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A sequential transit network design algorithm with optimal learning under correlated beliefs
Abstract
Mobility service route design requires demand information to operate in a service region. Transit planners and operators can access various data sources including household travel survey data and mobile device location logs. However, when implementing a mobility system with emerging technologies, estimating demand becomes harder because of limited data resulting in uncertainty. This study proposes an artificial intelligence-driven algorithm that combines sequential transit network design with optimal learning to address the operation under limited data. An operator gradually expands its route system to avoid risks from inconsistency between designed routes and actual travel demand. At the same time, observed information is archived to update the knowledge that the operator currently uses. Three learning policies are compared within the algorithm: multi-armed bandit, knowledge gradient, and knowledge gradient with correlated beliefs. For validation, a new route system is designed on an artificial network based on public use microdata areas in New York City. Prior knowledge is reproduced from the regional household travel survey data. The results suggest that exploration considering correlations can achieve better performance compared to greedy choices and other independent belief-based techniques in general. In future work, the problem may incorporate more complexities such as demand elasticity to travel time, no limitations to the number of transfers, and costs for expansion.
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This paper proposes a new approach to solve the problem of bus network design and frequency setting (BNDFS). Transit network design must satisfy the needs of both service users and transit operators. Numerous optimisation techniques have been proposed for BNDFS in the literature. Previous approaches tend to adopt a sequential optimisation strategy that conducts network routing and service frequency setting in two separate steps. To address the limitation of sequential optimisation, our new algorithm uses Reinforcement Learning for a simultaneous optimisation of three key components of BNDFS: the number of bus routes, the route design and service frequencies. The algorithm can design the best set of bus routes without defining the total number of bus routes in advance, which can reduce the overall computational time. The proposed algorithm was tested on the benchmark Mandl Swiss network. The algorithm is further extended to the routing of express services. The validation includes additional test scenarios which modify the transit demand level on the Mandl network. The new algorithm can be useful to assist transit agencies and planners in improving existing routing and service frequency to cope with changing demand conditions.
This study extends the two-sided day-today learning framework to simulate the performance of a mobility service using modular autonomous vehicles (MAVs) capable of en-route passenger transfers. An insertion heuristic is used to assign trips to a fleet of vehicles and to determine whether engaging in an en-route transfer is advantageous. The operator acts as an endogenous decision maker, updating the relative weight of the operator cost and user cost within the routing algorithm after each simulation day to optimize profit. Real transit ridership data from the United Arab Emirates are used for an empirical study of three operating strategies: door-to-door service within an urban core, commuter first/last mile service and a hub-and-spoke service. Results are compared with and without en-route transfers to quantify the advantage of the en-route transfer capability for each strategy.
While public transit network design has a wide literature, the study of line planning and route generation under uncertainty is not so well covered. Such uncertainty is present in planning for emerging transit technologies or operating models in which demand data is largely unavailable to make predictions on. In such circumstances, we propose a sequential route generation process in which an operator periodically expands the route set and receives ridership feedback. Using this sensor loop, we propose a reinforcement learning-based route generation methodology to support line planning for emerging technologies. The method makes use of contextual bandit problems to explore different routes to invest in while optimizing the operating cost or demand served. Two experiments are conducted. They (1) prove that the algorithm is better than random choice; and (2) show good performance with a gap of 3.7% relative to a heuristic solution to an oracle policy.
The distribution of passenger demand over the transit network is forecasted using transit assignment models which conventionally assume that passenger loads satisfy network equilibrium conditions. The approach taken in this study is to model transit path choice as a within-day dynamic process influenced by network state variation and real-time information. The iterative network loading process leading to steady-state conditions is performed by means of day-to-day learning implemented in an agent-based simulation model. We explicitly account for adaptation and learning in relation to service uncertainty, on-board crowding and information provision in the context of congested transit networks. This study thus combines the underlying assignment principles that govern transit assignment models and the disaggregate demand modeling enabled by agent-based simulation modeling. The model is applied to a toy network for illustration purposes, followed by a demonstration for the rapid transit network of Stockholm, Sweden. A full-scale application of the proposed model shows the day-to-day travel time and crowding development for different levels of network saturation and when deploying different levels of information availability.
We propose a ridesharing strategy with integrated transit in which a private on-demand mobility service operator may drop off a passenger directly door-to-door, commit to dropping them at a transit station or picking up from a transit station, or to both pickup and drop off at two different stations with different vehicles. We study the effectiveness of online solution algorithms for this proposed strategy. Queueing-theoretic vehicle dispatch and idle vehicle relocation algorithms are customized for the problem. Several experiments are conducted first with a synthetic instance to design and test the effectiveness of this integrated solution method, the influence of different model parameters, and measure the benefit of such cooperation. Results suggest that rideshare vehicle travel time can drop by 40–60% consistently while passenger journey times can be reduced by 50–60% when demand is high. A case study of Long Island commuters to New York City (NYC) suggests having the proposed operating strategy can substantially cut user journey times and operating costs by up to 54% and 60% each for a range of 10–30 taxis initiated per zone. This result shows that there are settings where such service is highly warranted.
