Articles de revista
http://hdl.handle.net/2117/3321
Mon, 26 Sep 2016 14:06:42 GMT
20160926T14:06:42Z

Interiorpoint solver for convex separable blockangular problems
http://hdl.handle.net/2117/90150
Interiorpoint solver for convex separable blockangular problems
Castro Pérez, Jordi
Constraints matrices with blockangular structures are pervasive in optimization. Interiorpoint methods have shown to be competitive for these structured problems by exploiting the linear algebra. One of these approaches solves the normal equations using sparse Cholesky factorizations for the block constraints, and a reconditioned conjugate gradient (PCG) for the linking constraints. The preconditioner is based on a power series expansion which approximates the inverse of the matrix of the linking constraints system. In this work, we present an efficient solver based on this algorithm. Some of its features are as follows: it solves linearly constrained convex separable problems (linear, quadratic or nonlinear); both Newton and secondorder predictor–corrector directions can be used, either with the Cholesky+PCG scheme or with a Cholesky factorization of normal equations; the preconditioner may include any number of terms of the power series; for any number of these terms, it estimates the spectral radius of the matrix in the power series (which is instrumental for the quality of the preconditioner). The solver has been hooked to the structureconveying modelling language (SML) based on the popular AMPL modeling language. Computational results are reported for some large and/or difficult instances in the literature: (1) multicommodity flow problems; (2) minimum congestion problems; (3) statistical data protection problems using and distances (which are linear and quadratic problems, respectively), and the pseudoHuber function, a nonlinear approximation to which improves the preconditioner. In the largest instances, of up to 25 millions of variables and 300,000 constraints, this approach is from 2 to 3 orders of magnitude faster than stateoftheart linear and quadratic optimization solvers.
Thu, 22 Sep 2016 15:31:40 GMT
http://hdl.handle.net/2117/90150
20160922T15:31:40Z
Castro Pérez, Jordi
Constraints matrices with blockangular structures are pervasive in optimization. Interiorpoint methods have shown to be competitive for these structured problems by exploiting the linear algebra. One of these approaches solves the normal equations using sparse Cholesky factorizations for the block constraints, and a reconditioned conjugate gradient (PCG) for the linking constraints. The preconditioner is based on a power series expansion which approximates the inverse of the matrix of the linking constraints system. In this work, we present an efficient solver based on this algorithm. Some of its features are as follows: it solves linearly constrained convex separable problems (linear, quadratic or nonlinear); both Newton and secondorder predictor–corrector directions can be used, either with the Cholesky+PCG scheme or with a Cholesky factorization of normal equations; the preconditioner may include any number of terms of the power series; for any number of these terms, it estimates the spectral radius of the matrix in the power series (which is instrumental for the quality of the preconditioner). The solver has been hooked to the structureconveying modelling language (SML) based on the popular AMPL modeling language. Computational results are reported for some large and/or difficult instances in the literature: (1) multicommodity flow problems; (2) minimum congestion problems; (3) statistical data protection problems using and distances (which are linear and quadratic problems, respectively), and the pseudoHuber function, a nonlinear approximation to which improves the preconditioner. In the largest instances, of up to 25 millions of variables and 300,000 constraints, this approach is from 2 to 3 orders of magnitude faster than stateoftheart linear and quadratic optimization solvers.

A cuttingplane approach for largescale capacitated multiperiod facility location using a specialized interiorpoint method
http://hdl.handle.net/2117/90149
A cuttingplane approach for largescale capacitated multiperiod facility location using a specialized interiorpoint method
Castro Pérez, Jordi; Nasini, Stefano; Saldanha da Gama, Francisco
We propose a cuttingplane approach (namely, Benders decomposition) for a class of capacitated multiperiod facility location problems. The novelty of this approach lies on the use of a specialized interiorpoint method for solving the Benders subproblems. The primal blockangular structure of the resulting linear optimization
problems is exploited by the interiorpoint method, allowing the (either exact or inexact) efficient solution of large instances. The consequences of different modeling
conditions and problem specifications on the computational performance are also investigated both theoretically and empirically, providing a deeper understanding of the significant factors influencing the overall efficiency of the cuttingplane method.
