A multiple type bike repositioning problem

This paper investigates a new static bicycle repositioning problem in which multiple types of bikes are considered. Some types of bikes that are in short supply at a station can be substituted by other types, whereas some types of bikes can occupy the spaces of other types in the vehicle during repositioning. These activities provide two new strategies, substitution and occupancy, which are examined in this paper. The problem is formulated as a mixed-integer linear programming problem to minimize the total cost, which consists of the route travel cost, penalties due to unmet demand, and penalties associated with the substitution and occupancy strategies. A combined hybrid genetic algorithm is proposed to solve this problem. This solution algorithm consists of (i) a modified version of a hybrid genetic search with adaptive diversity control to determine routing decisions and (ii) a proposed greedy heuristic to determine the loading and unloading instructions at each visited station and the substitution and occupancy strategies. The results show that the proposed method can provide high-quality solutions with short computing times. Using small examples, this paper also reveals problem properties and repositioning strategies in bike sharing systems with multiple types of bikes.     

Chemical reaction optimization for solving a static bike repositioning problem

In this paper, the single-vehicle static repositioning problem is studied. The objective of repositioning is to minimize the weighted sum of unmet customer demand and operational time on the vehicle route. To solve this problem, chemical reaction optimization (CRO) is proposed to handle the vehicle routes, and a subroutine is proposed to determine the loading and unloading quantities at each visited station. An enhanced version of CRO is proposed to improve the solution quality of the original CRO by adding new operators, rules, and intensive neighbor solution search methods. The concept of a neighbor-node set is proposed to narrow the solution search space. To illustrate the efficiency and accuracy of the enhanced CRO, different test scenarios are set and the results obtained from IBM ILOG CPLEX, the original CRO, and the enhanced CRO are compared. The computational results indicate that the enhanced CRO provides high-quality solutions with shorter computing times than those of IBM ILOG CPLEX and provides better solutions than the original CRO. The results also demonstrate that incorporation of the two neighbor-node sets into the enhanced CRO improves the solution quality, and the probability of running the intensive search should increase with iteration in the final part of the main stage of the algorithm to obtain better solutions.     

Dynamic green bike repositioning problem – A hybrid rolling horizon artificial bee colony algorithm approach

This paper introduces a new dynamic green bike repositioning problem (DGBRP) that simultaneously minimizes the total unmet demand of the bike-sharing system and the fuel and CO₂ emission cost of the repositioning vehicle over an operational period. The problem determines the route and the number of bikes loaded and unloaded at each visited node over a multi-period operational horizon during which the cycling demand at each node varies from time to time. To handle the dynamic nature of the problem, this study adopts a rolling horizon approach to break down the proposed problem into a set of stages, in which a static bike repositioning sub-problem is solved in each stage. An enhanced artificial bee colony (EABC) algorithm and a route truncation heuristic are jointly used to optimize the route design in each stage, and the loading and unloading heuristic is used to tackle the loading and unloading sub-problem along the route in a given stage. Numerical results show that the EABC algorithm outperforms Genetic Algorithm in solving the routing sub-problem. Computation experiments are performed to illustrate the effect of the stage duration on the two objective values, and the results show that longer stage duration leads to higher total unmet demand and total fuel and CO₂ emission cost. Numerical studies are also performed to illustrate the effects of the weight and the loading and unloading times on the two objective values and the tradeoff between the two objectives.     

Free-floating bike sharing: Solving real-life large-scale static rebalancing problems

