Robust Network Design Problem Research Articles

GRASP algorithms for the robust railway network design problem

This paper analyzes the solvability of a railway network design problem and its robust version. These problems are modeled as integer linear programming problems with binary variables, and their solutions provide topological railway networks maximizing the trip coverage in the presence of a competing mode, both assuming that the network works fine and that links can fail, respectively. Since these problems are computationally intractable for realistic sizes, GRASP heuristics are proposed for finding good feasible solutions. The results obtained in a computational experience indicate that our GRASP algorithms are suitable for railway network design problems.

Defending Transportation Networks against Random and Targeted Attacks

This paper explores several reliability and vulnerability measures for transportation networks and proposes three models for optimal resource allocation for transportation network design or defense to minimize the disruption caused by both random and targeted attacks. The common day-to-day disturbances with less severe consequences are referred to as random attacks, but targeted attacks include both coordinated terrorist strikes and large-scale natural disasters. For random attacks, the major concern would be the reliability of the total system travel time. A robust discrete network design problem is formulated to take into account random attacks in the planning stage. The transport capacity or the unsatisfied demand would be critical in case of emergency evacuation, and law enforcement forces could be deployed to prevent malicious attacks in the first place or to ensure a smooth evacuation operation. The proposed models feature an intrinsic trilevel game structure of the network users, the attacker, and the defender (planner). By exploring the unique properties of the proposed measures and reformulating the problems, the trilevel structure models are reduced to mixed-integer semi-infinite optimization programs. This paper further applies an active-set algorithm, combined with a cutting-plane scheme to solve the proposed models. Numerical examples indicate that the proposed formulations are valid and that the solution algorithm can solve the problems effectively and efficiently. The models for targeted attacks provide practical implications on identifying critical infrastructures for evacuation.

Static and dynamic routing under disjoint dominant extreme demands

This paper considers a special case of the robust network design problem where the dominant extreme points of the demand polyhedron have a disjoint support. In this case static and dynamic routing lead to the same optimal solution, both for the splittable and the unsplittable case. As a consequence, the robust network design problem with (splittable) dynamic routing is polynomially solvable, whereas it is co- N P -hard in the general case. This result applies to particular instances of the single-source Hose model.

Dynamic vs. Oblivious Routing in Network Design

Consider the robust network design problem of finding a minimum cost network with enough capacity to route all traffic demand matrices in a given polytope. We investigate the impact of different routing models in this robust setting: in particular, we compare oblivious routing, where the routing between each terminal pair must be fixed in advance, to dynamic routing, where routings may depend arbitrarily on the current demand. Our main result is a construction that shows that the optimal cost of such a network based on oblivious routing (fractional or integral) may be a factor of Ω(log n) more than the cost required when using dynamic routing. This is true even in the important special case of the asymmetric hose model. This answers a question in (Chekuri, SIGACT News 38(3):106–128, 2007), and is tight up to constant factors. Our proof technique builds on a connection between expander graphs and robust design for single-sink traffic patterns (Chekuri et al., Networks 50(1):50–54, 2007).

Robust Optimization Model for a Dynamic Network Design Problem Under Demand Uncertainty

This paper describes a robust optimization approach for a network design problem explicitly incorporating traffic dynamics and demand uncertainty. In particular, we consider a cell transmission model based network design problem of the linear programming type and use box uncertainty sets to characterize the demand uncertainty. The major contribution of this paper is to formulate such a robust network design problem as a tractable linear programming model and demonstrate the model robustness by comparing its solution performance with the nominal solution from the corresponding deterministic model. The results of the numerical experiments justify the modeling advantage of the robust optimization approach and provide useful managerial insights for enacting capacity expansion policies under demand uncertainty.

A game theoretic framework for the robust railway transit network design problem

This paper proposes a game theoretic framework for the problem of designing an uncapacitated railway transit network in the presence of link failures and a competing mode. It is assumed that when a link fails, another path or another transportation mode is provided to transport passengers between the endpoints of the affected link. The goal is to build a network that optimizes a certain utility function when failures occur. The problem is posed as a non-cooperative two-player zero-sum game with perfect information. The saddle points of the corresponding mixed enlarged game yield robust network designs.

On improving optimal oblivious routing

In this paper a generalization of the robust network design problem with oblivious routing is investigated, where the (uncertain) demands are served through two alternative routing templates. A mathematical programming model leading to tractable cases is presented, together with related algorithmic approaches. The proposed special cases strictly generalize the standard oblivious routing model.

Pareto Optimal Multiobjective Optimization for Robust Transportation Network Design Problem

A study was done to formulate and solve the multiobjective network design problem with uncertain demand. Various samples of demand are realized for optimal improvements in the network while the objectives of the expected total system travel time and the higher moment for total system travel time are minimized. A formulation is proposed for multi-objective robust network design, and a solution methodology is developed on the basis of a revised fast and elitist nondominated sorting genetic algorithm. The developed methodology has been tested on the Nguyen-Dupuis network, and various Pareto optimal solutions are compared with earlier work on the single-objective robust network design problem. A real medium-size network was solved to prove efficacy of the model. The results show better solutions for the multiobjective robust network design problem with relatively less computational effort.

Hardness of robust network design

AbstractThe authors settle the complexity status of the robust network design problem in undirected graphs. The fact that the flow‐cut gap in general graphs can be large, poses some difficulty in establishing a hardness result. Instead, the authors introduce a single‐source version of the problem where the flow‐cut gap is known to be one. They then show that this restricted problem is coNP‐Hard. This version also captures, as special cases, the fractional relaxations of several problems including the spanning tree problem, the Steiner tree problem, and the shortest path problem. © 2007 Wiley Periodicals, Inc. NETWORKS, Vol. 50(1), 50–54 2007

Robust Transportation Network Design Under Demand Uncertainty

Abstract: This article addresses the problem of a traffic network design problem (NDP) under demand uncertainty. The origin–destination trip matrices are taken as random variables with known probability distributions. Instead of finding optimal network design solutions for a given future scenario, we are concerned with solutions that are in some sense “good” for a variety of demand realizations. We introduce a definition of robustness accounting for the planner's required degree of robustness. We propose a formulation of the robust network design problem (RNDP) and develop a methodology based on genetic algorithm (GA) to solve the RNDP. The proposed model generates globally near‐optimal network design solutions, f, based on the planner's input for robustness. The study makes two important contributions to the network design literature. First, robust network design solutions are significantly different from the deterministic NDPs and not accounting for them could potentially underestimate the network‐wide impacts. Second, systematic evaluation of the performance of the model and solution algorithm is conducted on different test networks and budget levels to explore the efficacy of this approach. The results highlight the importance of accounting for robustness in transportation planning and the proposed approach is capable of producing high‐quality solutions.

Robust Discrete Optimization and Its Applications.

Preface. 1. Approaches to Handle Uncertainty In Decision Making. 2. A Robust Discrete Optimization Framework. 3. Computational Complexity Results of Robust Discrete Optimization Problems. 4. Easily Solvable Cases of Robust Discrete Optimization Problems. 5. Algorithmic Developments for Difficult Robust Discrete Optimization Problems. 6. Robust 1-Median Location Problems: Dynamic Aspects and Uncertainty. 7. Robust Scheduling Problems. 8. Robust Uncapacitated Network Design and International Sourcing Problems. 9. Robust Discrete Optimization: Past Successes and Future Challenges.