Multinomial values were previously introduced by one of the authors in reliability and extended later to all cooperative games. Here, we present for this subfamily of probabilistic values three new results, previously stated only for binomial semivalues in the literature. They concern the dimension of the subspace spanned by the multinomial values and two characterizations: one, individual, for each multinomial value; another, collective, for the whole subfamily they form. Finally, an application to simple games is provided
This is a post-peer-review, pre-copyedit version of an article published in "TOP". The final authenticated version is available online at: https://doi.org/10.1007/s11750-017-0464-1
We focus on generalized mixed modified semivalues, a family of coalitional values. They apply to games with a coalition structure by combining a (induced) semivalue in the quotient game, but share within each union the payoff so obtained by applying different (induced) semivalues to a game that concerns only the players of that union. A computation procedure in terms of the multilinear extension of the original game is also provided and an application to the Catalan Parliament (legislature 2012-2016) is shown
The final publication is available at Springer via http://dx.doi.org/10.1007/s11750-014-0356-6”.
Several relationships between simple games and a particular type of solu-
tions for cooperative games are studied in this paper. These solutions belong to the
set of semivalues and they are related to a unique parameter that explicitly provides
their weighting coefficients. Through the allocations offered by this family of solu-
tions, so-called binomial semivalues, and also from their respective potentials, some
characteristics of the simple games can be recovered. The paper analyzes the capacity
of binomial semivalues to summarize the structure of simple games, and, moreover,
a property of separation among simple games is given.
On current electricity markets the electrical utilities are faced with very sophisticated decision making problems under uncertainty. Moreover, when focusing in the short-term management, generation companies must include some medium-term products that directly influence their short-term strategies. In this work, the bilateral and physical futures contracts are included into the day-ahead market bid following MIBEL rules and a stochastic quadratic mixed-integer programming model is presented. The complexity of this stochastic programming problem makes unpractical the resolution of large-scale instances with general-purpose optimization codes. Therefore, in order to gain efficiency, a polyhedral outer approximation of the quadratic objective function obtained by means of perspective cuts (PC) is proposed. A set of instances of the problem has been defined with real data and solved with the PC methodology. The numerical results obtained show the efficiency of this methodology compared with standard mixed quadratic optimization solvers.
The purpose of the field of statistical disclosure control is to avoid that confidential information could be derived from statistical data released by, mainly, national statistical agencies. Controlled tabular adjustment (CTA) is an emerging technique for the protection of statistical tabular data. Given a table with sensitive information, CTA looks for the closest safe table. In this work we focus on CTA for three-dimensional tables using the L 1 norm for the distance between the original and protected tables. Three L 1-CTA models are presented, giving rise to six different primal block-angular structures of the constraint matrices. The resulting linear programming problems are solved by a specialized interior-point algorithm for this constraints structure which solves the normal equations by a combination of Cholesky factorization and preconditioned conjugate gradients (PCG). In the past this algorithm was shown to be one of the most efficient approaches for some classes of block-angular problems. The effect of quadratic regularizations is also analyzed, showing that for three of the six primal block-angular structures the performance of PCG is guaranteed to improve. Computational results are reported for a set of large instances, which provide linear optimization problems of up to 50 million variables and 25 million constraints. The specialized interior-point algorithm is compared with the state-of-the-art barrier solver of the CPLEX 12.1 package, showing to be a more efficient choice for very large L 1-CTA instances.
n this paper, a mathematical programming model and a heuristically derived solution is described to assist with the efficient planning of services for a set of auxiliary bus lines (a bus-bridging system) during disruptions of metro and rapid transit lines. The model can be considered static and takes into account the average flows of passengers over a given period of time (i.e., the peak morning traffic hour). Auxiliary bus services must accommodate very high demand levels, and the model presented is able to take into account the operation of a bus-bridging system under congested conditions. A general analysis of the congestion in public transportation lines is presented, and the results are applied to the design of a bus-bridging system. A nonlinear integer mathematical programming model and a suitable approximation of this model are then formulated. This approximated model can be solved by a heuristic procedure that has been shown to be computationally viable. The output of the model is as follows: (a) the number of bus units to assign to each of the candidate lines of the bus-bridging system; (b) the routes to be followed by users passengers of each of the origin–destination pairs; (c) the operational conditions of the components of the bus-bridging system, including the passenger load of each of the line segments, the degree of saturation of the bus stops relative to their bus input flows, the bus service times at bus stops and the passenger waiting times at bus stops. The model is able to take into account bounds with regard to the maximum number of passengers waiting at bus stops and the space available at bus stops for the queueing of bus units. This paper demonstrates the applicability of the model with two realistic test cases: a railway corridor in Madrid and a metro line in Barcelona.
This paper discusses the use of probabilistic or randomized algorithms for solving vehicle routing problems with non-smooth objective functions. Our approach employs non-uniform probability distributions to add a biased random behavior to the well-known savings heuristic. By doing so, a large set of alternative good solutions can be quickly obtained in a natural way and without complex configuration processes. Since the solution-generation process is based on the criterion of maximizing the savings, it does not need to assume any particular property of the objective function. Therefore, the procedure can be especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods—both of exact and approximate nature—may fail to reach their full potential. The results obtained so far are promising enough to suggest that the idea of using biased probability distributions to randomize classical heuristics is a powerful one that can be successfully applied in a variety of cases.
This paper considers the Optimum Communication Spanning Tree Problem.
An integer programming formulation that yields tight LP bounds is proposed.
Given that the computational effort required to obtain the LP bounds considerably
increases with the size of the instances when using commercial solvers, we propose
a Lagrangean relaxation that exploits the structure of the formulation. Since feasible
solutions to the Lagrangean function are spanning trees, upper bounds are also obtained.
These bounds are later improved with a simple local search. Computational
experiments have been run on several benchmark instances from the literature. The
results confirm the interest of the proposal since tight lower and upper bounds are
obtained, for instances up to 100 nodes, in competitive computational times.
We study here the protectionist role of blocking coalitions in a voting game. More precisely, we first present necessary properties that a family of coalitions must satisfy in order to be the blocking family of some game and show that they are sufficient conditions too. Furthermore, a procedure to determine all games having a given blocking family is provided. With regard to uniqueness and multiplicity, (a) the blocking families that univocally determine the game are characterized by means of a separation condition, and (b) it is shown that in the nonseparating case at least three games share each nonempty blocking family, and an upper bound is given for the number of such games. Some numerical examples illustrate our results. Finally, power indices related to the blocking structure are discussed.
Several families of objective functions for the PRV problem (minimizing the variation in the rate at which different products are produced on an assembly line) are formalized, relationships between them are established and it is demonstrated that, in very general conditions, they can be optimized by solving an assignment problem or a polynomially bounded sequence of assignment problems.