Free-floating bike sharing (FFBS) is an innovative bike sharing model. FFBS saves on start-up cost, in comparison to station-based bike sharing (SBBS), by avoiding construction of expensive docking stations and kiosk machines. FFBS prevents bike theft and offers significant opportunities for smart management by tracking bikes in real-time with built-in GPS. However, like SBBS, the success of FFBS depends on the efficiency of its rebalancing operations to serve the maximal demand as possible.Bicycle rebalancing refers to the reestablishment of the number of bikes at sites to desired quantities by using a fleet of vehicles transporting the bicycles. Static rebalancing for SBBS is a challenging combinatorial optimization problem. FFBS takes it a step further, with an increase in the scale of the problem. This article is the first effort in a series of studies of FFBS planning and management, tackling static rebalancing with single and multiple vehicles. We present a Novel Mixed Integer Linear Program for solving the Static Complete Rebalancing Problem. The proposed formulation, can not only handle single as well as multiple vehicles, but also allows for multiple visits to a node by the same vehicle. We present a hybrid nested large neighborhood search with variable neighborhood descent algorithm, which is both effective and efficient in solving static complete rebalancing problems for large-scale bike sharing programs.Computational experiments were carried out on the 1 Commodity Pickup and Delivery Traveling Salesman Problem (1-PDTSP) instances used previously in the literature and on three new sets of instances, two (one real-life and one general) based on Share-A-Bull Bikes (SABB) FFBS program recently launched at the Tampa campus of University of South Florida and the other based on Divvy SBBS in Chicago. Computational experiments on the 1-PDTSP instances demonstrate that the proposed algorithm outperforms a tabu search algorithm and is highly competitive with exact algorithms previously reported in the literature for solving static rebalancing problems in SBSS. Computational experiments on the SABB and Divvy instances, demonstrate that the proposed algorithm is able to deal with the increase in scale of the static rebalancing problem pertaining to both FFBS and SBBS, while deriving high-quality solutions in a reasonable amount of CPU time.     

A model for the layout of bike stations in public bike‐sharing systems

The problem of designing a layout of bike stations for public bike‐sharing systems entails selecting a number of stations and then constructing them within a planning area having many bike traffic zones and candidate bike stations. In this paper, we proposed a mathematical model to formulate the layout of public bike stations with the objective of minimizing users' total travel time and investment budget constraints. The model can guarantee that the needs for picking up and dropping off bikes amidst all bike travel demands are satisfied. Using this model, the number and locations of bike stations and the number of bikes and parking lockers at each bike station can be simultaneously determined. A typical example solved by lingo solver is created to illustrate the proposed model. Copyright © 2015 John Wiley & Sons, Ltd.     

The multiple vehicle routing problem with simultaneous delivery and pick-up points

Traditionally, the vehicle routing problem is thought of as a pure delivery or pickup problem. In many practical situations, however, the vehicle is often required to simultaneously drop off and pick up goods at the same stop. This paper first recognizes the possibility of simultaneous deliveries and pickups at the same node. Hence, the main objective of this paper is to develop a model and a solution procedure efficient enough to handle such real-world variants. To illustrate and demonstrate the real-world applicability of the suggested model and solution procedure, we have described and conducted a case study dealing with a public library distribution system in Franklin County, Ohio. The final result of the case study indicates that substantial time/distance savings can be achieved by using the proposed model and solution procedure.     

Efficient multiple model particle filtering for joint traffic state estimation and incident detection

This article proposes an efficient multiple model particle filter (EMMPF) to solve the problems of traffic state estimation and incident detection, which requires significantly less computation time compared to existing multiple model nonlinear filters. To incorporate the on ramps and off ramps on the highway, junction solvers for a traffic flow model with incident dynamics are developed. The effectiveness of the proposed EMMPF is assessed using a benchmark hybrid state estimation problem, and using synthetic traffic data generated by a micro-simulation software. Then, the traffic estimation framework is implemented using field data collected on Interstate 880 in California. The results show the EMMPF is capable of estimating the traffic state and detecting incidents and requires an order of magnitude less computation time compared to existing algorithms, especially when the hybrid system has a large number of rare models.     

Multiple objective optimization of the fleet sizing problem for road freight transportation

A fleet sizing problem (FSP) in a road freight transportation company with heterogeneous fleet and its own technical back‐up facilities is considered in the paper. The mathematical model of the decision problem is formulated in terms of multiple objective mathematical programming based on queuing theory. Technical and economical criteria as well as interests of different stakeholders are taken into account in the problem formulation. The solution procedure is composed of two steps. In the first one a sample of Pareto‐optimal solutions is generated by an original program called MEGROS. In the second step this set is reviewed and evaluated, according to the Decision Maker's (DM's) model of preferences. The evaluation of solutions is carried out with an application of an interactive multiple criteria analysis method, called Light Beam Search (LBS). Finally, the DM selects the most desirable, compromise solution.     

