日变交通路径调整模型与算法研究
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摘要
论文针对现有研究不足,借助行为动力学建模、数值模拟与数学优化理论等方法,从日变交通路径调整模型、调整算法与交通信息发布策略三个层面系统地展开研究。论文的主要创新工作总结如下：
(1)通过指证经典比例调整过程的两个行为不足(即弱鲁棒性与过度调整问题),建立了基于对向行为准则的非线性对向调整动力学(NPSD)模型,然后以此为基础,进一步探讨了受多日出行经历影响、有限理性情形及最短路导向行为准则下的交通路径调整行为,分别建立了多日NPSD (MNPSD)模型、有限理性NPSD (BRNPSD)模型以及最短路导向的非线性调整动力学(NMSD)模型。研究发现：i)以上四种路径调整模型均能避免弱鲁棒性与过度调整问题,进而维持迭代解集不变,同时各自的稳定路径流模式与其对应的用户均衡等价；ii) NPSD与NMSD均为理性行为调整过程,并且二者的连续型模型是全局稳定的。数值结果表明：i)用户反应灵敏度对网络交通流演化过程与结果具有重要影响；ii)路径调整中过分依赖过往出行经验反而可能增加网络的不稳定风险；iii)有限理性下的网络演化稳定性并非总比完美理性强；iv) DNPSD的稳定性优于DNMSD,并且前者更适用于开发交通流均衡求解算法。
(2)通过引入风险倾向型路径旅行时间测度MBTT,并将其与风险规避型测度METT进行凸组合,构建了可描述各种风险态度的路径旅行时间测度CMTT,再将其纳入旅行时间可靠性测度(RM)框架,提出了基于RM的NPSD (RMNPSD)模型,再将反应灵敏度回溯算子引入其中,提出了求解可靠性用户均衡(RMUE)的非线性对向调整算法(NPSA). NPSA无需参数可行性试错过程,且不依赖于导数也无需搜索迭代方向与步长。数值结果显示NPSA的计算效率较高、可作为其他局部收敛算法的初始点搜索方法。
(3)基于出行者的有限感知记忆能力假设,提出并建立了日变事后交通信息的适度矫正发布策略及其动态规划模型,鉴于模型目标函数非线性、连续不光滑且无封闭的显式表达式,论文视其为一个静态非线性规划,并提出一种改进型罗盘搜索算法对其进行求解。基于简单现实路网的数值模拟结果表明事后信息矫正发布策略可提升网络运行效率,并且改进型罗盘搜索具有良好的寻优能力。
Aiming at the shortcomings of the existing studies and employing the behavioral dynamics modeling, numerical simulation and mathematical optimization theory, this dissertation conducts a systematical research on three aspects including the day-to-day traffic route-swapping model, swapping algorithm and traffic information release strategy. The main innovations of this dissertation are summarized as follows:
(1) By indentifying and testifying two behavioral deficiencies, i.e., the weak robustness and over-swapping problem, in the classical proportional-switch adjustment process, a nonlinear pairwise swapping dynamics (NPSD) is proposed based on the pairwise route swapping behavior criterion. Along the analogous line, many other route swapping behaviors, affected by multi-day former experiences as well as conducted by bounded rationality and shortest-path-pursed swapping behavior criteria, are further investigated, and the corresponding multi-day NPSD (MNPSD), bounded-rationality NPSD (BRNPSD) and nonlinear min-cost-pursued swapping dynamics (NMSD) are proposed. It is verified that:i) the above four route swapping dynamics (i.e., NPSD, MNPSD, BRNPSD and NMSD) can avoid the weak robustness and over-swapping problem indentified in PAP, which makes the solutions of these swapping dynamics invariant; in addition, their stationary route traffic flow patterns are equivalent to their traffic equilibria; ii) NPSD and NMSD are both rational behavior adjustment process and their continuous-time versions are globally convergent. The numerical results suggest that:i) traverller's reaction sensitivity has significant effect on the network traffic evolution process and result; ii) too much dependence on experience can increase the risk of instability; iii) the traffic evolution stationarity under bounded rationality is not always stronger than that under perfect rationality; iv) the stationarity of DNPSD is superior to that of DNMSD, and the former is more applicable to develop swapping algorithm to solve the traffic equilibrium models.
(2) By introducing a risk-preference route travel time measure named mean-below travel time (MBTT), and making convex combination between it and the risk-preference mean-excess travel time (METT) measure, a full-risk-attitude route travel time measure named combined mean travel time (CMTT) is established and included into the framework of reliability measure (RM). The RM-based NPSD (RMNPSD) is presented and analyzed. Then a backtracking process associated with reaction sensitivity is further embedded into RMNPSD, deriving a novel swapping algorithm named the nonlinear pairwise swapping algorithm (NPSA) to indentify the RM-based traffic equilibrium. It is found that NPSA needs not the feasible trial and error process for the key parameter; also it is derivative-free and needs not consuming time to find the iteration direction and step length. The numerical results indicate that NPSA has good computing efficiency and can serve as a quick method to find a good initial point for local optimization algorithms.
(3) Based on the assumption that travelers are of bounded perception-memory, a day-to-day expost traffic information tailoring strategy and its dynamical programming model are proposed and established. Considering the objective function of the model is nonlinear, non-derivative and has not a close explicit expression, here it is viewed as a stationary programming and a revised compass direct search algorithm is proposed to solve it. Numerical results based on a simple actual traffic network indicate that the expost traffic information tailoring strategy can improve the network evolution efficiency and the revised algorithm performs well.
