Ángel Marín

Airport management: taxi planning

The Taxi Planning studies the aircraft routing and scheduling on the airport ground. This is a dynamic problem, which must be updated almost every time that a new aircraft enters or exits the system. Taxi Planning has been modelled using a linear multicommodity flow network model with side constraints and binary variables. The flow capacity constraints are used to represent the conflicts and competence between aircrafts using a given airport capacity. The “Branch and Bound” and “Fix and Relax” methodologies have been used. The computational tests have been run at the Madrid-Barajas airport, using actual data from the airport traffic.

TACTICAL DESIGN OF RAIL FREIGHT NETWORKS. PART I: EXACT AND HEURISTIC METHODS

Abstract The tactical planning of rail freight networks is studied with the help of non-convex optimization models which are difficult to solve using only exact methods. For this reason it is necessary to use heuristic methods to obtain the solution for realistic networks. In this paper, local search and Branch and Bound methods are compared. In Part I, the model and the methods are defined and tested. In Part II, the methods are compared among one another using statistical analysis. The problem is to decide the optimal assignment of the trains to the service network and simultaneously assign the demand of cars to the routes. The formulation includes some features such as car transfer and classification, different capacities and a limited fleet of trains available for use. Different heuristics have been developed to obtain the solution for the proposed model: Simulated Annealing, Tabu Search and a particular heuristic that will be mentioned with the name of ‘Descending’. The objective function becomes piece-wise linear if the investment cost to purchase trains is considered. For small size networks a reformulation of the problem is studied to compare the heuristic approaches with the exact solution provided by Branch and Bound. To solve large networks, only heuristic methods can be used.

Location of infrastructure in urban railway networks

The location of the infrastructure of the Rapid Transit Network considers at upper level a list of potential transit corridors and stations on the basis of its own constraints, so the network design is modelled on a discrete space of alternatives. At lower level the alternatives are evaluated based on the route and mode user decisions. The optimization objectives are to maximize the transit demand and minimize the private travel time, considering the users behavior, the physical network, budget constraints and the network design constraints. The design criteria are considered as location constraints, they have been traditionally defined by node and link compatibilities defining lines, but we define a new location constraints based in to minimize the number of routing intersections. The demand mode splitting constraints may be defined by all or nothing mode assignment or like it is proposed by us in this paper by Logit distribution. The models defined with the above alternatives are large integer multicommodity flow network design problems with side constraints. These sets of alternatives are computationally studied to obtain conclusions. The experiments are presented using two networks, a small network and a medium size network, simulating the city of Seville.

An integrated methodology for the rapid transit network design problem

The Rapid Transit System Network Design Problem consists of two intertwined location problems: the determination of alignments and that of the stations. The underlying space, a network or a region of the plane, mainly depends on the place in which the system is being constructed, at grade or elevated, or underground, respectively. For solving the problem some relevant criteria, among them cost and future utilisation, are applied. Urban planners and engineering consulting usually select a small number of corridors to be combined and then analysed. The way of selecting and comparing these alternatives is performed by the application of the four-stage transit planning model. Due to the complexity of the overall problem, during last ten years some efforts have been dedicated to modelling some aspects as optimisation problems and to provide Operations Research methods for solving them. This approach leads to the consideration of a higher number of candidates than that of the classic corridor analysis. The main aim of this paper is to integrate the steps of the transit planning model (trip attraction and generation, trip distribution, mode choice and traffic equilibrium) into an optimisation process.

Electric capacity expansion under uncertain demand: decomposition approaches

The authors present a stochastic model of electric capacity expansion planning under uncertainty in demand. The goal of this problem is to determine the most interesting investments (plants and capacity levels) over the considered planning time (up to several years). Periods are divided into smaller subperiods (e.g. weekly or monthly) for which demand is assumed uncertain and modeled as a continuous probability distribution function. This leads to consider the risk associated to each decision for the capacity to be used (electricity generation). A first approach as a nonlinear continuous model is presented. Benders decomposition and Lagrangean relaxation-decomposition are proposed as solution methods, where the structures of the related sub-problems are exploited to speed up the convergence. The authors provide a large computational experience and comparisons within these methods and other general purpose optimization packages, and focus the report on the advantages of each.

