Simultaneous Decision Making of Optimal Toll Levels and Locations in a Multi-Class Network Equilibrium: Genetic Algorithm Approach

The purpose of this thesis is to explore bi-level genetic algorithm (GA) based optimization models to make decisions simultaneously for the second-best optimal toll locations and toll levels. The upper-level subprogram is to minimize the total travel time (system cost). The lower-level subprogram is a user equilibrium problem where all users try to find the route that minimizes their own travel cost (or time). The demand is assumed to be fixed and given a priority. First, two different versions of GA based solution procedures are developed and applied to an example Sioux Falls network assuming homogeneous road users in the network. This kind of problem is referred to as a single-class optimization problem. However, in reality heterogeneous road users exist. As such, the two GA options are compared with one another and the preferred GA option is further applied to the network consisting of multi-class users with different value of times (VOTs). Another heuristic approach is also considered to determine toll rates only on the most congested links for both single-class and multi-class scenarios. Such heuristic toll rates are compared with the combined solution of optimal location and toll rates to demonstrate the most congested links in a network may not be considered as intuitive candidates for optimal toll locations

A methodology for solving the network toll design problem

Congestion pricing has been regarded as an efficient method to reduce network-wide travel cost. In this dissertation, a methodology for toll design is developed to provide policy-makers with suggestions on both where to charge tolls and how much the tolls should be. As opposed to the traditional approach of marginal social cost pricing, this methodology is capable of dealing with the more realistic case, in which only a small number of links can be tolled. Furthermore, this methodology is expanded to accommodate multiple user groups. The toll design problem can be formulated using both deterministic and stochastic route choice models. The most natural formulation of this problem in both cases is a bilevel formulation. Such formulations are very difficult to solve because of the nonconvexity and nondifferentiability of the constraint set. In this dissertation, the problem is converted into a single level, standard nonlinear optimization problem by making certain simplifying assumption. This single-level version of the toll design problem can be solved using a variety of well-developed algorithms. Tests show that this approach can be used to generate reasonable results and provide valuable decision support to policy-makers

Optimization of vehicle routing and scheduling with travel time variability - application in winter road maintenance

This study developed a mathematical model for optimizing vehicle routing and scheduling, which can be used to collect travel time information, and also to perform winter road maintenance operations (e.g., salting, plowing). The objective of this research was to minimize the total vehicle travel time to complete a given set of service tasks, subject to resource constraints (e.g., truck capacity, fleet size) and operational constraints (e.g., service time windows, service time limit). The nature of the problem is to design vehicle routes and schedules to perform the required service on predetermined road segments, which can be interpreted as an arc routing problem (ARP). By using a network transformation technique, an ARP can be transformed into a well-studied node routing problem (NRP). A set-partitioning (SP) approach was introduced to formulate the problem into an integer programming problem (I PP). To solve this problem, firstly, a number of feasible routes were generated, subject to resources and operational constraints. A genetic algorithm based heuristic was developed to improve the efficiency of generating feasible routes. Secondly, the corresponding travel time of each route was computed. Finally, the feasible routes were entered into the linear programming solver (CPL EX) to obtain final optimized results. The impact of travel time variability on vehicle routing and scheduling for transportation planning was also considered in this study. Usually in the concern of vehicle and pedestrian\u27s safety, federal, state governments and local agencies are more leaning towards using a conservative approach with constant travel time for the planning of winter roadway maintenance than an aggressive approach, which means that they would rather have a redundancy of plow trucks than a shortage. The proposed model and solution algorithm were validated with an empirical case study of 41 snow sections in the northwest area of New Jersey. Comprehensive analysis based on a deterministic travel time setting and a time-dependent travel time setting were both performed. The results show that a model that includes time dependent travel time produces better results than travel time being underestimated and being overestimated in transportation planning. In addition, a scenario-based analysis suggests that the current NJDOT operation based on given snow sector design, service routes and fleet size can be improved by the proposed model that considers time dependent travel time and the geometry of the road network to optimize vehicle routing and scheduling. In general, the benefit of better routing and scheduling design for snow plowing could be reflected in smaller minimum required fleet size and shorter total vehicle travel time. The depot location and number of service routes also have an impact on the final optimized results. This suggests that managers should consider the depot location, vehicle fleet sizing and the routing design problem simultaneously at the planning stage to minimize the total cost for snow plowing operations