(1)通过指证经典比例调整过程的两个行为不足(即弱鲁棒性与过度调整问题),建立了基于对向行为准则的非线性对向调整动力学(NPSD)模型,然后以此为基础,进一步探讨了受多日出行经历影响、有限理性情形及最短路导向行为准则下的交通路径调整行为,分别建立了多日NPSD (MNPSD)模型、有限理性NPSD (BRNPSD)模型以及最短路导向的非线性调整动力学(NMSD)模型。研究发现：i)以上四种路径调整模型均能避免弱鲁棒性与过度调整问题,进而维持迭代解集不变,同时各自的稳定路径流模式与其对应的用户均衡等价；ii) NPSD与NMSD均为理性行为调整过程,并且二者的连续型模型是全局稳定的。数值结果表明：i)用户反应灵敏度对网络交通流演化过程与结果具有重要影响；ii)路径调整中过分依赖过往出行经验反而可能增加网络的不稳定风险；iii)有限理性下的网络演化稳定性并非总比完美理性强；iv) DNPSD的稳定性优于DNMSD,并且前者更适用于开发交通流均衡求解算法。
(2)通过引入风险倾向型路径旅行时间测度MBTT,并将其与风险规避型测度METT进行凸组合,构建了可描述各种风险态度的路径旅行时间测度CMTT,再将其纳入旅行时间可靠性测度(RM)框架,提出了基于RM的NPSD (RMNPSD)模型,再将反应灵敏度回溯算子引入其中,提出了求解可靠性用户均衡(RMUE)的非线性对向调整算法(NPSA). NPSA无需参数可行性试错过程,且不依赖于导数也无需搜索迭代方向与步长。数值结果显示NPSA的计算效率较高、可作为其他局部收敛算法的初始点搜索方法。
(3)基于出行者的有限感知记忆能力假设,提出并建立了日变事后交通信息的适度矫正发布策略及其动态规划模型,鉴于模型目标函数非线性、连续不光滑且无封闭的显式表达式,论文视其为一个静态非线性规划,并提出一种改进型罗盘搜索算法对其进行求解。基于简单现实路网的数值模拟结果表明事后信息矫正发布策略可提升网络运行效率,并且改进型罗盘搜索具有良好的寻优能力。
Aiming at the shortcomings of the existing studies and employing the behavioral dynamics modeling, numerical simulation and mathematical optimization theory, this dissertation conducts a systematical research on three aspects including the day-to-day traffic route-swapping model, swapping algorithm and traffic information release strategy. The main innovations of this dissertation are summarized as follows:
(1) By indentifying and testifying two behavioral deficiencies, i.e., the weak robustness and over-swapping problem, in the classical proportional-switch adjustment process, a nonlinear pairwise swapping dynamics (NPSD) is proposed based on the pairwise route swapping behavior criterion. Along the analogous line, many other route swapping behaviors, affected by multi-day former experiences as well as conducted by bounded rationality and shortest-path-pursed swapping behavior criteria, are further investigated, and the corresponding multi-day NPSD (MNPSD), bounded-rationality NPSD (BRNPSD) and nonlinear min-cost-pursued swapping dynamics (NMSD) are proposed. It is verified that:i) the above four route swapping dynamics (i.e., NPSD, MNPSD, BRNPSD and NMSD) can avoid the weak robustness and over-swapping problem indentified in PAP, which makes the solutions of these swapping dynamics invariant; in addition, their stationary route traffic flow patterns are equivalent to their traffic equilibria; ii) NPSD and NMSD are both rational behavior adjustment process and their continuous-time versions are globally convergent. The numerical results suggest that:i) traverller's reaction sensitivity has significant effect on the network traffic evolution process and result; ii) too much dependence on experience can increase the risk of instability; iii) the traffic evolution stationarity under bounded rationality is not always stronger than that under perfect rationality; iv) the stationarity of DNPSD is superior to that of DNMSD, and the former is more applicable to develop swapping algorithm to solve the traffic equilibrium models.
(2) By introducing a risk-preference route travel time measure named mean-below travel time (MBTT), and making convex combination between it and the risk-preference mean-excess travel time (METT) measure, a full-risk-attitude route travel time measure named combined mean travel time (CMTT) is established and included into the framework of reliability measure (RM). The RM-based NPSD (RMNPSD) is presented and analyzed. Then a backtracking process associated with reaction sensitivity is further embedded into RMNPSD, deriving a novel swapping algorithm named the nonlinear pairwise swapping algorithm (NPSA) to indentify the RM-based traffic equilibrium. It is found that NPSA needs not the feasible trial and error process for the key parameter; also it is derivative-free and needs not consuming time to find the iteration direction and step length. The numerical results indicate that NPSA has good computing efficiency and can serve as a quick method to find a good initial point for local optimization algorithms.
(3) Based on the assumption that travelers are of bounded perception-memory, a day-to-day expost traffic information tailoring strategy and its dynamical programming model are proposed and established. Considering the objective function of the model is nonlinear, non-derivative and has not a close explicit expression, here it is viewed as a stationary programming and a revised compass direct search algorithm is proposed to solve it. Numerical results based on a simple actual traffic network indicate that the expost traffic information tailoring strategy can improve the network evolution efficiency and the revised algorithm performs well.
引文
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