Applying spatial-temporal analysis and retail location theory to public bikes site selection in Taipei

In order to turn Taipei into a sustainable, green metropolis, in 2009, the Department of Transportation of Taipei City Government launched a public bike rental system (YouBike) to meet people’s daily commute and/or leisure needs. Given that users may return bikes to sites differing from their starting locations, rental stations frequently lack bikes or bike racks. This study sought to identify lacking-bike and/or lacking-bike rack hot spots utilizing spatial-temporal analysis. In addition, it applied retail location theory to determine site selection of further rental stations. Historical data indicated that shortage of bikes was much more severe than shortage of bike racks in the YouBike public bike system and lacking-bike and lacking-bike rack hot spots were clustered significantly. The study demonstrated that spatial-temporal analysis can be used to effectively identify rental stations’ spatial patterns, determine the most suitable locations for further installation of rental stations, help to provide public bike users with a more effective rental system, and greatly assist public bikes’ operational management and decision-making in Taiwan.     

Time-dependent Hyperstar algorithm for robust vehicle navigation

The vehicle navigation problem studied in Bell (2009) is revisited and a time-dependent reverse Hyperstar algorithm is presented. This minimises the expected time of arrival at the destination, and all intermediate nodes, where expectation is based on a pessimistic (or risk-averse) view of unknown link delays. This may also be regarded as a hyperpath version of the Chabini and Lan (2002) algorithm, which itself is a time-dependent A^* algorithm. Links are assigned undelayed travel times and maximum delays, both of which are potentially functions of the time of arrival at the respective link. Probabilities for link use are sought that minimise the driver’s maximum exposure to delay on the approach to each node, leading to the determination of a pessimistic expected time of arrival at the destination and all intermediate nodes. Since the context considered is vehicle navigation, the probability of link use measures link attractiveness, so a link with a zero probability of use is unattractive while a link with a probability of use equal to one will have no attractive alternatives. A solution algorithm is presented and proven to solve the problem provided the node potentials are feasible and a FIFO condition applies to undelayed link travel times. The paper concludes with a numerical example.     

Application of multiple criteria decision making for network improvement

In this paper we propose application of multiple criteria decision making to problems of a metropolitan network improvement plan. Initially, a bilevel multiple objective network design model is considered in two objectives which are minimal government budget and minimal total travel time of road users. We seek feasible improvement alternatives among those bottleneck links in an existing road network structure and travel demand. We present an effective heuristic algorithm to obtain noninferior solutions; then ELECTRE III multiple criteria decision making and group decision making are used to evaluate and to select a compromise solution among those noninferior solutions. From the design phase in multiple criteria decision making, multiple objective mathematical programming is used to formulate a continuous network design model. However, from the phase of evaluation, multiple criteria decision making to solve the discrete network design problem. The network of metropolitan Taipei is taken as an example to illustrate the operation of this model.     

Solving the Median Shortest Path Problem in the Planning and Design of Urban Transportation Networks Using a Vector Labeling Algorithm

This paper proposes an alternative algorithm to solve the median shortest path problem (MSPP) in the planning and design of urban transportation networks. The proposed vector labeling algorithm is based on the labeling of each node in terms of a multiple and conflicting vector of objectives which deletes cyclic, infeasible and extreme-dominated paths in the criteria space imposing cyclic break (CB), path cost constraint (PCC) and access cost parameter (ACP) respectively. The output of the algorithm is a set of Pareto optimal paths (POP) with an objective vector from predetermined origin to destination nodes. Thus, this paper formulates an algorithm to identify a non-inferior solution set of POP based on a non-dominated set of objective vectors that leaves the ultimate decision to decision-makers. A numerical experiment is conducted using an artificial transportation network in order to validate and compare results. Sensitivity analysis has shown that the proposed algorithm is more efficient and advantageous over existing solutions in terms of computing execution time and memory space used.     

