long-term uncertainty due to land use change and policy decisions). Sources of uncertainty arise from nonrecurrent congestion because of accidents, earthquake, traffic signal failure, or road maintenance or because of recurrent congestion, that is, regular change in demand throughout the day. It is desirable to design a network so that it is resilient to such conditions. Most studies adopted stochastic programming (SP) to model such situations (10–12). However, SP models account for only the first moment of the uncertain variable by minimizing the expected system costs. The robust network design problem (RNDP) is a recent advancement in network design paradigms which accounts for the sensitivity of the design by account- ing for higher moments. The genesis of RNDP can be traced back to robust optimization (RO), a modeling methodology for solving optimization problems in which data are uncertain (13–16 ). The approach is to seek optimal or near-optimal solutions that are not overly sensitive to any realization of uncertainty (17 ). It aims for a solution that is robust or insensitive to the uncertainty considered and thus is an efficient solution in practice. In addition, this approach can obtain robust solutions by solving a problem that is not harder than the deterministic problem (15). A distinction between RO and SP methods is that whereas the latter accounts for uncertainty by minimization of the expected value objective function, the former considers higher moments of the probability distribution in addition to the expected value of the objective function. Although both RO and SP allow the NDP problem to account for uncertainty, the RO model has little sensitivity to demand. The RNDP proposed by Ukkusuri et al. has two objectives: a higher moment of probability distribution, that is, standard deviation of total system travel time, and expected value of total system travel time under demand uncertainty (14). The objective function for the proposed RO model is minimize TSTT where the varying demand, which is realized in the future, is denoted by ω∈ℜ n to {ω 1 , ω 2 , . .., ω s } for each scenario s ∈ S. The total sys- tem travel time is represented by TSTT for each demand realization ω after solving traffic equilibrium problem. The measure of solution robustness is captured by σ(  ) which denotes the expected value of the TSTT for all demand realizations and λ(  ) to as a measure of the variability of the TSTT for all the realized demands. This measure was used in modeling with weights given to λ(  ) and σ(  ). The weight ρ can vary from [0, 1] ∈ℜ. The problem was solved by converting both objectives into a single objective by adding them and then multiplying them by a user-specified weight. Since RNDP is a nonlinear and ρσ ω ω ω ρλ ω ω TSTT TSTT , , ,..., , , ,..., 1 2 1 2 1 s ( ) + - ( ) ω s ( ) () 1 Pareto Optimal Multiobjective Optimization for Robust Transportation Network Design Problem Sushant Sharma, Satish V. Ukkusuri, and Tom V. Mathew 95 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. The network design problem (NDP) determines what facilities are to be added to a transportation network under a given budget constraint considering both user and system objectives. This decision taken by the planner affects the route choice behavior of road users such that the flow satisfies user equilibrium conditions. It can be formulated as a bilevel problem that has an upper level representing a system- optimal design and a lower level representing traveler’s route choice behavior. The first discrete network design formulation was proposed by LeBlanc (1), and later Abdulaal and LeBlanc extended it to a continuous version (2). Several variations of the NDP have since been studied extensively. Optimization of road tolls under queuing and congestion (3), optimization of reserve capacity of a signal-controlled network (4, 5), estimation of trip matrix and optimization of traffic signal (6), maximization of reliability index (7 ), and capacity expan- sion of a large city network (8) are some variations of the network design problems. All these problems are normally formulated as bilevel programming problems in which the lower-level problems are deterministic or stochastic user equilibrium (9). Most work so far has concentrated primarily on developing methodologies for the deter- ministic NDP. The recent advances in transportation network design are based on uncertainty associated with the origin–destination (O-D) demand, available link capacity, and link cost function parameters, which can arise because of multiple factors, including operational characteristics of the system (whether related to user perception or S. Sharma and T. V. Mathew, Indian Institute of Technology Bombay, Mumbai 400076, India. S. V. Ukkusuri, Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, Troy, NY 12061. Corresponding author: S. V. Ukkusuri, ukkuss@rpi.edu. Transportation Research Record: Journal of the Transportation Research Board, No. 2090, Transportation Research Board of the National Academies, Washington, D.C., 2009, pp. 95–104. DOI: 10.3141/2090-11