Alpha Reliable Network Design Problem

Abstract

Uncertainties are unavoidable in engineering applications. A new model is proposed for designing networks under uncertainty of future demands. The objective is to minimize the total travel time budget required to satisfy the total travel time reliability constraint while considering the route choice behavior of network users. The model adopts the value-at-risk risk measure instead of the utility function to model planner risk preferences. It allows the planners to specify their risk preferences by using a confidence level of alpha on the total travel time reliability. This alpha reliable network design model is formulated as a stochastic bilevel optimization problem. The upper-level subprogram is a variant of the chance-constrained model that minimizes the total travel time budget subject to a chance constraint with a user-specified confidence level, a budget constraint, and design variable constraints; the lower-level subprogram is a user-equilibrium problem under demand uncertainty. A simulation-based genetic algorithm procedure is developed to solve this complex network design problem (NDP). Two numerical examples are presented to illustrate the features of the proposed NDP model.

Robust improvement schemes for road networks under demand uncertainty

“…Another plausible approach is to design the system using high-consequence scenarios, given that optimizing against the worst case may lead to an overly-conservative design. For example, Chen et al (2007) adopted a risk measure called as a-value-at-risk and essentially optimized the performance against a set of demand scenarios whose collective probability of occurrence is a. In contrast, this paper applies the robust optimization approach to develop a new min-max network design model.…”

Evaluation and Design of Transport Network Capacity under Demand Uncertainty

“…Adopting the chance-constraint concept in (7,9), the chance-constraint of the equilibrated stochastic link flow, based on the desired level of link capacity reliability, is shown in Figure 1. In Figure 1, the link capacity reliability can be evaluated from the frequency that the equilibrated stochastic link flow is less than or equal to total deterministic link capacity.…”

“…An analytical approach to solve the FNDP follows the implicit programming approach (6,9,10). The fmincon solver in MATLAB, which implements Sequential Quadratic Programming (SQP) algorithm, is used to find an optimal solution.…”

“…The chance-constraint could be also referred to as the Value-at-Risk in Chen et al (9). The objective function of this problem is defined as a weighted sum of the mean and SD of the increased demands.…”

Bi-objective bimodal urban road network design using hybrid metaheuristics

“…Traditionally, these problems are considered in two forms: the Discrete NDP (DNDP) and the Continuous NDP (CNDP). The DNDP, such as street construction and street orientation, is concerned with the discrete decision variables (e.g., Poorzahedy and Turnquist 1982;Wong and Yang 1997;Chen et al 2002Chen et al , 2007Chen et al , 2010aChen and Yang 2004;Gao et al 2005;Meng and Khoo 2008;, and the CNDP, such as setting signal timing and toll, is concerned with continuous attributes of the network (e.g., Yin 2000;Meng et al 2001;Meng and Yang 2002;Gao and Song 2002;Chiou 2008aChiou ,b, 2009aYin et al 2009;Chen et al 2010b). Another less investigated form is the Mixed Network Design Problem (MNDP) which deals with both continuous and discrete decision variables.…”