Network modeling and design : a distributed problem solving approach

This dissertation is concerned with developing new solution algorithms for network modeling and design problems using a distributed problem solving approach. Network modeling and design are fundamental problems in the field of transportation science, and numerous transportation applications such as urban travel demand forecasting, congestion pricing, defining optimal toll values, and scheduling traffic lights all involve some form of network modeling or network design. The first part of this dissertation focuses on developing a distributed scheme for the static traffic assignment problem, based on a spatial decomposition. The objective of the traffic assignment problem is to estimate traffic flows on a network and the resulting congestion considering the mutual interactions between travelers. A traffic assignment model takes as input the network topology, link performance functions, and a demand matrix indicating the traffic volume between each pair of origin-destination nodes. There are efficient algorithms to solve the traffic assignment problem, but, as computational hardware and algorithms advance, attention shifts to more demanding applications of the traffic assignment problem (bilevel programs whose solution often requires the solution of many traffic assignment problem instances as subproblems, accounting for forecasting errors with Monte Carlo simulation of input parameters, and broadening the geographic scope of models to the statewide or national levels.) In Chapter 2, we propose a network contraction technique based on the theory of equilibrium sensitivity analysis. In the proposed algorithm, we replace the routes between each origin-destination (OD) pair with a single artificial link. These artificial links model the travel time between the origin and destination nodes of each OD pair as a function of network demands. The network contraction method can be advantageous in network design applications where many equilibrium problems must be solved for different design scenarios. The network contraction procedure can also be used to increase the accuracy of subnetwork analysis. The accuracy and complexity of the proposed methodology are evaluated using the network of Barcelona, Spain. Further, numerical experiments on the Austin, Texas regional network validate its performance for subnetwork analysis applications. Using this network contraction technique, we then develop a decentralized (distributed) algorithm for static traffic assignment in Chapter 3. In this scheme, which we term a decentralized approach to the static traffic assignment problem (DSTAP), the complete network is divided into smaller networks, and the algorithm alternates between equilibrating these networks as subproblems, and master iterations using a simplified version of the full network. The simplified network used for the master iterations is based on linearizations to the equilibrium solution for each subnetwork obtained using sensitivity analysis techniques. We prove that the DSTAP method converges to the equilibrium solution on the complete network, and demonstrate computational savings of 35-70% on the Austin network. Natural applications of this method are statewide or national assignment problems, or cities with rivers or other geographic features where subnetworks can be easily defined. The second part of this dissertation, found in Chapter 4, deals with network design problems. In a network design problem, the goal is to optimize an objective function (minimize the travel time, pollution, maximize safety, social welfare, etc.) by making investment decisions subject to budget and feasibility constraints. Network design is a bi-level problem where the leader chooses the design parameters, and travelers, as followers, react to the leader’s decision by changing their route. These problems are hard to solve, and distributed problem solving approach can be used to develop an efficient framework for scaling these problems. In the proposed distributed algorithm for network design problems, different planning agencies may have different objective functions and priorities, while a regional agent (state or federal officials) allocates the finding between the urban cities. In this model, the urban planning agencies do their own planning and design independently while capturing the system-level effects of their local decisions and plans. The regional agent has limited and indirect authorities over the subnetworks through budget allocation. In addition to computational advantages for traditional bi-level network design problems, the proposed algorithm can be used to model the linkage between different entities for multi-resolution applications. We develop a solution algorithm based on a sensitivity-analysis heuristic, and test our algorithm on two case studies: a hypothetical network composed of two copies of Sioux Falls network, and the Austin regional network. We evaluate the correctness of the decentralized algorithm, and discuss the benefits of the algorithm in modeling the global impacts of local decisions. Furthermore, the implementation of distributed algorithm on Austin regional network demonstrates a computational saving of 22%.Civil, Architectural, and Environmental Engineerin

Programación binivel y equilibrios conjeturados: resultados teóricos y algoritmos numéricos.

This thesis presents the fruit of 3 years of research. During this time 3 works were developed, each one with its own mathematical formulations and results. These works are, of course, related to each other and will be further developed in the near future. The first work of this thesis is presented in chapter 1 and addresses the problem of defining an optimality criterion for a semi-public company in a semi-mixed duopoly model. Here, we have two agents competing, the semi-public company and a private firm, both producing a homogeneous good to satisfy the demand in the market. The private firm, as usual, seeks to maximize its net profit, while the semi-public company has a commitment to watch over the economy of the population, but at the same time, does not neglect its own profit. The compromise between these two objectives for the semipublic company is described by a parameter β ∈ (0, 1], where β → 0 represents that the semi-public company thinks only for its own net profit, and β = 1 represents that the semi-public company cares solely for the economy of the population without seeking its own benefit

Dynamic pricing and long-term planning models for managed lanes with multiple entrances and exits

