A Survey of Network Design Problems

Network design problems arise in many different application areas such as air freight, highway traffic, and communication systems. The intention of this survey is to present a coherent unified view of a number of papers in the network design literature. We discuss suggested solution procedures, computational experience, relations between various network models, and potential application areas. Promising topics of research for improving, solving, and extending the models reviewed in this survey are also indicated.Supported in part by the U.S. Department of Transportation under contract DOT-TSC-1058, Transportation Advanced Research Program (TARP)

Achieving target equilibria in network routing games without knowing the latency functions

The analysis of network routing games typically assumes precise, detailed information about the latency functions. Such information may, however, be unavailable or difficult to obtain. Moreover, one is often primarily interested in enforcing a desired target flow as an equilibrium. We ask whether one can achieve target flows as equilibria without knowing the underlying latency functions. We give a crisp positive answer to this question. We show that one can efficiently compute edge tolls that induce a given target multicommodity flow in a nonatomic routing game using a polynomial number of queries to an oracle that takes tolls as input and outputs the resulting equilibrium flow. This result is obtained via a novel application of the ellipsoid method, and extends to various other settings. We obtain improved query-complexity bounds for series-parallel networks, and single-commodity routing games with linear latency functions. Our techniques provide new insights into network routing games

An Examination of Railroad Capacity and its Implications for Rail-Highway Intermodal Transportation

After many years of decline in market share, railroads are now experiencing an increasing demand for their services. Service intensive intermodal transportation seems to be an especially promising market area. Since the historic decline in traffic has been accompanied by a reduction in network infrastructure, however, the railroads\u27 ability to handle sizable traffic increases, at least in the short term, is in question. Since rail transportation is critical to the domestic economy of the nation, and is increasingly important in international logistics channels, shortfalls in railroad capacity are not desirable. The published literature on railroad capacity is relatively sparse, especially in comparison to the highway mode. Much of what is available pertains to individual network components such as lines or terminals. Evaluation of system capacity, considering the interactive effects of traffic flowing through a network of lines and terminals, has received less attention. A tool specifically designed for evaluating freight railroad system capacity issues could be a useful addition to the rail analyst\u27s toolbox. The research conducted in this study resulted in the formulation and application of RAILNET, a multicomrnodity, multicarrier network model for predicting equilibrium flows within a railroad network. Designed for strategic planning with a short term horizon, the model assumes fixed external demand. The predicted flows meet the conditions for Wardropian system equilibrium. At completion, the solution algorithm predicts the expected delay per train on each link, allowing the analyst to identify areas of congestion. Following completion of the model, it was applied to a case study examining the railroad network in the southeastern U.S. The public use version of the Interstate Commerce Commission\u27s Commodity Waybill Sample (CWS) provided flow data. The dissertation describes the procedure used to develop the case study and presents some results. The case points to major deficiencies in the CWS data which resulted in substantially less traffic in the network than is actually present. In general, given this limitation, the model behaved well and results appear reasonable, although not necessarily reflective of actual network conditions

Achieving Target Equilibria in Network Routing Games without Knowing the Latency Functions

The analysis of network routing games typically assumes, right at the onset, precise and detailed information about the latency functions. Such information may, however, be unavailable or difficult to obtain. Moreover, one is often primarily interested in enforcing a desirable target flow as the equilibrium by suitably influencing player behavior in the routing game. We ask whether one can achieve target flows as equilibria without knowing the underlying latency functions. Our main result gives a crisp positive answer to this question. We show that, under fairly general settings, one can efficiently compute edge tolls that induce a given target multicommodity flow in a nonatomic routing game using a polynomial number of queries to an oracle that takes candidate tolls as input and returns the resulting equilibrium flow. This result is obtained via a novel application of the ellipsoid method, and applies to arbitrary multicommodity settings and non-linear latency functions. Our algorithm extends easily to many other settings, such as (i) when certain edges cannot be tolled or there is an upper bound on the total toll paid by a user, and (ii) general nonatomic congestion games. We obtain tighter bounds on the query complexity for series-parallel networks, and single-commodity routing games with linear latency functions, and complement these with a query-complexity lower bound applicable even to single-commodity routing games on parallel-link graphs with linear latency functions. We also explore the use of Stackelberg routing to achieve target equilibria and obtain strong positive results for series-parallel graphs. Our results build upon various new techniques that we develop pertaining to the computation of, and connections between, different notions of approximate equilibrium, properties of multicommodity flows and tolls in series-parallel graphs, and sensitivity of equilibrium flow with respect to tolls. Our results demonstrate that one can indeed circumvent the potentially-onerous task of modeling latency functions, and yet obtain meaningful results for the underlying routing game

Achieving target equilibria in network routing games without knowing the latency functions

The analysis of network routing games typically assumes precise, detailed information about the latency functions. Such information may, however, be unavailable or difficult to obtain. Moreover, one is often primarily interested in enforcing a desired target flow as an equilibrium. We ask whether one can achieve target flows as equilibria without knowing the underlying latency functions. We give a crisp positive answer to this question. We show that one can efficiently compute edge tolls that induce a given target multicommodity flow in a nonatomic routing game using a polynomial number of queries to an oracle that takes tolls as input and outputs the resulting equilibrium flow. This result is obtained via a novel application of the ellipsoid method, and extends to various other settings. We obtain improved query-complexity bounds for series-parallel networks, and single-commodity routing games with linear latency functions. Our techniques provide new insights into network routing games

