Isabel M. Ribeiro

The eigenvalue complementarity problem

Abstract In this paper an eigenvalue complementarity problem (EiCP) is studied, which finds its origins in the solution of a contact problem in mechanics. The EiCP is shown to be equivalent to a Nonlinear Complementarity Problem, a Mathematical Programming Problem with Complementarity Constraints and a Global Optimization Problem. A finite Reformulation–Linearization Technique (Rlt)-based tree search algorithm is introduced for processing the EiCP via the lattermost of these formulations. Computational experience is included to highlight the efficacy of the above formulations and corresponding techniques for the solution of the EiCP.

On the asymmetric eigenvalue complementarity problem

In this paper, we discuss the eigenvalue complementarity problem (EiCP) where at least one of its defining matrices is asymmetric. A sufficient condition for the existence of a solution to the EiCP is established. The EiCP is shown to be equivalent to finding a global minimum of an appropriate merit function on a convex set Ω defined by linear constraints. A sufficient condition for a stationary point of this function on Ω to be a solution of the EiCP is presented. A branch-and-bound procedure is developed for finding a global minimum of this merit function on Ω. In addition, a sequential enumerative algorithm for the computation of the minimum and the maximum eigenvalues is also discussed. Computational experience is included to highlight the efficiency and efficacy of the proposed methodologies to solve the asymmetric EiCP.

Integer Programming to Optimize Tamping in Railway Tracks as Preventive Maintenance

In the area with railway engineering, scheduling preventive maintenance actions is an important issue for engineers and railway administrations because the optimization of maintenance actions at a preventive level allows maintenance costs to be reduced during the life cycle of the track, with the guarantee of its geometrical quality. This paper describes a model designed to optimize the tamping operations in ballasted tracks as preventive maintenance. The model, formulated as mixed 0–1 linear program, considers real technical aspects as constraints, which is a novel approach in the optimization of track maintenance over time. Global optimization is used to predict and to schedule tamping, taking into account four aspects: the evolution of the track degradation over time; the track layout; the dependency of the track quality recovery on the track quality at the moment of the maintenance operation; the track quality limits that depend on the maximum permissible train speed. Computational experience with two track stretches of the Portuguese Northern Railway Line is included to highlight the efficacy of the proposed methodology.

A Complementarity-based Partitioning and Disjunctive Cut Algorithm for Mathematical Programming Problems with Equilibrium Constraints

In this paper a branch-and-bound algorithm is proposed for finding a global minimum to a Mathematical Programming Problem with Complementarity (or Equilibrium) Constraints (MPECs), which incorporates disjunctive cuts for computing lower bounds and employs a Complementarity Active-Set Algorithm for computing upper bounds. Computational results for solving MPECs associated with Bilivel Problems, NP-hard Linear Complementarity Problems, and Hinge Fitting Problems are presented to highlight the efficacy of the procedure in determining a global minimum for different classes of MPECs.

On the Solution of NP-hard Linear Complementarity Problems

In this paper two enumerative algorithms for the Linear Complementarity Problems (LCP) are discussed. These procedures exploit the equivalence of theLCP into a nonconvex quadratic and a bilinear programs. It is shown that these algorithms are efficient for processing NP-hardLCPs associated with reformulations of the Knapsack problem and should be recommended to solve difficultLCPs.

Railway condition-based maintenance model with stochastic deterioration

AbstractThe application of mathematical programming for scheduling preventive maintenance in railways is relatively new. This paper presents a stochastic mathematical model designed to optimize and to predict tamping operations in ballasted tracks as preventive condition-based maintenance. The model is formulated as a mixed 0–1 nonlinear program that considers real technical aspects as constraints: the reduction of the geometrical track quality over time is characterized by the deterioration rate of the standard deviation of the longitudinal level; the track layout; the dependency of the track recovery on its quality at the moment of the maintenance operation; the limits for preventive maintenance that depend on the maximum permissible train speed. In the model application, a railway stretch with 51.2 km of length is analysed for a time period of five years. The deterioration model is stochastic and represents the reduction of the standard deviation of the longitudinal level over time. The deterioration r...

The fully actuated traffic control problem solved by global optimization and complementarity

Global optimization and complementarity are used to determine the signal timing for fully actuated traffic control, regarding effective green and red times on each cycle. The average values of these parameters can be used to estimate the control delay of vehicles. In this article, a two-phase queuing system for a signalized intersection is outlined, based on the principle of minimization of the total waiting time for the vehicles. The underlying model results in a linear program with linear complementarity constraints, solved by a sequential complementarity algorithm. Departure rates of vehicles during green and yellow periods were treated as deterministic, while arrival rates of vehicles were assumed to follow a Poisson distribution. Several traffic scenarios were created and solved. The numerical results reveal that it is possible to use global optimization and complementarity over a reasonable number of cycles and determine with efficiency effective green and red times for a signalized intersection.

On the use of bilevel programming for solving a structural optimization problem with discrete variables

In this paper, a bilevel formulation of a structural optimization problem with discrete variables is investigated. The bilevel programming problem is transformed into a Mathematical Program with Equilibrium (or Complementarity) Constraints (MPEC) by exploiting the Karush-Kuhn-Tucker conditions of the follower’s problem.

TRHUMIDADE - A water diffusivity model to predict moisture content profiles

Abstract The study of moisture transfer in porous building materials after a long contact with liquid water is crucial to prevent damages, in particular, when it comes to extreme rain events or floodings. Several experimental techniques are available to measure the moisture content evolution during water absorption tests, although the great majority of them are time-consuming and require expensive equipment. For this reason, the use of validated hygrothermal simulation tools is essential for a faster analysis without losing accuracy. The main goal of this paper is to compare the simulated moisture content profiles provided by the program TRHUMIDADE with those obtained by the gamma-ray attenuation method and by WUFI program. In TRHUMIDADE the heat and moisture phenomenon is described by the moisture content gradient, which may be more appropriate in predicting scenarios involving liquid water transport. The obtained results showed a good agreement for the red-brick and the autoclaved cellular concrete, which contributes to validate the future use of the program in the development of advanced hygrothermic studies in multi-layered building walls.

Optimal one-way and roundtrip journeys design by mixed-integer programming

ABSTRACT The introduction of multimodal/intermodal networks in transportation problems, especially when considering roundtrips, adds complexity to the models. This article presents two models for the optimization of intermodal trips as a contribution to the integration of transport modes in networks. The first model is devoted to one-way trips while the second one is dedicated to roundtrips. The original contribution of this research to transportation is mainly the consideration of roundtrips in the optimization process of intermodal transport, especially because the transport mode between two nodes on the return trip should be the same as the one on the outward trip if both nodes are visited on the return trip, which is a valuable aspect for transport companies. The mathematical formulations of both models leads to mixed binary linear programs, which is not a common approach for this type of problem. In this article, as well as the model description, computational experience is included to highlight the importance and efficiency of the proposed models, which may provide a valuable tool for transport managers.