The methodology proposed allowed the solution of instances of up to 200 potential locations, one million customers and three periods, resulting in mixed integer linear optimization problems of up to 600 binary and 600 millions of continuous variables. Those problems were solved by the specialized approach in less than one hour and a half, outperforming other stateoftheart methods, which exhausted the (144 Gigabytes of) available memory in the largest instances.
Thu, 22 Sep 2016 15:07:07 GMT
http://hdl.handle.net/2117/90149
20160922T15:07:07Z
Castro Pérez, Jordi
Nasini, Stefano
Saldanha da Gama, Francisco
We propose a cuttingplane approach (namely, Benders decomposition) for a class of capacitated multiperiod facility location problems. The novelty of this approach lies on the use of a specialized interiorpoint method for solving the Benders subproblems. The primal blockangular structure of the resulting linear optimization
problems is exploited by the interiorpoint method, allowing the (either exact or inexact) efficient solution of large instances. The consequences of different modeling
conditions and problem specifications on the computational performance are also investigated both theoretically and empirically, providing a deeper understanding of the significant factors influencing the overall efficiency of the cuttingplane method.
The methodology proposed allowed the solution of instances of up to 200 potential locations, one million customers and three periods, resulting in mixed integer linear optimization problems of up to 600 binary and 600 millions of continuous variables. Those problems were solved by the specialized approach in less than one hour and a half, outperforming other stateoftheart methods, which exhausted the (144 Gigabytes of) available memory in the largest instances.

A mathematical programming approach for different scenarios of bilateral bartering
http://hdl.handle.net/2117/85754
A mathematical programming approach for different scenarios of bilateral bartering
Nasini, Stefano; Castro Pérez, Jordi; Fonseca Casas, Pau
The analysis of markets with indivisible goods and fixed exogenous prices has played an important role in economic models, especially in relation to wage rigidity and unemployment. This paper provides a novel mathematical programming based approach to study pure exchange economies where discrete amounts of commodities are exchanged at fixed prices. Barter processes, consisting in sequences of elementary reallocations of couple of commodities among couples of agents, are formalized as local searches converging to equilibrium allocations. A direct application of the analysed processes in the context of computational economics is provided, along with a Java implementation of the described approaches.
Fri, 15 Apr 2016 15:03:14 GMT
http://hdl.handle.net/2117/85754
20160415T15:03:14Z
Nasini, Stefano
Castro Pérez, Jordi
Fonseca Casas, Pau
The analysis of markets with indivisible goods and fixed exogenous prices has played an important role in economic models, especially in relation to wage rigidity and unemployment. This paper provides a novel mathematical programming based approach to study pure exchange economies where discrete amounts of commodities are exchanged at fixed prices. Barter processes, consisting in sequences of elementary reallocations of couple of commodities among couples of agents, are formalized as local searches converging to equilibrium allocations. A direct application of the analysed processes in the context of computational economics is provided, along with a Java implementation of the described approaches.

Importancia de la potencia y la hipótesis en el valor p
http://hdl.handle.net/2117/85046
Importancia de la potencia y la hipótesis en el valor p
Cortés Martínez, Jordi; Casals, Martí; Langohr, Klaus; González Alastrué, José Antonio
Los lectores de Medicina Clínica conocen bien la importancia de definir bien el denominador de una proporción para estimar una probabilidad: “No es lo mismo la probabilidad de que un católico sea Papa que la de que un Papa sea católico”. De forma similar, en un diagnóstico, no es lo mismo la probabilidad de que un enfermo dé positivo (sensibilidad), que la de que un caso que ha dado positivo esté enfermo (valor predictivo de un positivo).