Selfish versus coordinated routing in network games

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2004.Includes bibliographical references (p. 159-170) and index.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.A common assumption in network optimization models is that a central authority controls the whole system. However, in some applications there are independent users, and assuming that they will follow directions given by an authority is not realistic. Individuals will only accept directives if they are in their own interest or if there are incentives that encourage them to do so. Actually, it would be much easier to let users make their own decisions hoping that the outcome will be close to the authority's goals. Our main contribution is to show that, in static networks subject to congestion, users' selfish decisions drive the system close to optimality with respect to various common objectives. This connection to individual decision making proves fruitful; not only does it provide us with insights and additional understanding of network problems, but it also allows us to design approximation algorithms for computationally difficult problems. More specifically, the conflicting objectives of the users prompt the definition of a network game in which they minimize their own latencies. We show that the so-called price of anarchy is small in a quite general setting. Namely, for networks with side constraints and non-convex, non-differentiable, and even discontinuous latency functions, we show that although an arbitrary equilibrium need not be efficient, the total latency of the best equilibrium is close to that of an optimal solution. In addition, when the measure of the solution quality is the maximum latency, equilibria in networks without constraints are also near-optimal. We provide the first analysis of the problem of minimizing that objective in static networks with congestion.(cont.) As this problem is NP-hard, computing an equilibrium represents a constant-factor approximation algorithm. In some situations, the network authority might still want to do better than in equilibrium. We propose to use a solution that minimizes the total latency, subject to constraints designed to improve the solution's fairness. For several real-world instances, we compute traffic assignments of notably smaller total latency than an equilibrium, yet of similar fairness. Furthermore, we provide theoretical results that explain the conclusions derived from the computational study.by Nicolás E. Stier-Moses.Ph.D

Multipath Routing Algorithms for Communication Networks: Ant Routing and Optimization Based Approaches

In this dissertation, we study two algorithms that accomplish multipath routing in communication networks. The first algorithm that we consider belongs to the class of Ant-Based Routing Algorithms (ARA) that have been inspired by experimental observations of ant colonies. It was found that ant colonies are able to `discover' the shorter of two paths to a food source by laying and following `pheromone' trails. ARA algorithms proposed for communication networks employ probe packets called ant packets (analogues of ants) to collect measurements of various quantities (related to routing performance) like path delays. Using these measurements, analogues of pheromone trails are created, which then influence the routing tables. We study an ARA algorithm, proposed earlier by Bean and Costa, consisting of a delay estimation scheme and a routing probability update scheme, that updates routing probabilities based on the delay estimates. We first consider a simple scenario where data traffic entering a source node has to be routed to a destination node, with N available parallel paths between them. An ant stream also arrives at the source and samples path delays en route to the destination. We consider a stochastic model for the arrival processes and packet lengths of the streams, and a queuing model for the link delays. Using stochastic approximation methods, we show that the evolution of the link delay estimates can be closely tracked by a deterministic ODE (Ordinary Differential Equation) system. A study of the equilibrium points of the ODE enables us to obtain the equilibrium routing probabilities and the path delays. We then consider a network case, where multiple input traffic streams arriving at various sources have to be routed to a single destination. For both the N parallel paths network as well as for the general network, the vector of equilibrium routing probabilities satisfies a fixed point equation. We present various supporting simulation results. The second routing algorithm that we consider is based on an optimization approach to the routing problem. We consider a problem where multiple traffic streams entering at various source nodes have to be routed to their destinations via a network of links. We cast the problem in a multicommodity network flow optimization framework. Our cost function, which is a function of the individual link delays, is a measure of congestion in the network. Our approach is to consider the dual optimization problem, and using dual decomposition techniques we provide primal-dual algorithms that converge to the optimal routing solution. A classical interpretation of the Lagrange multipliers (drawing an analogy with electrical networks) is as `potential differences' across the links. The link potential difference can be then thought of as `driving the flow through the link'. Using the relationships between the link potential differences and the flows, we show that our algorithm converges to a loop-free routing solution. We then incorporate in our framework a rate control problem and address a joint rate control and routing problem

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

Scheduled service network design for integrated planning of rail freight transportation

