pollution becomes a difficult issue that urban development should face up to.In this dissertation,we discussed the vehicle emission effects on urban traffic system,especially on traffic assignment,travel behavior.We established a general traffic assignment model considering emission effects,and a road network bi-level model considering reducing congestion and emission simultaneously.We introduced emission pricing,which could be used to restrain emission amount on certain link or district,in order to optimize travel behavior and travel pattern.Our goal of using this concept is to guarantee the total emission inventory of certain road network not exceed a given threshold so that we can approach the so-called equity objective.We mainly do research as follows:
(1) On the basis of traditional traffic assignment model,we put forward a general,multi-class traffic assignment model considering emission effects.Emission factors were explicitly considered in our model,we used TRANSYT-7F model in emission factor model,then transferred variational inequality problem into optimization problem,introduced modified projection algorithm to solve it.By turning variatioal inequality problem into a series of quadratic programming sub-problem,and considering two classes of preferable emission sensitive travelers in the numerical examples,we found that the optimal link and path flow solution is convergent and meet Wardrop equilibrium conditions as well.The results also showed that modified projection algorithm can efficiently improve the solution process of general equilibrium problem and is feasible.In addition,we adopted a self-adaptive projection and contraction method to solve the multi-class traffic assignment model considering emission effects and its equivable nonlinear complementarity problem.By using SA-PC method,we got the user equilibrium solution of generalized travel cost function of above model.Numerical results showed that compared with other algorithms,the SA-PC method had higher solution efficiency while solving optimization problem with generalized travel cost function.
(2) On the basis of Venigalla's work,we adopted two path-based algorithms, namely,gradient projection algorithm and disaggregated simplicial decomposition algorithm to solve nonadditive path cost traffic assignment problem under different engine operating modes.We compared the above two algorithms in a network example which showed that compared with the traditional Frank-Wolfe algorithm, the two path-based algorithms had a more quicker convergency while getting optimal solution,and it can obtain a satisfying solution in most cases.Additionally, with the increasing of road network congestion,the computation times of DSD and GP algorithm will also increased,however,DSD is more quicker than GP.Due to these two algorithms only used fewer shortest path while searching optimal solution, it can be applied to medium and larger size network.The compution time and convergent speed are not ideal with the increasing of network scale.
(3) We discussed a road network design problem considering lessening emission and congestion simultaneously.In the bi-level programming model we established,vehicle delay on road links due to queuing was considered,and the emissions on road links were also considered at the same time.We introduced road pricing to restrict road link emissions especially on some key links,to guarantee the total emission inventory of road network not exceed a given threshold.Also,we count on it can lessen the congestion of road network.Road pricing had proved to be a great meaning of decreasing financial pressure of government,improving road network structure,providing travelers better services and eventually increasing their satisfactory degree.We used a modified particle wwarm optimization algorithm and an improved quantum evolutionary algorithm to solve the upper level problem of the above bi-level programming model respectively.As for lower level problem,we adopt Frank-Wolfe algorithm to solve it.Numerical results showed that both algorithms had an efficient solution while solving the bi-level programming model considering lessening emission and congestion.
(4) We firstly introduced the concept of emission pricing,and then selected a small scale road network to analysize the road network design problem considering lessening emission and congestion from both theoretical and practical point of view. We adopt a newly bionic optimization algorithm,that is,quantum evolutionary algorithm to validate the correctness and feasibility of our model.
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