Federico Perea

Revisiting a game theoretic framework for the robust railway network design against intentional attacks

This paper discusses and extends some competitive aspects of the games proposed in an earlier work, where a robust railway network design problem was proposed as a non-cooperative zero-sum game in normal form between a designer/operator and an attacker. Due to the importance of the order of play and the information available to the players at the moment of their decisions, we here extend those previous models by proposing a formulation of this situation as a dynamic game. Besides, we propose a new mathematical programming model that optimizes both the network design and the allocation of security resources over the network. The paper also proposes a model to distribute security resources over an already existing railway network in order to minimize the negative effects of an intentional attack. For the sake of readability, all concepts are introduced with the help of an illustrative example.

Modeling cooperation on a class of distribution problems

In this paper we study models of cooperation between the nodes of a network that represents a distribution problem. The distribution problem we propose arises when, over a graph, a group of nodes offers certain commodity, some other nodes require it and a third group of nodes neither need this material nor offer it but they are strategically relevant to the distribution plan. The delivery of one unit of material to a demand node generates a fixed profit, and the shipping of the material through the arcs has an associated cost. We show that in such a framework cooperation is beneficial for the different parties. We prove that the cooperative situation arising from this distribution problem is totally balanced by finding a set of stable allocations (in the core of an associated cooperative game). In order to overcome certain fairness problems of these solutions, we introduce two new solution concepts and study their properties.

Integrating Robust Railway Network Design and Line Planning under Failures

Traditionally, when designing robust transportation systems, one wants to increase the functionality of the system in presence of failures, even though they might not work optimally when no failures occur, which is the usual case. In this paper we make an attempt to integrate robust network design and line planning without decreasing the efficiency of the system when no failures occur. Therefore, extra costs must be met (price of robustness). Two different concepts of robustness are considered: one from the users point of view, which aims at minimizing total travel time, and one from the operators point of view, which aims at minimizing extra costs, both assuming possible disruptions.

Finding the nucleolus of any n-person cooperative game by a single linear program

Abstract In this paper we show a new method for calculating the nucleolus by solving a unique minimization linear program with O ( 4 n ) constraints whose coefficients belong to { − 1 , 0 , 1 } . We discuss the need of having all these constraints and empirically prove that they can be reduced to O ( k max 2 n ) , where kmax is a positive integer comparable with the number of players. A computational experience shows the applicability of our method over (pseudo)random transferable utility cooperative games with up to 18 players.

Models and matheuristics for the unrelated parallel machine scheduling problem with additional resources

In this paper we analyze a parallel machine scheduling problem in which the processing of jobs on the machines requires a number of units of a scarce resource. This number depends both on the job and on the machine. The availability of resources is limited and fixed throughout the production horizon. The objective considered is the minimization of the makespan. We model this problem by means of two integer linear programming problems. One of them is based on a model previously proposed in the literature. The other one, which is based on the resemblance to strip packing problems, is an original contribution of this paper. As the models presented are incapable of solving medium-sized instances to optimality, we propose three matheuristic strategies for each of these two models. The algorithms proposed are tested over an extensive computational experience. Results show that the matheuristic strategies significantly outperform the mathematical models.

A cooperative location game based on the 1-center location problem

In this paper we introduce and analyze new classes of cooperative games related to facility location models defined on general metric spaces. The players are the customers (demand points) in the location problem and the characteristic value of a coalition is the cost of serving its members. Specifically, the cost in our games is the service radius of the coalition. We call these games the Minimum Radius Location Games (MRLG). We study the existence of core allocations and the existence of polynomial representations of the cores of these games, focusing on network spaces, i.e., finite metric spaces induced by undirected graphs and positive edge lengths, and on the lp metric spaces defined over .

Cooperative location games based on the minimum diameter spanning Steiner subgraph problem

In this paper we introduce and analyze new classes of cooperative games related to facility location models. The players are the customers (demand points) in the location problem and the characteristic value of a coalition is the cost of serving its members. Specifically, the cost in our games is the service diameter of the coalition. We study the existence of core allocations for these games, focusing on network spaces, i.e., finite metric spaces induced by undirected graphs and positive edge lengths.

Dynamic programming analysis of the TV game "Who wants to be a millionaire?"

Abstract This paper uses dynamic programming to investigate when contestants should use lifelines or when they should just stop answering in the TV quiz show ‘Who wants to be a millionaire?’. It obtains the optimal strategies to maximize the expected reward and to maximize the probability of winning a given amount of money.

GRASP algorithms for the robust railway network design problem

This paper analyzes the solvability of a railway network design problem and its robust version. These problems are modeled as integer linear programming problems with binary variables, and their solutions provide topological railway networks maximizing the trip coverage in the presence of a competing mode, both assuming that the network works fine and that links can fail, respectively. Since these problems are computationally intractable for realistic sizes, GRASP heuristics are proposed for finding good feasible solutions. The results obtained in a computational experience indicate that our GRASP algorithms are suitable for railway network design problems.

Greedy and

The multidimensional assignment (MDA) problem is a combinatorial optimization problem arising in many applications, for instance multitarget tracking (MTT). The objective of an MDA problem of dimension d ∈ N is to match groups of d objects in such a way that each measurement is associated with at most one track and each track is associated with at most one measurement from each list, optimizing a certain objective function. It is well known that the MDA problem is NP-hard for d ≥ 3. In this paper five new polynomial time heuristics to solve the MDA problem arising in MTT are presented. They are all based on the semi-greedy approach introduced in earlier research. Experimental results on the accuracy and speed of the proposed algorithms in MTT problems are provided.