Many cities in China have opened a subway, which has become an important part of urban public transport. How the metro line forms the metro network, and then changes the urban traffic pattern, is a problem worthy of attention. From 2005 to 2018, 10 metro lines were opened in Nanjing, which provides important reference data for the study of the spatial and temporal evolution of the Metro network. In this study, using the complex network method, according to the opening sequence of 10 metro lines in Nanjing, space L and space P models are established, respectively. In view of the evolution of metro network parameters, four parameters—network density, network centrality, network clustering coefficient, and network average distance—are proposed for evaluation. In view of the spatial structure change of the metro network, this study combines the concept of node degree in a complex network, analyzes the starting point, terminal point, and intersection point of metro line, and puts forward the concepts of star structure and ring structure. The analysis of the space‒time evolution of Nanjing metro network shows that with the gradual opening of metro lines, the metro network presents a more complex structure; the line connection tends to important nodes, and gradually outlines the city’s commercial space pattern.
We study an autonomous transport service for population where users buy future time slots in which they are guaranteed service. A bilevel fleet sizing-vehicle routing-time slot pricing model, sensitive to users’ activity scheduling decisions in the lower level is developed. Upper level model is solved using Bender’s decomposition and the results are sent to lower level finding an equilibrium using the values of willingness to pay by population under different pricing mechanisms. The values of willingness to pay and the reservation of vehicles among users depends on the fleet size and routing/scheduling results obtained from the upper level model, where spatial temporal distribution of the demand for ride by users impacts the solution to fleet sizing problem. Numerical models are used to explain the methods, to test scalability of the proposed solution algorithms, and to illustrate the potential application of the proposed formulation in simultaneous assessment and modeling of population behavior and optimum fleet sizing model.
Traditionally vehicles act only as servers in transporting passengers and goods. With increasing sensor equipment in vehicles, including automated vehicles, there is a need to test algorithms that consider the dual role of vehicles as both servers and sensors. We formulate a sequential route selection problem as a shortest path problem with on-time arrival reliability under a multi-armed bandit setting, a type of reinforcement learning model. A decision maker has to sequentially make a finite set of decisions on departure time and path between a fixed origin-destination pair such that on-time reliability is maximized while travel time is minimized. The Upper Confidence Bound algorithm is extended to handle this problem. We conduct several tests. First, simulated data successfully verifies the method. We then construct a real-data New York City scenario of a hotel shuttle service from midtown Manhattan providing hourly access to the John F Kenney International Airport. Results suggest that route selection with multi-armed bandit learning algorithms can be effective but neglecting passenger scheduling constraints can negatively impact on-time arrival reliability by as much as 4.8% and combined reliability and travel time by 66.1%.
With the proliferation of electric vehicles, the electrical distribution grids are more prone to overloads. In this paper, we study an intelligent pricing and power control mechanism based on contextual bandits to provide incentives for distributing charging load and preventing network failure. The presented work combines the microscopic mobility simulator SUMO with electric network simulator SIMONA and thus produces reliable electrical distribution load values. Our experiments are carefully conducted under realistic conditions and reveal that conditional bandit learning outperforms context-free reinforcement learning algorithms and our approach is suitable for the given problem. As reinforcement learning algorithms can be adapted rapidly to include new information we assume these to be suitable as part of a holistic traffic control scenario.
In a two-tiered city logistics system, an urban logistics company usually partitions the urban area into regions and allocates its delivery fleet (e.g., vehicles, couriers) to these regions. On a daily basis, the delivery station in each region receives the delivery packages from the city distribution centers and delivers them to customers within the region, using its allocated delivery vehicles. A tactical decision in such a city logistics system is the allocation of its delivery fleet to the regions to minimize the expected operational cost of the entire system. However, because of the complexity of the urban delivery operations and the day-to-day variance of the customer demand, an accurate evaluation of the expected operational cost associated with an allocation decision can be very expensive. We propose a learning policy that adaptively selects the fleet allocation to learn the underlying expected operational cost function by incorporating the value of information. Specifically, we exploit the monotonicity of the expected operational cost in the number of allocated delivery vehicles in a region and extend the idea of knowledge gradient with discrete priors with resampling and regeneration (KGDP-R&R). Our numerical results demonstrate the effectiveness of KGDP-R&R against other learning policies as well as its managerial implications compared with heuristics in practice.
The online appendix is available at https://doi.org/10.1287/trsc.2018.0861 .