Cette thèse étudie une approche intégrant la gestion de l’horaire et la conception de réseaux de services pour le transport ferroviaire de marchandises. Le transport par rail s’articule autour d’une structure à deux niveaux de consolidation où l’affectation des wagons aux blocs ainsi que des blocs aux services représentent des décisions qui complexifient grandement la gestion des opérations. Dans cette thèse, les deux processus de consolidation ainsi que l’horaire d’exploitation sont étudiés simultanément. La résolution de ce problème permet d’identifier un plan d’exploitation rentable comprenant les politiques de blocage, le routage et l’horaire des trains, de même que l’habillage ainsi que l’affectation du traffic. Afin de décrire les différentes activités ferroviaires au niveau tactique, nous étendons le réseau physique et construisons une structure de réseau espace-temps comprenant trois couches dans lequel la dimension liée au temps prend en considération les impacts temporels sur les opérations. De plus, les opérations relatives aux trains, blocs et wagons sont décrites par différentes couches. Sur la base de cette structure de réseau, nous modélisons ce problème de planification ferroviaire comme un problème de conception de réseaux de services. Le modèle proposé se formule comme un programme mathématique en variables mixtes. Ce dernie r s’avère très difficile à résoudre en raison de la grande taille des instances traitées et de sa complexité intrinsèque. Trois versions sont étudiées : le modèle simplifié (comprenant des services directs uniquement), le modèle complet (comprenant des services directs et multi-arrêts), ainsi qu’un modèle complet à très grande échelle. Plusieurs heuristiques sont développées afin d’obtenir de bonnes solutions en des temps de calcul raisonnables. Premièrement, un cas particulier avec services directs est analysé. En considérant une cara ctéristique spécifique du problème de conception de réseaux de services directs nous développons un nouvel algorithme de recherche avec tabous. Un voisinage par cycles est privilégié à cet effet. Celui-ci est basé sur la distribution du flot circulant sur les blocs selon les cycles issus du réseau résiduel. Un algorithme basé sur l’ajustement de pente est développé pour le modèle complet, et nous proposons une nouvelle méthode, appelée recherche ellipsoidale, permettant d’améliorer davantage la qualité de la solution. La recherche ellipsoidale combine les bonnes solutions admissibles générées par l’algorithme d’ajustement de pente, et regroupe les caractéristiques des bonnes solutions afin de créer un problème élite qui est résolu de facon exacte à l’aide d’un logiciel commercial. L’heuristique tire donc avantage de la vitesse de convergence de l’algorithme d’ajustement de pente et de la qualité de solution de la recherche ellipsoidale. Les tests numériques illustrent l’efficacité de l’heuristique proposée. En outre, l’algorithme représente une alternative intéressante afin de résoudre le problème simplifié. Enfin, nous étudions le modèle complet à très grande échelle. Une heuristique hybride est développée en intégrant les idées de l’algorithme précédemment décrit et la génération de colonnes. Nous proposons une nouvelle procédure d’ajustement de pente où, par rapport à l’ancienne, seule l’approximation des couts liés aux services est considérée. La nouvelle approche d’ajustement de pente sépare ainsi les décisions associées aux blocs et aux services afin de fournir une décomposition naturelle du problème. Les résultats numériques obtenus montrent que l’algorithme est en mesure d’identifier des solutions de qualité dans un contexte visant la résolution d’instances réelles.This thesis studies a scheduled service network design problem for rail freight transportation planning. Rails follow a special two level consolidation organization, and the car-to-block, block-to-service handling procedure complicates daily operations. In this research, the two consolidation processes as well as the operation schedule are considered simultaneously, and by solving this problem, we provide an overall cost-effective operating plan, including blocking policy, train routing, scheduling, make-up policy and traffic distribution. In order to describe various rail operations at the tactical level, we extend the physical network and construct a 3-layer time-space structure, in which the time dimension takes into consideration the temporal impacts on operations. Furthermore, operations on trains, blocks, and cars are described in different layers. Based on this network structure, we model the rail planning problem to a service network design formulation. The proposed model relies on a complex mixed-integer programming formulation. The problem is very hard to solve due to the computational difficulty as well as the tremendous size of the application instances. Three versions of the problem are studied, which are the simplified model (with only non-stop services), complete model (with both non-stop and multi-stop services) and very-large-scale complete model. Heuristic algorithms are developed to provide good feasible solutions in reasonable computing efforts. A special case with non-stop services is first studied. According to a specific characteristic of the direct service network design problem, we develop a tabu search algorithm. The tabu search moves in a cycle-based neighborhood, where flows on blocks are re-distributed according to the cycles in a conceptual residual network. A slope scaling based algorithm is developed for the complete model, and we propose a new method, called ellipsoidal search, to further improve the solution quality. Ellipsoidal search combines the good feasible solutions generated from the slope scaling, and collects the features of good solutions into an elite problem, and solves it with exact solvers. The algorithm thus takes advantage of the convergence speed of slope scaling and solution quality of ellipsoidal search, and is proven effective. The algorithm also presents an alternative for solving the simplified problem. Finally, we work on the very-large-size complete model. A hybrid heuristic is developed by integrating the ideas of previous research with column generation. We propose a new slope scaling scheme where, compared with the previous scheme, only approximate service costs instead of both service and block costs are considered. The new slope scaling scheme thus separates the block decisions and service decisions, and provide a natural decomposition of the problem. Experiments show the algorithm is good to solve real-life size instances

Convergence theories of distributed iterative processes: a survey

Bibliography: p. 43-45."October, 1984." (Revision of LIDS-P-1342)" NSF-ECS-8217668" " ONR/N00014-75-C-1183" " ONR-N00014-77-C-0532(NR041-519)" ONR N00014-84-K-0519"Dimitri P. Bertsekas, John N. Tsitsiklis, Michael Athans