A new estimation approach for the multiple discrete–continuous probit (MDCP) choice model

This paper develops a blueprint (complete with matrix notation) to apply Bhat’s (2011) Maximum Approximate Composite Marginal Likelihood (MACML) inference approach for the estimation of cross-sectional as well as panel multiple discrete–continuous probit (MDCP) models. A simulation exercise is undertaken to evaluate the ability of the proposed approach to recover parameters from a cross-sectional MDCP model. The results show that the MACML approach does very well in recovering parameters, as well as appears to accurately capture the curvature of the Hessian of the log-likelihood function. The paper also demonstrates the application of the proposed approach through a study of individuals’ recreational (i.e., long distance leisure) choice among alternative destination locations and the number of trips to each recreational destination location, using data drawn from the 2004 to 2005 Michigan statewide household travel survey.     

Trading mechanisms for bottleneck permits with multiple purchase opportunities

This paper extends the theory of tradable bottleneck permits system to cases with multiple period markets and designs its implementation mechanism. The multiple period markets can achieve more efficient resource allocation than a single period market when users’ valuations of tradable permits change over time. To implement the multiple period trading markets, we propose an evolutionary mechanism that combines a dynamic auction with a capacity control rule that adjusts a number of permits issued for each market. Then, we prove that the proposed mechanism has the following desirable properties: (i) the dynamic auction is strategy-proof within each period and guarantees that the market choice of each user is optimal under a perfect information assumption of users and (ii) the mechanism maximizes the social surplus in a finite number of iterations. Finally, we show that the proposed mechanism may work well even for an incomplete information case.     

Synopsis of bicycle demand in the City of Toronto: Investigating the effects of perception,consciousness and comfortability on the purpose of biking and bike ownership

This paper provides an empirical basis for the evaluation of policies and programs that can increase the usage of bikes for different purposes as well as bike ownership. It uses an integrated econometric model of latent variable connecting multiple discrete choices. Empirical models are estimated by using a bicycle demand survey conducted in the City of Toronto in 2009. Empirical investigations reveal that latent perceptions of ‘bikeability’ and ‘safety consciousness’ directly influence the choice of biking. It is also found that the choice of the level of bike ownership (number of bikes) is directly influenced by latent ‘comfortability of biking’. The number of bikes owned moreover has a strong influence on the choices of biking for different purposes. It is clear that bike users in the City of Toronto are highly safety conscious. Increasing on-street and separate bike lanes proved to have the maximum effects on attracting more people to biking by increasing the perception of bikeability in the city, comfortability of biking in the city and increasing bike users’ sense of safety. In terms of individuals’ characteristics, older males are found to be the most conformable and younger females are the least comfortable group of cyclists in Toronto.     

Dynamic system-optimal traffic assignment using a state space model

We propose a new mathematical formulation for the problem of optimal traffic assignment in dynamic networks with multiple origins and destinations. This problem is motivated by route guidance issues that arise in an Intelligent Vehicle-Highway Systems (IVHS) environment. We assume that the network is subject to known time-varying demands for travel between its origins and destinations during a given time horizon. The objective is to assign the vehicles to links over time so as to minimize the total travel time experienced by all the vehicles using the network. We model the traffic network over the time horizon as a discrete-time dynamical system. The system state at each time instant is defined in a way that, without loss of optimality, avoids complete microscopic detail by grouping vehicles into platoons irrespective of origin node and time of entry to network. Moreover, the formulation contains no explicit path enumeration. The state transition function can model link travel times by either impedance functions, link outflow functions, or by a combination of both. Two versions (with different boundary conditions) of the problem of optimal traffic assignment are studied in the context of this model. These optimization problems are optimal control problems for nonlinear discrete-time dynamical systems, and thus they are amenable to algorithmic solutions based on dynamic programming. The computational challenges associated with the exact solution of these problems are discussed and some heuristics are proposed.     