Building evolution model of supply chain networks could be helpful to understand its development law. However, specific characteristics and attributes of real supply chains are often neglected in existing evolution models. This work proposes a new evolution model of supply chain with manufactures as the core, based on external market demand and internal competition-cooperation. The evolution model assumes the external market environment is relatively stable, considers several factors, including specific topology of supply chain, external market demand, ecological growth and flow conservation. The simulation results suggest that the networks evolved by our model have similar structures as real supply chains. Meanwhile, the influences of external market demand and internal competition-cooperation to network evolution are analyzed. Additionally, 38 benchmark data sets are applied to validate the rationality of our evolution model, in which, nine manufacturing supply chains match the features of the networks constructed by our model.
This paper is concerned with the problem of finding optimal sub-routes from a set of predefined candidate transit routes with the objectives of maximizing transit ridership as well as minimizing operational costs. The main contributions of this paper are: (1) considering transit ridership maximization in a multi-objective bi-level optimization framework; (2) proposing a greedy algorithm for the multi-objective design problem; (3) applying an efficient path-based algorithm to solve the lower level multi-modal traffic assignment problem. Numerical experiments indicate that the proposed algorithm is not only able to approximate the Pareto-optimal solutions with satisfactory accuracy, but also achieves a fast performance even for problems of real-world scale.
Despite a growing number of studies in stochastic dynamic network optimization, the field remains less well defined and unified than other areas of network optimization. Due to the need for approximation methods like approximate dynamic programming, one of the most significant problems yet to be solved is the lack of adequate benchmarks. The values of the perfect information policy and static policy are not sensitive to information propagation while the myopic policy does not distinguish network effects in the value of flexibility. We propose a scalable reference policy value defined from theoretically consistent real option values based on sampled sequences, and estimate it using extreme value distributions. The reference policy is evaluated on an existing network instance with known sequences (Sioux Falls network from Chow and Regan, 2011a): the Weibull distribution demonstrates good fit and sampling consistency with more than 200 samples. The reference policy is further applied in computational experiments with two other types of adaptive network design: a facility location and timing problem on the Simchi-Levi and Berman (1988) network, and Hyytiä et al.’s (2012) dynamic dial-a-ride problem. The former experiment represents an application of a new problem class and use of the reference policy as an upper bound for evaluating sampled policies, which can reach 3% gap with 350 samples. The latter experiment demonstrates that sensitivity to parameters may be greater than expected, particularly when benchmarked against the proposed reference policy.
This paper analyzes the influence of urban development density on transit network design with stochastic demand by considering two types of services, rapid transit services, such as rail, and flexible services, such as dial-a-ride shuttles. Rapid transit services operate on fixed routes and dedicated lanes, and with fixed schedules, whereas dial-a-ride services can make use of the existing road network, hence are much more economical to implement. It is obvious that the urban development densities to financially sustain these two service types are different. This study integrates these two service networks into one multi-modal network and then determines the optimal combination of these two service types under user equilibrium (UE) flows for a given urban density. Then we investigate the minimum or critical urban density required to financially sustain the rapid transit line(s). The approach of robust optimization is used to address the stochastic demands as captured in a polyhedral uncertainty set, which is then reformulated by its dual problem and incorporated accordingly. The UE principle is represented by a set of variational inequality (VI) constraints. Eventually, the whole problem is linearized and formulated as a mixed-integer linear program. A cutting constraint algorithm is adopted to address the computational difficulty arising from the VI constraints. The paper studies the implications of three different population distribution patterns, two CBD locations, and produces the resultant sequences of adding more rapid transit services as the population density increases.
The paper deals with a procedure for solving the bus network design problem with elastic demand in a large urban area and its application in a real context (city of Rome). The solution procedure consists of a set of heuristics, which includes a first routine for route generation based on the flow concentration process and a genetic algorithm for finding a sub-optimal set of routes with the associated frequencies. The design criteria are addressed to develop an intensive rather than extensive bus network in order to improve efficiency, integration among direct routes and effective transfer points that strongly affect service quality and ridership. The performances of the transportation system are estimated on a multimodal network taking into account the elasticity of the demand. The final goal of the research is to develop a design framework aiming at shifting the modal split towards the public transport.
This paper uses a genetic algorithm to systematically examine the underlying characteristics of the optimal bus transit route network design problem (BTRNDP) with variable transit demand. A multiobjective nonlinear mixed integer model is formulated for the BTRNDP. The proposed solution framework consists of three main components: an initial candidate route set generation procedure (ICRSGP) that generates all feasible routes incorporating practical bus transit industry guidelines; and a network analysis procedure (NAP) that decides transit demand matrix, assigns transit trips, determines service frequencies, and computes performance measures; and a genetic algorithm procedure (GAP) that combines these two parts, guides the candidate solution generation process, and selects an optimal set of routes from the huge solution space. A C++ program code is developed to implement the proposed solution methodology for the BTRNDP with variable transit demand. An example network is successfully tested as a pilot study. Sensitivity analyses are performed. Comprehensive characteristics underlying the BTRNDP, including the effect of route set size, the effect of demand aggregation, and the redesign of the existing transit network issue, are also presented.