Tactical design of rail freight networks. Part II: Local search methods with statistical analysis

Abstract This paper deals with the statistical study of the local search methods which we used in Part I of this work. In that part, a tactical planning model of the rail freight transportation was defined as a network design model. Different local search methods have been used to solve it: Simulated Annealing, Tabu Search and a ‘Descent’ method. The solution and method convergence depends on the initial feasible solution and the convexity of the feasible region, so the comparison among them will be made with the help of statistical theory. Assuming the hypothesis that the distribution of local minima can be represented by the Weibull distribution, it is possible to obtain an approach to the global minimum and a confidence interval of this. The global minimum estimation has been used to compare the heuristic methods and the parameters for a given heuristic, and to obtain a stopping criterion.

Urban rapid transit network design: accelerated Benders decomposition

This paper presents an urban rapid transit network design model, which consists of the location of train alignments and stations in an urban traffic context. The design attempts to maximize the public transportation demand using the new infrastructure, considering a limited budget and number of transit lines. The location problem also incorporates the fact that users can choose their transportation mode and trips. In real cases, this problem is complex to solve because it has thousands of binary variables and constraints, and cannot be solved efficiently by Branch and Bound. For this reason, some algorithms based on Benders decomposition have been defined in order to solve it. These algorithms have been compared in test networks.

Urban Multimodal Interchange Design Methodology

In this paper an Urban Multimodal Interchange Design model is proposed, which considers simultaneously the interchange location problem in a main transit network and the design problem of a secondary transit network which feeds the interchanges, at strategical level. The problem of the design of these interchange facilities, such as the capacity and fares of parking lots is also considered at tactical level. The problem has been formulated by means of a bi-level model. At upper level the design decisions are considered and at lower level, the combined multimodal demand share. To solve this some heuristic algorithms based on the simulating annealing and greedy techniques have been proposed. Computational results in some test networks are presented.

Simultaneous estimation of the origin-destination matrices and the parameters of a nested logit model in a combined network equilibrium model

This paper deals with the inverse problem of a type of traffic equilibrium models with combined modes. This problem consists of obtaining a parametrization of the equilibrium model from a set of observations of the outputs for the model. The inputs for the model are an origin-destination (O-D) trip matrix for the various alternatives that have been considered, and a set of parameters for a nested logit model used as a demand model. This model has been formulated by using a new approach called the calibration and demand adjustment model (CDAM) based on bilevel programming which simultaneously estimates an O-D matrix and the parameters for the nested logit model. In this paper, the CDAM properties are studied and it is proved the CDAM solution exists. This paper develops a heuristic column (paths/hyperpaths) generation algorithm for the CDAM. This algorithm iterates between the network equilibrium problem and that which is used to obtain a set of paths when equilibrium is attained, and the CDAM is restricted to the set of previously generated columns (the so-called restricted CDAM). The restricted CDAM is formulated as a single level model under certain hypotheses and it furnishes a solution upon which to base a new estimation of the O-D matrix and the vector of parameters. The computational tests on the algorithm have been carried out using data from a multi-modal network in Madrid.

New algorithmic alternatives for the O-D matrix adjustment problem on traffic networks

Abstract In the last years the O–D matrix adjustment problem using link counts on a traffic network modelled by means of a static user equilibrium approach has been formulated advantageously by means of bilevel programs. The algorithms developed to solve the problem present heuristic components in a lesser or greater degree. In this paper two new algorithmic alternatives are presented for this problem. The first alternative is an hybrid scheme proximal point-steepest descent that is based on a development of Codina for the approximation of the steepest descent direction of the upper level function and the second alternative is developed by Garcia and Marin and consists of solving a sequence of simplified bilevel programs. In order to highlight the characteristics of the two methods a set of test problems have been solved in conjunction with other well known methods, such as the method of Spiess, the method of Chan, the method of Yang as well as with an adaptation of the Wolfe’s conjugate directions method for non-differentiable optimization, in order to provide a better perspective of their advantages and tradeoffs.