Multi-objective re-synchronizing of bus timetable: Model,complexity and solution

This work is originally motived by the re-planning of a bus network timetable. The existing timetable with even headways for the network is generated using line by line timetabling approach without considering the interactions between lines. Decision-makers (i.e., schedulers) intend to synchronize vehicle timetable of lines at transfer nodes to facilitate passenger transfers while being concerned with the impacts of re-designed timetable on the regularity of existing timetable and the accustomed trip plans of passengers. Regarding this situation, we investigate a multi-objective re-synchronizing of bus timetable (MSBT) problem, which is characterized by headway-sensitive passenger demand, uneven headways, service regularity, flexible synchronization and involvement of existing bus timetable. A multi-objective optimization model for the MSBT is proposed to make a trade-off between the total number of passengers benefited by smooth transfers and the maximal deviation from the departure times of the existing timetable. By clarifying the mathematical properties and solution space of the model, we prove that the MSBT problem is NP-hard, and its Pareto-optimal front is non-convex. Therefore, we design a non-dominated sorting genetic (NSGA-II) based algorithm to solve this problem. Numerical experiments show that the designed algorithm, compared with enumeration method, can generate high-quality Pareto solutions within reasonable times. We also find that the timetable allowing larger flexibility of headways can obtain more and better Pareto-optimal solutions, which can provide decision-makers more choice.     

System optimal dynamic traffic assignment: Properties and solution procedures in the case of a many-to-one network

Thanks to its high dimensionality and a usually non-convex constraint set, system optimal dynamic traffic assignment remains one of the most challenging problems in transportation research. This paper identifies two fundamental properties of the problem and uses them to design an efficient solution procedure. We first show that the non-convexity of the problem can be circumvented by first solving a relaxed problem and then applying a traffic holding elimination procedure to obtain the solution(s) of the original problem. To efficiently solve the relaxed problem, we explore the relationship between the relaxed problems based on different traffic flow models (PQ, SQ, CTM) and a minimal cost flow (MCF) problem for a special space-expansion network. It is shown that all the four problem formulations produce the same minimal system cost and share one common solution which does not involve inside queues in the network. Efficient solution algorithms such as the network simplex method can be applied to solve the MCF problem and identify such an optimal traffic pattern. Numerical examples are also presented to demonstrate the efficiency of the proposed solution procedure.     

Ant Colony Routing algorithm for freeway networks

Dynamic traffic routing refers to the process of (re)directing vehicles at junctions in a traffic network according to the evolving traffic conditions. The traffic management center can determine desired routes for drivers in order to optimize the performance of the traffic network by dynamic traffic routing. However, a traffic network may have thousands of links and nodes, resulting in a large-scale and computationally complex non-linear, non-convex optimization problem. To solve this problem, Ant Colony Optimization (ACO) is chosen as the optimization method in this paper because of its powerful optimization heuristic for combinatorial optimization problems. ACO is implemented online to determine the control signal – i.e., the splitting rates at each node. However, using standard ACO for traffic routing is characterized by four main disadvantages: 1. traffic flows for different origins and destinations cannot be distinguished; 2. all ants may converge to one route, causing congestion; 3. constraints cannot be taken into account; and 4. neither can dynamic link costs. These problems are addressed by adopting a novel ACO algorithm with stench pheromone and with colored ants, called Ant Colony Routing (ACR). Using the stench pheromone, the ACR algorithm can distribute the vehicles over the traffic network with less or no traffic congestion, as well as reduce the number of vehicles near some sensitive zones, such as hospitals and schools. With colored ants, the traffic flows for multiple origins and destinations can be represented. The proposed approach is also implemented in a simulation-based case study in the Walcheren area, the Netherlands, illustrating the effectiveness of the approach.     

Generalized extreme value (GEV)-based error structures for multiple discrete-continuous choice models

This paper formally derives the class of multiple discrete-continuous generalized extreme value (MDCGEV) models, a general class of multiple discrete-continuous choice models based on generalized extreme value (GEV) error specifications. Specifically, the paper proves the existence of, and derives the general form of, closed-form consumption probability expressions for multiple discrete-continuous choice models with GEV-based error structures. In addition to deriving the general form, the paper derives a compact and readily usable form of consumption probability expressions that can be used to estimate multiple discrete-continuous choice models with general cross-nested error structures.The cross-nested version of the MDCGEV model is applied to analyze household annual expenditure patterns in various transportation-related expenses using data from a Consumer Expenditure Survey in the United States. Model estimation results and predictive log-likelihood based validation tests indicate the superiority of the cross-nested model over the mutually exclusively nested and non-nested model specifications. Further, the cross-nested model was amenable to the accommodation of socio-demographic heterogeneity in inter-alternative covariance across decision-makers through a parameterization of the allocation parameters.