The coupled map lattice (CML) model can present rich spatiotemporal dynamic behaviors of complex systems, e.g., it has been observed to have good adaptability in the cascading failure modeling of subway networks (SNs). However, most studies rarely considered an interdependency between an SN and a bus network (BN), which reveals an open problem concerning the CML model's adaptability to a multimodal public transit system (MPTS). This paper develops an improved CML model to simulate interdependent cascading failures of an MPTS and quantify bus route service disruptions for amplifying severe consequences of failures. Remarkably, an interdependency integrating operational and nonlinear geographical interdependencies is proposed to modify the node state evolutionary function and model cascading failures across layers. Moreover, an estimation method for the node initial state is proposed to accommodate the initial value-sensitive dependence due to a logistic chaotic map involved in the evolutionary function. Finally, a case is simulated to verify the model's adaptability and enlighten operation management. Results indicate that (i) the neglect of interdependency causes an overestimation of the severity of cascading failures of an SN while a severe underestimation of those of a BN; (ii) the management and engineering measures to adjust transfers both have a phase transition point on the controllability of cascading failures, and the latter exhibits more a direct and comprehensive effect.
Dynamic routing of electric commercial vehicles can be a challenging problem since besides the uncertainty of energy consumption there are also random customer requests. This paper introduces the Dynamic Stochastic Electric Vehicle Routing Problem (DS-EVRP). A Safe Reinforcement Learning method is proposed for solving the problem. The objective is to minimize expected energy consumption in a safe way, which means also minimizing the risk of battery depletion while en route by planning charging whenever necessary. The key idea is to learn offline about the stochastic customer requests and energy consumption using Monte Carlo simulations, to be able to plan the route predictively and safely online. The method is evaluated using simulations based on energy consumption data from a realistic traffic model for the city of Luxembourg and a high-fidelity vehicle model. The results indicate that it is possible to save energy at the same time maintaining reliability by planning the routes and charging in an anticipative way. The proposed method has the potential to improve transport operations with electric commercial vehicles capitalizing on their environmental benefits.
The metro systems of some megacities are facing serious oversaturation problem due to the heavy passenger flow during high peak hours. We consider the bus transit network design problem based on an existing metro network that can balance the modal split between metro and bus transit systems. The challenges facing this problem lie in that passengers have a different preference between metro and bus services, and the bus travel time and passenger demand may exhibit significant variations. This paper develops a two-step model framework to determine a bus transit network and departure frequency with consideration of travel time and passenger demand uncertainties. Firstly, we develop a column generation method to identify the candidate set of bus transit lines and passenger paths. Then a stochastic linear programming model is developed to optimize the bus line frequency and passenger path flow under demand and bus travel time uncertainty. To solve this model, a primal-dual online algorithm based on the online convex optimization theory is built to obtain the optimal solution with a theoretical performance guarantee. Finally, we implement the developed framework into an illustrative network and a real-world Beijing Second Ring public transit network to demonstrate its applicability and promising effects. The computational results show that the method can provide significant benefits for public transit systems.
The emergence of electromobility along with recent developments in wireless power transfer (WPT) technology offer potentials to improve the carbon footprint of bus transport, while offering quality services. Indeed, the deployment of fast charging stations and dynamic charging roadway segments (lanes) can ensure fast energy transmission to electricity-powered buses, mitigating existing energy-related concerns and limitations. Existing models for public transport network design cannot adequately capture the dependence between electric vehicle charging infrastructure requirements and route operational characteristics. In this context, this paper investigates the combined Transit Route Network Design and Charging Infrastructure Location Problem and proposes a bi-level formulation to handle both planning stages. At the upper level, candidate route sets are generated and evaluated, while at the lower-level wireless charging infrastructures are optimally deployed. A multi-objective Particle Swarm Optimization (MO-PSO) algorithm embedded with an integer programming solver is employed to handle the complexity of the problem and the conflicting design objectives related to passengers and operators. The resulting model is applied to an established benchmark network to assess the tradeoffs arising between user-oriented and operator-oriented solutions and highlight the complex decision process associated with the deployment of electric public transport networks.
Approximate dynamic programming (ADP) is a general methodological framework for multistage stochastic optimization problems in transportation, finance, energy, and other domains. We propose a new approach to the exploration/exploitation dilemma in ADP that leverages two important concepts from the optimal learning literature: first, we show how a Bayesian belief structure can be used to express uncertainty about the value function in ADP; second, we develop a new exploration strategy based on the concept of value of information and prove that it systematically explores the state space. An important advantage of our framework is that it can be integrated into both parametric and nonparametric value function approximations, which are widely used in practical implementations of ADP. We evaluate this strategy on a variety of distinct resource allocation problems and demonstrate that, although more computationally intensive, it is highly competitive against other exploration strategies.
