A method for reliability-based optimization with multiple non-normal stochastic parameters: a simplified airshed management study

Abstract

We develop methodologies to enable applications of reliability-based design optimization (RBDO) to environmental policy setting problems. RBDO considers uncertainty as random variables and parameters in an optimization framework with probabilistic constraints. Three challenges in environmental decision-making problems not addressed by current RBDO methods are efficient methods in handling: (1) non-normally distributed random parameters, (2) discrete random parameters, and (3) joint reliability constraints (e.g., meeting constraints simultaneously with a single reliability). We propose a modified sequential quadratic programming algorithm to address these challenges. An active set strategy is combined with a reliability contour formulation to solve problems with multiple non-normal random parameters. The reliability contour formulation can also handle discrete random parameters by converting them to equivalent continuous ones. Joint reliability constraints are estimated by their theoretical upper bounds using reliability indexes and angles of normal vectors between active constraints. To demonstrate the methods, we consider a simplified airshed example where CO and NOx standards are violated and are brought into compliance by reducing the speed limits of two nearby highways. This analytical example is based on the CALINE4 model. Results show the potential of this approach to handle complex large-scale environmental regulation problems.

Optimal design and impact analysis of urban traffic regulations under ambient uncertainty

“…The corresponding dispersion coefficient values from Table 5 are also available. The existence of discrete variables in the Gaussian dispersion model means that a probabilistic constraint will be formulated as Bayesian conditional probability such that continuous distributions are used to approximate the distributions of a, c, d, f as discussed in Chan et al (2010).…”

“…In this work we focus on the air pollution of on-road vehicles to the extent that transportation policies can be evaluated using novel engineering optimization techniques. Similar attempts in policy-setting exist in the literature; for example, Nijkamp and Blaas (1994) provided a general framework for decision-making in transportation policy planning; Haldenbilen and Ceylan (2005) applied a genetic algorithm to assist policy design with traffic demand estimation; Ü lengin et al (2005) developed a transportation decision support system that uses Bayesian causal map to analyze possible scenarios of transportation policies with long term demand projections; Chan et al (2010) demonstrated the use of advanced optimization techniques in policy decision-making on a simplified tworoad case with constant traffic flow. However many of the previous studies focus on well simplified urban models that are generally unsuitable to the complexities of today's world.…”