This paper proposes a bi-level transit network design problem where the transit routes and frequency settings are determined simultaneously. The upper-level problem is formulated as a mixed integer non-linear program with the objective of minimizing the number of passenger transfers, and the lower-level problem is the transit assignment problem with capacity constraints. A hybrid artificial bee colony (ABC) algorithm is developed to solve the bi-level problem. This algorithm relies on the ABC algorithm to design route structures and a proposed descent direction search method to determine an optimal frequency setting for a given route structure. The descent direction search method is developed by analyzing the optimality condition of the lower-level problem and using the relationship between the lowerand upper-level objective functions. The step size for updating the frequency setting is determined by solving a linear integer program. To efficiently repair route structures, a node insertion and deletion strategy is proposed based on the average passenger demand for the direct services concerned. To increase the computation speed, a lower bound of the objective value for each route design solution is derived and used in the fitness evaluation of the proposed algorithm. Various experiments are set up to demonstrate the performance of our proposed algorithm and the properties of the problem.

This article proposes a cell-based multi-class dynamic traffic assignment problem that considers the random evolution of traffic states. Travelers are assumed to select routes based on perceived effective travel time, where effective travel time is the sum of mean travel time and safety margin. The proposed problem is formulated as a fixed point problem, which includes a Monte-Carlobased stochastic cell transmission model to capture the effect of physical queues and the random evolution of traffic states during flow propagation. The fixed point problem is solved by the self-regulated averaging method. The results illustrate the properties of the problem and the effectiveness of the solution method.The key findings include the following: (1) Reducing perception errors on traffic conditions may not be able to reduce the uncertainty of estimating system performance, (2) Using the self-regulated averaging method can give a much faster rate of convergence in most test cases compared with using the method of successive averages, (3) The combination of the values of the step size parameters highly affects the speed of convergence, (4) A higher demand, a better information quality, or a higher degree of the risk aversion of drivers can lead to a higher computation time, (5) More driver classes do not necessarily result in a longer computation time, and (6) Computation time can be significantly reduced by using small sample sizes in the early stage of solution processes.

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Sustainability has three dimensions, including social, economic, and environmental dimensions. However, existing road network design studies only focus on one or at most two dimensions, which do not allow decision makers to consider social, economic, and environmental impacts on human simultaneously. This paper proposes a multi-objective bilevel optimization model to consider all three dimensions in road network design. To examine the effect of road network design on landowner inequity and intergeneration inequity, land-use transport interaction over time is also captured in the model. The variance of discounted landowner profit and the variance of discounted generalized user cost over time are proposed as sustainability indicators of landowner inequity and intergeneration inequity respectively. Artificial bee colony algorithm (ABC) is proposed to search the network design solutions of the upper level problem, while the method of successive averages (MSA) and the Frank-Wolfe algorithm is adopted to solve the lower-level time-dependent land-use transport problem. Numerical studies are set up to illustrate the tradeoff between the three dimensions of sustainability objectives, the performance of the proposed algorithm, and the existence of landowner inequity and spatial inequity of residents.