This paper presents the results of the first phase of an ambitious research project aiming at modeling the changes over a 15-year period in the bus network of the city of Mississauga, Ontario, Canada, a fast-growing suburb in the greater Toronto area. Data for the Mississauga transit network, along with a host of demographic and socioeconomic variables, were analyzed. For each main route, a buffer zone representing its vicinity was constructed, and the relevant variables captured inside these zones were computed for inclusion in the proposed empirical models. Other global variables for the city were included as well to account for other effects. Results from multiple regression and simultaneous equation models attempting to relate transit supply to this group of demographic, socioeconomic, and route-specific variables are presented. Time and demand–supply interactions were taken into consideration in the simultaneous equation models. The models show that supply increases with demand and population density and decreases with number of schoolchildren in the vicinity.
The first analytical stochastic and dynamic model for optimizing transit service switching is proposed for “smart transit” applications and for operating shared autonomous transit fleets. The model assumes a region that requires many-to-one last mile transit service either with fixed-route buses or flexible-route, on-demand buses. The demand density evolves continuously over time as an Ornstein-Uhlenbeck process. The optimal policy is determined by solving the switching problem as a market entry and exit real options model. Analysis using the model on a benchmark computational example illustrates the presence of a hysteresis effect, an indifference band that is sensitive to transportation system state and demand parameters, as well as the presence of switching thresholds that exhibit asymmetric sensitivities to transportation system conditions. The proposed policy is computationally compared in a 24-hour simulation to a “perfect information” set of decisions and a myopic policy that has been dominant in the flexible transit literature, with results that suggest the proposed policy can reduce by up to 72% of the excess cost in the myopic policy. Computational experiments of the “modular vehicle” policy demonstrate the existence of an option premium for having flexibility to switch between two vehicle sizes.
This paper explores how the selection of public transit modes can be optimized over a planning horizon. This conceptual analysis sacrifices geographic detail in order to better highlight the relations among important factors. First, a set of static models is proposed to identify which type of service, e.g., bus only, rail only, or bus and rail, is the most cost-effective in terms of the average trip cost for given demand. After analyzing essential factors in a long-term planning process, e.g., economies of scale in rail extension and future cost discounting, a dynamic model incorporating such considerations is formulated to optimize the decision over a planning horizon. While analytical solutions can be obtained for some decision variables, the final model is solved with a graphical method by exploring the tradeoffs between the initial and recurring costs. Major findings from this study include: (a) there exists a minimum economic length for a rail line, which can be determined numerically; (b) economies of scale favor large extensions and excess supplied capacity; (c) the rail-only service is largely dominated by the feeder-trunk service, even in the long run.
We model and solve the Railway Rapid Transit Network Design and Line Planning (RRTNDLP) problem, which integrates the two first stages in the Railway Planning Process. The model incorporates costs relative to the network construction, fleet acquisition, train operation, rolling stock and personnel management. This implies decisions on line frequencies and train capacities since some costs depend on line operation. We assume the existence of an alternative transportation system (e.g. private car, bus, bicycle) competing with the railway system for each origin-destination pair. Passengers choose their transportation mode according to the best travel times. Since the problem is computationally intractable for realistic size instances, we develop an Adaptive Large Neighborhood Search (ALNS) algorithm, which can simultaneously handle the network design and line planning problems considering also rolling stock and personnel planning aspects. The ALNS performance is compared with state-of-the-art commercial solvers on a small-size artificial instance. In a second stream of experiments, the ALNS is used to design a railway rapid transit network in the city of Seville.
Traffic congestion causes important problems such as delays, increased fuel consumption and additional pollution. In this paper we propose a new method to optimize traffic flow, based on reinforcement learning. We show that a traffic flow optimization problem can be formulated as a Markov Decision Process. We use Q-learning to learn policies dictating the maximum driving speed that is allowed on a highway, such that traffic congestion is reduced. An important difference between our work and existing approaches is that we take traffic predictions into account. A series of simulation experiments shows that the resulting policies significantly reduce traffic congestion under high traffic demand, and that inclusion of traffic predictions improves the quality of the resulting policies. Additionally, the policies are sufficiently robust to deal with inaccurate speed and density measurements.
