Dynamic Congestion and Tolls with Mobile Source Emission

This paper proposes a dynamic congestion pricing model that takes into account mobile source emissions. We consider a tollable vehicular network where the users selfishly minimize their own travel costs, including travel time, early/late arrival penalties and tolls. On top of that, we assume that part of the network can be tolled by a central authority, whose objective is to minimize both total travel costs of road users and total emission on a network-wide level. The model is formulated as a mathematical program with equilibrium constraints (MPEC) problem and then reformulated as a mathematical program with complementarity constraints (MPCC). The MPCC is solved using a quadratic penalty-based gradient projection algorithm. A numerical study on a toy network illustrates the effectiveness of the tolling strategy and reveals a Braess-type paradox in the context of traffic-derived emission.Comment: 23 pages, 9 figures, 5 tables. Current version to appear in the Proceedings of the 20th International Symposium on Transportation and Traffic Theory, 2013, the Netherland

Solving Mathematical Programs with Equilibrium Constraints as Nonlinear Programming: A New Framework

We present a new framework for the solution of mathematical programs with equilibrium constraints (MPECs). In this algorithmic framework, an MPECs is viewed as a concentration of an unconstrained optimization which minimizes the complementarity measure and a nonlinear programming with general constraints. A strategy generalizing ideas of Byrd-Omojokun's trust region method is used to compute steps. By penalizing the tangential constraints into the objective function, we circumvent the problem of not satisfying MFCQ. A trust-funnel-like strategy is used to balance the improvements on feasibility and optimality. We show that, under MPEC-MFCQ, if the algorithm does not terminate in finite steps, then at least one accumulation point of the iterates sequence is an S-stationary point

A MPCC-NLP approach for an electric power market problem

The electric power market is changing - it has passed from a regulated market, where the government of each country had the control of prices, to a deregulated market economy. Each company competes in order to get more clients and maximize its profits. This market is represented by a Stackelberg game with two firms, leader and follower, and the leader anticipates the reaction of the follower. The problem is formulated as a Mathematical Program with Complementarity Constraints (MPCC). It is shown that the constraint qualifications usually assumed to prove convergence of standard algorithms fail to hold for MPCC. To circumvent this, a reformulation for a nonlinear problem (NLP) is proposed. Numerical tests using the NEOS server platform are presented

A MPCC approach on a Stackelberg game in an electric power market : changing the leadership

An electric power market is studied as a Stackelberg game where two firms, A and B, produce energy. It is analyzed two distinct situations, according to the firm who plays the leader role: the first one, when the firm A is the leader and the other firm is the follower, and the second that is the reverse of the players roles. The main goal is to understand the behavior of the various agents that compose the electric power network, such as transmissions capacity, quantities of power generated and demanded, when changing leadership. The problem is formulated as a Mathematical Program with Complementarity Constraints (MPCC) and reformulated into a Nonlinear Program (NLP), allowing the use of robust NLP solvers. Numerical results are presented and some final considerations are carried out.Universidade do Minho. Centro AlgoritmiFundação para a Ciência e a Tecnologia (FCT

Numerical experiments with a modified regularization scheme for mathematical programs with complementarity constraints

On this paper we present a modified regularization scheme for Mathematical Programs with Complementarity Constraints. In the regularized formulations the complementarity condition is replaced by a constraint involving a positive parameter that can be decreased to zero. In our approach both the complementarity condition and the nonnegativity constraints are relaxed. An iterative algorithm is implemented in MATLAB language and a set of AMPL problems from MacMPEC database were tested

Solving a signalized traffic intersection problem with NLP solvers

Mathematical Programs with Complementarity Constraints (MPCC) finds many applications in areas such engineering design, economic equilibrium and mathematical theory itself. In this work we consider a queuing system model resulting from a single signalized traffic intersection regulated by pre-timed control in an urban traffic network. The model is formulated as an MPCC problem and may be used to ascertain the optimal cycle and the green split allocation. This MPCC problem is also formulated as its NLP equivalent reformulation. The goal of this work is to solve the problem, using both MPCC and NLP formulations, minimizing two objective functions: the average queue length over all queues and the average waiting time over the worst queue. The problem was codified in AMPL and solved using some optimization software packages.Fundação para a Ciência e a Tecnologia (FCT) FCOMP-01-0124-FEDER-022674 (R&D unit Algoritmi)PEst-OE/MAT/UI4080/201