El valor p (o valor de p, o pvalor, o simplemente p) guarda cierta analogía con las probabilidades diagnósticas, ya que se define como la probabilidad de obtener un resultado tan significativo o más que el observado —dar positivo en la prueba diagnóstica— asumiendo cierta una hipótesis H: el paciente está sano. No obstante, a un investigador o a un clínico le puede resultar más interesante conocer el valor positivo de una prueba: cuán probable es una hipótesis H —que el paciente esté enfermo— habiendo observado unos resultados extremos.
Fri, 01 Apr 2016 10:51:58 GMT
http://hdl.handle.net/2117/85046
20160401T10:51:58Z
Cortés Martínez, Jordi
Casals, Martí
Langohr, Klaus
González Alastrué, José Antonio
Los lectores de Medicina Clínica conocen bien la importancia de definir bien el denominador de una proporción para estimar una probabilidad: “No es lo mismo la probabilidad de que un católico sea Papa que la de que un Papa sea católico”. De forma similar, en un diagnóstico, no es lo mismo la probabilidad de que un enfermo dé positivo (sensibilidad), que la de que un caso que ha dado positivo esté enfermo (valor predictivo de un positivo).
El valor p (o valor de p, o pvalor, o simplemente p) guarda cierta analogía con las probabilidades diagnósticas, ya que se define como la probabilidad de obtener un resultado tan significativo o más que el observado —dar positivo en la prueba diagnóstica— asumiendo cierta una hipótesis H: el paciente está sano. No obstante, a un investigador o a un clínico le puede resultar más interesante conocer el valor positivo de una prueba: cuán probable es una hipótesis H —que el paciente esté enfermo— habiendo observado unos resultados extremos.

Scheduling policies for multiperiod services
http://hdl.handle.net/2117/84649
Scheduling policies for multiperiod services
Núñez del Toro, Alma Cristina; Fernández Aréizaga, Elena; Kalcsics, Jörg; Nickel, Stefan
This paper discusses a multiperiod service scheduling problem. In this problem, a set of customers is given who periodically require service over a finite time horizon. To satisfy the service demands, a set of operators is given, each with a fixed capacity in terms of the number of customers an operator can serve per period. The task is to determine for each customer the periods in which he will be visited by an operator such that the periodic service requests of the customers are adhered to and the total number of operators used over the time horizon is minimal. Two alternative policies for scheduling customer visits are considered. In the first one, a customer is visited just on time, i.e., in the period where he or she has a demand for service. The second policy allows service visits ahead of time. The rationale behind this policy is that allowing irregular visits may reduce the overall number of operators needed throughout the time horizon. To solve the problem, integer linear programming formulations are proposed for both policies and numerical experiments are presented that show the reduction in the number of operators used when visits ahead of time are allowed. As only small instances can be solved optimally, a heuristic algorithm is introduced in order to obtain good quality solutions and shorter computing times.
Thu, 17 Mar 2016 15:09:08 GMT
http://hdl.handle.net/2117/84649
20160317T15:09:08Z
Núñez del Toro, Alma Cristina
Fernández Aréizaga, Elena
Kalcsics, Jörg
Nickel, Stefan
This paper discusses a multiperiod service scheduling problem. In this problem, a set of customers is given who periodically require service over a finite time horizon. To satisfy the service demands, a set of operators is given, each with a fixed capacity in terms of the number of customers an operator can serve per period. The task is to determine for each customer the periods in which he will be visited by an operator such that the periodic service requests of the customers are adhered to and the total number of operators used over the time horizon is minimal. Two alternative policies for scheduling customer visits are considered. In the first one, a customer is visited just on time, i.e., in the period where he or she has a demand for service. The second policy allows service visits ahead of time. The rationale behind this policy is that allowing irregular visits may reduce the overall number of operators needed throughout the time horizon. To solve the problem, integer linear programming formulations are proposed for both policies and numerical experiments are presented that show the reduction in the number of operators used when visits ahead of time are allowed. As only small instances can be solved optimally, a heuristic algorithm is introduced in order to obtain good quality solutions and shorter computing times.