This paper develops a reliability-based formulation for rapid transit network design under demand uncertainty. We use the notion of service reliability to confine the stochastic demand into a bounded uncertainty set that the rapid transit network is designed to cover. To evaluate the outcome of the service reliability chosen, flexible services are introduced to carry the demand overflow that exceeds the capacity of the rapid transit network such designed. A two-phase stochastic program is formulated, in which the transit line alignments and frequencies are determined in phase 1 for a specified level of service reliability; whereas in phase 2, flexible services are determined depending on the demand realization to capture the cost of demand overflow. Then the service reliability is optimized to minimize the combined rapid transit network cost obtained in phase 1, and the flexible services cost and passenger cost obtained in phase 2. The transit line alignments and passenger flows are studied under the principles of system optimal (SO) and user equilibrium (UE). We then develop a two-phase solution algorithm that combines the gradient method and neighborhood search and apply it to a series of networks. The results demonstrate the advantages of utilizing the two-phase formulation to determine the service reliability as compared with the traditional robust formulation that pre-specifies a robustness level.
I analyse the frequentist regret of the famous Gittins index strategy for
multi-armed bandits with Gaussian noise and a finite horizon. Remarkably it
turns out that this approach leads to finite-time regret guarantees comparable
to those available for the popular UCB algorithm. Along the way I derive
finite-time bounds on the Gittins index that are asymptotically exact and may
be of independent interest. I also discuss some computational issues and
present experimental results suggesting that a particular version of the
Gittins index strategy is a modest improvement on existing algorithms with
finite-time regret guarantees such as UCB and Thompson sampling.
Many past researchers have ignored the multi-objective nature of the transit route network design problem (TrNDP), recognizing user or operator cost as their sole objective. The main purpose of this study is to identify the inherent conflict among TrNDP objectives in the design process. The conventional scheme for transit route design is addressed. A route constructive genetic algorithm is proposed to produce a vast pool of candidate routes that reflect the objectives of design, and then, a set covering problem (SCP) is formulated for the selection stage. A heuristic algorithm based on a randomized priority search is implemented for the SCP to produce a set of nondominated solutions that achieve different tradeoffs among the identified objectives. The solution methodology has been tested using Mandl's benchmark network problem. The test results showed that the methodology developed in this research not only outperforms solutions previously identified in the literature in terms of strategic and tactical terms of design, but it is also able to produce Pareto (or near Pareto) optimal solutions. A real-scale network of Rivera was also tested to prove the proposed methodology's reliability for larger-scale transit networks. Although many efficient meta-heuristics have been presented so far for the TrNDP, the presented one may take the lead because it does not require any weight coefficient calibration to address the multi-objective nature of the problem.
This paper addresses transit technology investment issues under urban population volatility
using a real option approach. Two important problems are investigated: which transit
technology should be selected and when should it be introduced. A real option model is
proposed to incorporate explicitly the effects of transit technology investment on urban spatial
structure in terms of households’ residential location choices and housing market. The trigger
population thresholds for investing in a transit technology project and for shifting from a
transit technology to another are explored analytically. Comparative static analyses of the
urban system and transit technology investment are also carried out. It was found that (i)
transit technology investment can induce urban sprawl; (ii) ignoring the effects of transit
technology investment on urban spatial equilibrium can lead to a late investment; and (iii)
there is a significant difference in the trigger population thresholds for transit technology shift
estimated by the net present value approach and the real option approach.
The problem of determining an optimal feeder bus route, feeding a major intermodal transfer station (or a central business district), in a service area is considered. Subject to geographic, capacity, and budget constraints, a total cost function, consisting of user and supplier costs, is developed for determining the optimal bus route location and its headway considering intersection delays, irregular grid street patterns, heterogeneous demand distributions, and realistically geographic variations. The criterion for the optimality is to minimize the total cost objective function. The number of feasible bus routes increases drastically with the increased number of the links (streets), and thus this problem is computationally intractable for realistic urban networks. This paper presents examples and demonstrates that the proposed genetic algorithm efficiently converges to the optimal solution, which is validated by the optimal solution obtained by applying an exhaustive search algorithm.
This research provides a new and efficient approach to solve the transit route design (TRD ) problem. This is considered the most complex and cumbersome problem across network route allocation problems. The wide range of the TRD characteristics creates difficulties to formalize the problem uniquely. At the same time, the TRD complexity type creates combinatorial problems, and its formulation cannot be solved via known mathematical programming approaches and packages. The suggested model deals with both its complexity and its practical issues. This is the first time that three transit operational components are being considered simultaneously: route design; timetabling (frequencies); and vehicle scheduling. The approach used has an impact on three components involved: the operator, the user, and the considered authority. The objectives of these three components do not always coincide. From the operator viewpoint, the system should minimize its expenses while, from the user perspective, the system should maximize its level-of-service. This trade-off situation creates this work’s optimization framework. The formulation of this work contains two objective functions each to be minimized. However, it is impossible to treat both functions simultaneously, and hence, multiobjective programming is being used. This multiobjective programming technique was not used, to our knowledge, for solving the TRD problem. In fact, due to the problem complexity, the ordinary mathematical programming methods cannot be used in this technique, and therefore, a new approach is provided. This new procedure is heuristic in nature and divided into two phases: (a) generation of finite sets of alternative efficient non-inferior solutions, and (b) evaluation and selection of the various solutions using multiobjective preference techniques for discrete variables (“compromise programming” procedure). This approach enables to solve the complex TRD problem. It combines mathematical programming with decision-making methods, using search and enumeration processes while performing the optimization. Thus, it is possible to encounter relatively large-scale problems (networks) with the possibility to interact with the solution method during intermediate steps.