Express lanes or priced managed lanes provide a reliable alternative to travelers by charging dynamic tolls in exchange for traveling on lanes with no congestion. These lanes have various locations of entrances and exits and allow travelers to adapt their route based on the toll and travel time information received at a toll gantry. In this dissertation, we incorporate this adaptive lane choice behavior in improving the dynamic pricing and long-term planning models for managed lanes with multiple entrances and exits. Lane choice of travelers minimizing their disutility is affected by the real-time information about tolls and travel time through variable message signs and perceived information from past experiences. In this dissertation, we compare various adaptive lane choice models differing in their reliance on real-time information or historic information or both. We propose a decision route lane choice model that efficiently compares the disutility over multiple routes on an express lane. Assuming drivers’ disutility is only affected by tolls and travel times, we show that the decision route model generates only up to 0.93% error in expected costs compared to the optimal adaptive lane choice model, making it a suitable choice for modeling lane choice of travelers. Next, using the decision route lane choice framework, we improve the current dynamic pricing models for express lanes that commonly ignore adaptive lane choice, assume simplified traffic dynamics, and/or are based on simplified heuristics. Formulating the dynamic pricing problem as an MDP, we optimize the tolls for various objectives including maximizing revenue and minimizing total system travel time (TSTT). Three solution algorithms are evaluated: (a) an algorithm based on value-function approximation, (b) a multiagent reinforcement learning algorithm with decentralized tolling at each gantry, and (c) a deep reinforcement learning assuming partial observability of traffic state. These algorithms are shown to outperform other heuristics such as feedback control heuristics by generating up to 10% higher revenues and up to 9% lower delays. Our findings also reveal that the revenue-maximizing optimal policies follow a “jam-and-harvest” behavior where the toll-free lanes are pushed towards congestion in the earlier time steps to generate higher revenue later, a characteristic not observed for the policies minimizing TSTT. We use reward shaping methods to overcome the undesired behavior of toll policies and confirm transferability of the algorithms to new input domains. We also offer recommendations on real-time implementations of pricing algorithms based on solving MDPs. Last, we incorporate adaptive lane choice in existing long-term planning models for express lanes which commonly represent these lanes as fixed-toll facilities and ignore en route adaptation of lane choices. Defining the improved model as an equilibrium over adaptive lane choices of self-optimizing travelers and formulating it as a convex program, we show that long-term traffic forecasts can be underestimated by up to 45% if adaptive route choice is ignored. For solving the equilibrium, we develop a gradient-projection algorithm which is shown to be efficient than existing link-state algorithms in the literature. Additionally, we estimate the sensitivity of equilibrium expected costs with demand variation by formulating it as a convex program solved using a variant of the gradient projection algorithm proposed earlier. This analysis simplifies a complex express lane network as a single directed link, allowing integration of adaptive lane choice for planning of express lanes without significantly altering the components of traditional planning models. Overall these models improve the state-of-the-art of pricing and planning for managed lanes useful for evaluating future express lane projects and for operations of express lanes with multiple objectives.Civil, Architectural, and Environmental Engineerin

Network Maintenance and Capacity Management with Applications in Transportation

abstract: This research develops heuristics to manage both mandatory and optional network capacity reductions to better serve the network flows. The main application discussed relates to transportation networks, and flow cost relates to travel cost of users of the network. Temporary mandatory capacity reductions are required by maintenance activities. The objective of managing maintenance activities and the attendant temporary network capacity reductions is to schedule the required segment closures so that all maintenance work can be completed on time, and the total flow cost over the maintenance period is minimized for different types of flows. The goal of optional network capacity reduction is to selectively reduce the capacity of some links to improve the overall efficiency of user-optimized flows, where each traveler takes the route that minimizes the traveler’s trip cost. In this dissertation, both managing mandatory and optional network capacity reductions are addressed with the consideration of network-wide flow diversions due to changed link capacities. This research first investigates the maintenance scheduling in transportation networks with service vehicles (e.g., truck fleets and passenger transport fleets), where these vehicles are assumed to take the system-optimized routes that minimize the total travel cost of the fleet. This problem is solved with the randomized fixed-and-optimize heuristic developed. This research also investigates the maintenance scheduling in networks with multi-modal traffic that consists of (1) regular human-driven cars with user-optimized routing and (2) self-driving vehicles with system-optimized routing. An iterative mixed flow assignment algorithm is developed to obtain the multi-modal traffic assignment resulting from a maintenance schedule. The genetic algorithm with multi-point crossover is applied to obtain a good schedule. Based on the Braess’ paradox that removing some links may alleviate the congestion of user-optimized flows, this research generalizes the Braess’ paradox to reduce the capacity of selected links to improve the efficiency of the resultant user-optimized flows. A heuristic is developed to identify links to reduce capacity, and the corresponding capacity reduction amounts, to get more efficient total flows. Experiments on real networks demonstrate the generalized Braess’ paradox exists in reality, and the heuristic developed solves real-world test cases even when commercial solvers fail.Dissertation/ThesisDoctoral Dissertation Industrial Engineering 201