Hybrid ACDC offshore wind power plant topology: optimal design
http://hdl.handle.net/2117/83730
Hybrid ACDC offshore wind power plant topology: optimal design
Prada Gil, Mikel de; Igualada González, Lucía; Corchero García, Cristina; Gomis Bellmunt, Oriol; Sumper, Andreas
The aim of this paper is to present a hybrid ACDC offshore wind power plant (OWPP) topology and to optimize its design in order to minimize the OWPP's total cost. This hybrid concept is based on clustering wind turbines and connecting each group to an AC/DC power converter installed on a collector platform which is located between the AC wind turbine array and the HVDC offshore platform. Thereby, individual power converters of each wind turbine are not required, since such AC/DC converters can provide variable speed generator control for each cluster. The optimal design for an OWPP based on the hybrid ACDC topology is formulated as a MINLP problem. The capital costs of each component within the OWPP as well as the costs associated to the inherent losses of this topology are minimized. The optimal number of AC/DC converters and offshore collector platforms needed, as well as their locations, are determined. The cable route connecting the wind turbines between each other is also optimized. The results suggests a good potential for the hybrid ACDC OWPP topology achieving a total cost saving of 3.76% for the case study compared to the conventional OWPP topology.
Wed, 02 Mar 2016 18:34:17 GMT
http://hdl.handle.net/2117/83730
20160302T18:34:17Z
Prada Gil, Mikel de
Igualada González, Lucía
Corchero García, Cristina
Gomis Bellmunt, Oriol
Sumper, Andreas
The aim of this paper is to present a hybrid ACDC offshore wind power plant (OWPP) topology and to optimize its design in order to minimize the OWPP's total cost. This hybrid concept is based on clustering wind turbines and connecting each group to an AC/DC power converter installed on a collector platform which is located between the AC wind turbine array and the HVDC offshore platform. Thereby, individual power converters of each wind turbine are not required, since such AC/DC converters can provide variable speed generator control for each cluster. The optimal design for an OWPP based on the hybrid ACDC topology is formulated as a MINLP problem. The capital costs of each component within the OWPP as well as the costs associated to the inherent losses of this topology are minimized. The optimal number of AC/DC converters and offshore collector platforms needed, as well as their locations, are determined. The cable route connecting the wind turbines between each other is also optimized. The results suggests a good potential for the hybrid ACDC OWPP topology achieving a total cost saving of 3.76% for the case study compared to the conventional OWPP topology.

A novel model for arc territory design: promoting Eulerian districts
http://hdl.handle.net/2117/82920
A novel model for arc territory design: promoting Eulerian districts
Garcia Ayala, Gariela; González Velarde, José Luis; Rios Mercados, Roger; Fernández Aréizaga, Elena
The problem of district design for the implementation of arc routing activities is addressed. The aim is to partition a road network into a given number of sectors to facilitate the organization of the operations to be implemented within the region. This problem arises in numerous applications such as postal delivery, meter readings, winter gritting, road maintenance, and municipal solid waste collection. An integer linear programming model is proposed where a novel set of node parity constraints to favor Eulerian districts is introduced. Series of instances were solved to assess the impact of these parity constraints on the objective function and deadhead distance. Networks with up to 401 nodes and 764 edges were successfully solved. The model is useful at a tactical level as it can be used to promote workload balance, compactness, deadhead distance reduction and parity in districts.
