Location Design of Electrification Road in Transportation Networks for On-Way Charging

Electric vehicles tend to be a great mobility option for the potential benefits in energy consumption and emission reduction. On-way charging (OWC) has been recognized to be a promising solution to extend driving range for electric vehicles. Location of the electrification road (ER) is a critical issue for future urban traffic management to accommodate the new mobility option. This paper proposes a mathematical program with equilibrium constraint (MPEC) approach to solve this problem, which minimizes the total travel time with a limited construction budget. To describe the drivers’ routing choice, a path-constrained network equilibrium model is proposed to minimize their travel time and prevent running out of charge. We develop a modified active set algorithm to solve the MPEC model. Numerical experiments are presented to demonstrate the performance of the model and the solution algorithm and analyze the impact of charging efficiency, battery size, and comfortable range.

The stellar atmosphere physical system II. An operative sequential algorithm to solve the stellar atmosphere problem

In this paper, the second and the last of the series, we present a sequential algorithm to solve the stellar atmosphere problem that may serve as a paradigm for the solution of more general non-linear and non-local problems. The Iteration Factors (IF) Method is applied to achieve a solution of the radiative transfer equations, consistent with the radiative equilibrium constraint.

The Role of Initial Credit Distribution Scheme in Managing Network Mobility and Maximizing Reserve Capacity: Considering Traveler’s Cognitive Illusion

The role of initial credit distribution scheme (ICDS) in managing network mobility has long been overlooked in previous studies of tradable credit scheme (TCS), which may make their results disputable in the reality, as the travelers possessing leftover credits can get some subsidy from the credit market and offset part of travel cost. In this paper, the disequilibrium phenomenon of previous user equilibrium (UE) solution is shown when traveler’s cognitive illusion (CI) is considered. Then, a new UE condition with TCS is defined with the ICDS and CI explicitly considered. To comprehensively reveal the impacts of ICDS on UE solution, four different types of ICDS are introduced and analyzed in a unified variational inequality (VI) modeling framework. The uniqueness of the UE link flow and market equilibrium (ME) credit price is also investigated. Furthermore, the mathematical program with equilibrium constraint (MPEC) for the optimal ICDS design problem is established, with the optimization objective being maximizing network reserve capacity. A modified relaxation algorithm is adopted to solve the MPEC. The numerical example shows that a properly designed ICDS can not only improve the network reserve capacity, but also decrease the travel cost of all the travelers in the network simultaneously.

A Low Mach Number Model for Moist Atmospheric Flows

A low Mach number model for moist atmospheric flows is introduced that accurately incorporates reversible moist processes in flows whose features of interest occur on advective rather than acoustic time scales. Total water is used as a prognostic variable, so that water vapor and liquid water are diagnostically recovered as needed from an exact Clausius–Clapeyron formula for moist thermodynamics. Low Mach number models can be computationally more efficient than a fully compressible model, but the low Mach number formulation introduces additional mathematical and computational complexity because of the divergence constraint imposed on the velocity field. Here, latent heat release is accounted for in the source term of the constraint by estimating the rate of phase change based on the time variation of saturated water vapor subject to the thermodynamic equilibrium constraint. The authors numerically assess the validity of the low Mach number approximation for moist atmospheric flows by contrasting the low Mach number solution to reference solutions computed with a fully compressible formulation for a variety of test problems.

Estimating the Capacity of Urban Transportation Networks with an Improved Sensitivity Based Method

The throughput of a given transportation network is always of interest to the traffic administrative department, so as to evaluate the benefit of the transportation construction or expansion project before its implementation. The model of the transportation network capacity formulated as a mathematic programming with equilibrium constraint (MPEC) well defines this problem. For practical applications, a modified sensitivity analysis based (SAB) method is developed to estimate the solution of this bilevel model. The high-efficient origin-based (OB) algorithm is extended for the precise solution of the combined model which is integrated in the network capacity model. The sensitivity analysis approach is also modified to simplify the inversion of the Jacobian matrix in large-scale problems. The solution produced in every iteration of SAB is restrained to be feasible to guarantee the success of the heuristic search. From the numerical experiments, the accuracy of the derivatives for the linear approximation could significantly affect the converging of the SAB method. The results also show that the proposed method could obtain good suboptimal solutions from different starting points in the test examples.