This chapter describes the knowledge gradient policy, which maximizes the rate of learning, and offers both theoretical and practical features in a Bayesian setting which focuses on minimizing expected opportunity cost. The chapter provides a compact modeling framework and highlights some important problem classes. It identifies the major classes of policies, which we then use to identify opportunities for optimal learning. The chapter provides an introduction to the basic problem of tuning the parameters of a policy and introduces several popular heuristic policies. It presents optimal policies for learning, including a characterization of the optimal policy for learning as a dynamic program with a pure belief state. Finally, the chapter ends with a discussion of optimal learning in the presence of a physical state, which is the challenge we face in approximate dynamic programming (ADP). dynamic programming; heuristic programming
We introduce a class of incremental network design problems focused on investigating the optimal choice and timing of network expansions. We concentrate on an incremental network design problem with shortest paths. We investigate structural properties of optimal solutions, show that the simplest variant is NP-hard, analyze the worst-case performance of natural greedy heuristics, derive a 4-approximation algorithm, and conduct a small computational study.
Due to an increasing demand for public transportation and intra-urban mobility, an efficient organization of public transportation has gained significant importance in the last decades. In this paper we present a model formulation for the bus rapid transit route design problem, given a fixed number of routes to be offered. The problem can be tackled using a decomposition strategy, where route design and the determination of frequencies and passenger flows will be dealt with separately. We propose a hybrid metaheuristic based on a combination of Large Neighborhood Search (LNS) and Linear Programming (LP). The algorithm as such is iterative. Decision upon the design of routes will be handled using LNS. The resulting passenger flows and frequencies will be determined by solving a LP. The solution obtained may then be used to guide the exploration of new route designs in the following iterations within LNS. Several problem specific operators are suggested and have been tested. The proposed algorithm compares extremely favorable and is able to obtain high quality solutions within short computational times.
In this paper, a new model for a route planning system based on multi-agent reinforcement learning (MARL) algorithms is proposed. The combined Q-value based dynamic programming (QVDP) with Boltzmann distribution was used to solve vehicle delay's problems by studying the weights of various components in road network environments such as weather, traffic, road safety, and fuel capacity to create a priority route plan for vehicles. The important part of the study was to use a multi-agent system (MAS) with learning abilities which in order to make decisions about routing vehicles between Malaysia's cities. The evaluation was done using a number of case studies that focused on road networks in Malaysia. The results of these experiments indicated that the travel durations for the case studies predicted by existing approaches were between 0.00 and 12.33% off from the actual travel times by the proposed method. From the experiments, the results illustrate that the proposed approach is a unique contribution to the field of computational intelligence in the route planning system.
In recent years, well-designed bus rapid transit (BRT) systems have become a real alternative to more expensive rail-based public transportation systems around the world. However, once the BRT system is operational, its success often depends on the routes offered to passengers. Thus, the bus rapid transit route design problem (BRTRDP) is the problem of finding a set of routes and frequencies that minimizes the operational and passenger costs (travel time) while simultaneously satisfying the system's technical constraints, such as meeting the demands for trips, bus frequencies, and lane capacities. To address this problem, we propose a mathematical formulation of the BRTRDP as a mixed-integer program (MIP) with an underlying network structure. However, because of the vast number of routes, solving the MIP via branch and bound is out of reach for most practical instances. Hence, we propose a decomposition strategy that, given a certain set of routes, decouples the route selection decisions from the BRT system performance evaluation. The latter evaluation is done by solving a linear optimization problem using a column generation scheme. We embedded this decomposition strategy in a hybrid genetic algorithm (HGA) and tested it in 14 instances ranging from 5 to 40 stations with different BRT system topologies. The results show that in 8 of 14 problems, the HGA was able to obtain a solution that is provably optimal within 0.20%. Additionally, in 4 of 14 instances, HGA obtained the optimal solution.
This paper describes a procedure for solving the bus network design problem and its application in a large urban area (the city of Rome), characterized by: (a) a complex road network topology; (b) a multimodal public transport system (rapid rail transit system, buses and tramways lines); (c) a many-to-many transit demand. The solving procedure consists of a set of heuristics, which includes a first routine for the route generation based on the flow concentration process and a parallel genetic algorithm for finding a sub-optimal set of routes with the associated frequencies. The final goal of the research is to develop an operative tool to support the mobility agency of Rome for the bus network design phase.