Mon, 15 Feb 2016 12:00:47 GMT
http://hdl.handle.net/2117/82920
20160215T12:00:47Z
Garcia Ayala, Gariela
González Velarde, José Luis
Rios Mercados, Roger
Fernández Aréizaga, Elena
The problem of district design for the implementation of arc routing activities is addressed. The aim is to partition a road network into a given number of sectors to facilitate the organization of the operations to be implemented within the region. This problem arises in numerous applications such as postal delivery, meter readings, winter gritting, road maintenance, and municipal solid waste collection. An integer linear programming model is proposed where a novel set of node parity constraints to favor Eulerian districts is introduced. Series of instances were solved to assess the impact of these parity constraints on the objective function and deadhead distance. Networks with up to 401 nodes and 764 edges were successfully solved. The model is useful at a tactical level as it can be used to promote workload balance, compactness, deadhead distance reduction and parity in districts.

On the collaboration uncapacitated arc routing problem
http://hdl.handle.net/2117/81939
On the collaboration uncapacitated arc routing problem
Fernández Aréizaga, Elena; Fontana, Dario; Speranza, M. Grazia
© 2015 Elsevier Ltd. All rights reserved.
This paper introduces a new arc routing problem for the optimization of a collaboration scheme among carriers. This yields to the study of a profitable uncapacitated arc routing problem with multiple depots, where carriers collaborate to improve the profit gained. In the first model the goal is the maximization of the total profit of the coalition of carriers, independently of the individual profit of each carrier. Then, a lower bound on the individual profit of each carrier is included. This lower bound may represent the profit of the carrier in the case no collaboration is implemented. The models are formulated as integer linear programs and solved through a branchandcut algorithm. Theoretical results, concerning the computational complexity, the impact of collaboration on profit and a game theoretical perspective, are provided. The models are tested on a set of 971 instances generated from 118 benchmark instances for the Privatized Rural Postman Problem, with up to 102 vertices. All the 971 instances are solved to optimality within few seconds.
Mon, 25 Jan 2016 09:33:18 GMT
http://hdl.handle.net/2117/81939
20160125T09:33:18Z
Fernández Aréizaga, Elena
Fontana, Dario
Speranza, M. Grazia
© 2015 Elsevier Ltd. All rights reserved.
This paper introduces a new arc routing problem for the optimization of a collaboration scheme among carriers. This yields to the study of a profitable uncapacitated arc routing problem with multiple depots, where carriers collaborate to improve the profit gained. In the first model the goal is the maximization of the total profit of the coalition of carriers, independently of the individual profit of each carrier. Then, a lower bound on the individual profit of each carrier is included. This lower bound may represent the profit of the carrier in the case no collaboration is implemented. The models are formulated as integer linear programs and solved through a branchandcut algorithm. Theoretical results, concerning the computational complexity, the impact of collaboration on profit and a game theoretical perspective, are provided. The models are tested on a set of 971 instances generated from 118 benchmark instances for the Privatized Rural Postman Problem, with up to 102 vertices. All the 971 instances are solved to optimality within few seconds.

A BRILS metaheuristic for nonsmooth flowshop problems with failurerisk costs
http://hdl.handle.net/2117/81738
A BRILS metaheuristic for nonsmooth flowshop problems with failurerisk costs
Ferrer Biosca, Alberto; Guimarans, Daniel; Ramalhino Lourenço, Helena; Juan Pérez, Ángel Alejandro
This paper analyzes a realistic variant of the Permutation FlowShop Problem (PFSP) by considering a nonsmooth objective function that takes into account not only the traditional makespan cost but also failurerisk costs due to uninterrupted operation of machines. After completing a literature review on the issue, the paper formulates an original mathematical model to describe this new PFSP variant. Then, a BiasedRandomized Iterated Local Search (BRILS) algorithm is proposed as an efficient solving approach. An oriented (biased) random behavior is introduced in the wellknown NEH heuristic to generate an initial solution. From this initial solution, the algorithm is able to generate a large number of alternative good solutions without requiring a complex setting of parameters. The relative simplicity of our approach is particularly useful in the presence of nonsmooth objective functions, for which exact optimization methods may fail to reach their full potential. The gains of considering failurerisk costs during the exploration of the solution space are analyzed throughout a series of computational experiments. To promote reproducibility, these experiments are based on a set of traditional benchmark instances. Moreover, the performance of the proposed algorithm is compared against other stateoftheart metaheuristic approaches, which have been conveniently adapted to consider failurerisk costs during the solving process. The proposed BRILS approach can be easily extended to other combinatorial optimization problems with similar nonsmooth objective functions.