This paper shows the iterative approach to solving transit network design problem, particularly with variable transit demand under a given fixed total demand. Although recent studies, which use a simplified combinatorial search approach, showed their capability of building optimal transit networks and handling the complicated transit travel time characteristics, only this iterative approach is believed to properly handle the dynamic characteristics of the relationship between variable transit trip demand and optimal transit network design. Since transit demand depends on the configuration of the transit network and frequencies of the routes, this approach is more desirable for transit network planning than combinatorial approach. The basic approach generates the optimal transit network from the initial network, which requires the shortest in-vehicle travel time, through iterating the assignment procedure and the improvement procedure until there is no more improvement in the network. With variable transit demand, the modal split procedure is added to the basic model to generate the optimal transit network and to estimate transit demand simultaneously. This paper also shows the relationship between optimal transit network design and critical design inputs, such as transit operating speed, total demand size, and transfer penalty. As results of the analysis, synergistic effect of variable transit demand and the optimal transit network are discussed.
Transit route network design for urban bus systems involves the selection of a set of routes and the associated frequencies that achieve the desired objective, subject to the operational constraints. This can be formulated as an optimization problem that minimizes the total system cost, which can be expressed as a function of bus operating cost and passenger total travel time. In the first phase of a two-phase solution process, a large set of candidate route is generated using a candidate route generation algorithm. In the second phase, a solution route set is selected from the candidate route set using genetic algorithms, a search and optimization method based. on natural genetics. The simultaneous route and frequency coded model proposed in this investigation considers the frequency of the route as the variable, thus differing from the earlier models in terms of coding scheme adopted. A sample study on a medium-sized network has established that the coding scheme adopted for the route network design enhanced the performance of the model.
In this paper we propose a new model showing how genetic algorithms can be manipulated to help optimize bus transit routing design, incorporating unique service frequency settings for each route. The main lesson is in the power that can be given to heuristic methods if problem content is exploited appropriately. In this example, seven proposed genetic operators are designed for this specific problem to facilitate the search within a reasonable amount of time. In addition, headway coordination is applied by the ranking of transfer demands at the transfer terminals. The model is applied on a benchmark network to test its efficiency, and performance results are presented. It is shown that the proposed model is more efficient than the binary-coded genetic algorithm benchmark, in which problem content cannot be utilized.
In this paper we present a Lisp-implemented route generation algorithm (RGA) for the design of transit networks. Along with an analysis procedure and an improvement algorithm, this algorithm constitutes one of the three major components of an AI-based hybrid solution approach to solving the transit network design problem. Such a hybrid approach incorporates the knowledge and expertise of transit network planners and implements efficient search techniques using AI tools, algorithmic procedures developed by others, and modules for tools implemented in conventional languages. RGA is a design algorithm that 1.(a) is heavily guided by the demand matrix,2.(b) allows the designer's knowledge to be implemented so as to reduce the search space, and3.(c) generates different sets of routes corresponding to different trade-offs among conflicting objectives (user and operator costs). We explain in detail the major components of RGA, illustrate it on data generated for the transit network of the city of Austin, TX, and report on the numerical experiments conducted to test the performance of RGA.
A bilevel model is presented to optimize the fare structure for transit networks with elastic demand under the assumption of fixed transit service frequency. It is known that the transit fare structure has significant effects on passengers' demand and route choice behavior. The transit operator therefore should predict passengers' response to changing fare charges. A bilevel programming method is developed to determine the optimal fare structure for the transit operator while taking passengers' response into account. The upper-level problem seeks to maximize the operator's revenue, whereas the lower-level problem is a stochastic user equilibrium transit assignment model with capacity constraints. A heuristic solution algorithm based on sensitivity analysis is proposed. Finally, a numerical example is given together with some useful discussion.
Urban bus route network design involves determining a route configuration with a set of transit routes and associated frequencies that achieves the desired objective. This can be formulated as an optimization problem of minimizing the overall cost (both the user`s and the operator`s) incurred. In this paper, the use of genetic algorithms (GAs), a search and optimization method based on natural genetics and selection, in solving the route network design problem is reported. The design is done in two phases. First, a set of candidate routes competing for the optimum solution is generated. Second, the optimum set is selected using a GA. The GA is solved by adopting the usual fixed string length coding scheme along with a new variable string length coding proposed in this study. The former assumes a solution route set size, and tries to find that many best routes from the candidate route set, using a GA. The route set size is varied iteratively to find the optimum solution. In the newly proposed variable string length coding method, the solution route set size and the set of solution routes are found simultaneously. The model is applied to a case study network, and results are presented.