Wed, 20 Jan 2016 13:51:16 GMT
http://hdl.handle.net/2117/81738
20160120T13:51:16Z
Ferrer Biosca, Alberto
Guimarans, Daniel
Ramalhino Lourenço, Helena
Juan Pérez, Ángel Alejandro
This paper analyzes a realistic variant of the Permutation FlowShop Problem (PFSP) by considering a nonsmooth objective function that takes into account not only the traditional makespan cost but also failurerisk costs due to uninterrupted operation of machines. After completing a literature review on the issue, the paper formulates an original mathematical model to describe this new PFSP variant. Then, a BiasedRandomized Iterated Local Search (BRILS) algorithm is proposed as an efficient solving approach. An oriented (biased) random behavior is introduced in the wellknown NEH heuristic to generate an initial solution. From this initial solution, the algorithm is able to generate a large number of alternative good solutions without requiring a complex setting of parameters. The relative simplicity of our approach is particularly useful in the presence of nonsmooth objective functions, for which exact optimization methods may fail to reach their full potential. The gains of considering failurerisk costs during the exploration of the solution space are analyzed throughout a series of computational experiments. To promote reproducibility, these experiments are based on a set of traditional benchmark instances. Moreover, the performance of the proposed algorithm is compared against other stateoftheart metaheuristic approaches, which have been conveniently adapted to consider failurerisk costs during the solving process. The proposed BRILS approach can be easily extended to other combinatorial optimization problems with similar nonsmooth objective functions.

Mathematical programming approaches for classes of random network problems
http://hdl.handle.net/2117/81111
Mathematical programming approaches for classes of random network problems
Castro Pérez, Jordi; Nasini, Stefano
Random simulations from complicated combinatorial sets are often needed in many classes of stochastic problems. This is particularly true in the analysis of complex networks, where researchers are usually interested in assessing whether an observed network feature is expected to be found within families of networks under some hypothesis (named conditional random networks, i.e., networks satisfying some linear constraints). This work presents procedures to generate networks with specified structural properties which rely on the Solution of classes of integer optimization problems. We show that, for many of them, the constraints matrices are totally unimodular, allowing the efficient generation of conditional random networks by specialized interiorpoint methods. The computational results suggest that the proposed methods can represent a general framework for the efficient generation of random networks even beyond the models analyzed in this paper. This work also opens the posSibility for other applications of mathematical programming in the analysis of complex networks. (C) 2015 Elsevier B.V. All rights reserved.
Thu, 07 Jan 2016 16:32:22 GMT
http://hdl.handle.net/2117/81111
20160107T16:32:22Z
Castro Pérez, Jordi
Nasini, Stefano
Random simulations from complicated combinatorial sets are often needed in many classes of stochastic problems. This is particularly true in the analysis of complex networks, where researchers are usually interested in assessing whether an observed network feature is expected to be found within families of networks under some hypothesis (named conditional random networks, i.e., networks satisfying some linear constraints). This work presents procedures to generate networks with specified structural properties which rely on the Solution of classes of integer optimization problems. We show that, for many of them, the constraints matrices are totally unimodular, allowing the efficient generation of conditional random networks by specialized interiorpoint methods. The computational results suggest that the proposed methods can represent a general framework for the efficient generation of random networks even beyond the models analyzed in this paper. This work also opens the posSibility for other applications of mathematical programming in the analysis of complex networks. (C) 2015 Elsevier B.V. All rights reserved.