GNOM - Grup d´Optimització Numèrica i Modelització
http://hdl.handle.net/2117/3320
2016-09-24T22:47:59ZInterior-point solver for convex separable block-angular problems
http://hdl.handle.net/2117/90150
Interior-point solver for convex separable block-angular problems
Castro Pérez, Jordi
Constraints matrices with block-angular structures are pervasive in optimization. Interior-point 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 second-order 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 structure-conveying 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 pseudo-Huber 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 state-of-the-art linear and quadratic optimization solvers.
2016-09-22T15:31:40ZCastro Pérez, JordiConstraints matrices with block-angular structures are pervasive in optimization. Interior-point 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 second-order 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 structure-conveying 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 pseudo-Huber 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 state-of-the-art linear and quadratic optimization solvers.A cutting-plane approach for large-scale capacitated multi-period facility location using a specialized interior-point method
http://hdl.handle.net/2117/90149
A cutting-plane approach for large-scale capacitated multi-period facility location using a specialized interior-point method
Castro Pérez, Jordi; Nasini, Stefano; Saldanha da Gama, Francisco
We propose a cutting-plane approach (namely, Benders decomposition) for a class of capacitated multi-period facility location problems. The novelty of this approach lies on the use of a specialized interior-point method for solving the Benders subproblems. The primal block-angular structure of the resulting linear optimization
problems is exploited by the interior-point 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 cutting-plane 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 state-of-the-art methods, which exhausted the (144 Gigabytes of) available memory in the largest instances.
2016-09-22T15:07:07ZCastro Pérez, JordiNasini, StefanoSaldanha da Gama, FranciscoWe propose a cutting-plane approach (namely, Benders decomposition) for a class of capacitated multi-period facility location problems. The novelty of this approach lies on the use of a specialized interior-point method for solving the Benders subproblems. The primal block-angular structure of the resulting linear optimization
problems is exploited by the interior-point 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 cutting-plane 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 state-of-the-art methods, which exhausted the (144 Gigabytes of) available memory in the largest instances.Numerical implementation and computational results of nonlinear network optimization with linear side constraints
http://hdl.handle.net/2117/89385
Numerical implementation and computational results of nonlinear network optimization with linear side constraints
Heredia, F.-Javier (Francisco Javier); Nabona Francisco, Narcís
2016-08-25T13:03:53ZHeredia, F.-Javier (Francisco Javier)Nabona Francisco, NarcísOptimal location of fast charging stations in Barcelona: a flow-capturing approach
http://hdl.handle.net/2117/89381
Optimal location of fast charging stations in Barcelona: a flow-capturing approach
Cruz Zambrano, Miguel; Corchero García, Cristina; Igualada González, Lucía; Bernardo, Valeria
The aim of this paper is to find the optimal location of electric vehicle (EV) fast charging stations by means of two methodologies: a classical flow-capturing optimization model involving only mobility needs, and an advanced flow-capturing optimization model including distribution network and location costs. While the first model aims to maximize the public service provided by the fast charging stations, the second also considers the incurred cost for providing it. Results from both models are compared in order to analyse the effect of both planning approaches in total cost of installation. As a case study it has been chosen the city of Barcelona.
2016-08-24T08:57:52ZCruz Zambrano, MiguelCorchero García, CristinaIgualada González, LucíaBernardo, ValeriaThe aim of this paper is to find the optimal location of electric vehicle (EV) fast charging stations by means of two methodologies: a classical flow-capturing optimization model involving only mobility needs, and an advanced flow-capturing optimization model including distribution network and location costs. While the first model aims to maximize the public service provided by the fast charging stations, the second also considers the incurred cost for providing it. Results from both models are compared in order to analyse the effect of both planning approaches in total cost of installation. As a case study it has been chosen the city of Barcelona.A stochastic programming model for the tertiary control of microgrids
http://hdl.handle.net/2117/87023
A stochastic programming model for the tertiary control of microgrids
Citores, Leire; Corchero García, Cristina; Heredia, F.-Javier (Francisco Javier)
In this work a scenario-based two-stage stochastic programming model is proposed to solve a microgrid’s tertiary control optimization problem taking into account some renewable energy resource’s uncertainty as well as uncertain energy deviation prices in the electricity market. Scenario generation methods for wind speed realizations are also studied. Results show that the introduction of stochastic programming represents a significant improvement over a deterministic model.
2016-05-12T14:15:37ZCitores, LeireCorchero García, CristinaHeredia, F.-Javier (Francisco Javier)In this work a scenario-based two-stage stochastic programming model is proposed to solve a microgrid’s tertiary control optimization problem taking into account some renewable energy resource’s uncertainty as well as uncertain energy deviation prices in the electricity market. Scenario generation methods for wind speed realizations are also studied. Results show that the introduction of stochastic programming represents a significant improvement over a deterministic model.Potential externalities savings due to electric vehicle smart charge
http://hdl.handle.net/2117/86395
Potential externalities savings due to electric vehicle smart charge
Benveniste Pérez, Gabriela; Corchero García, Cristina; Cruz Zambrano, Miguel
This work focuses on the analysis developed in order to demonstrate how smart charging, using tailored control algorithms, contributes to minimize the environmental impact and economic costs associated to the electric vehicles under an LCA perspective. The analysis considers the Spanish grid mix profile and specific charging patterns.The LCA methodology adopted implies a comprehensive assessment of the impacts and costs occurring upstream and downstream the charging event. For the environmental analysis, the LCA impact categories are considered, while for the economic assessment, data regarding the costs associated to the electricity price and the pollutants generation have been adopted.
2016-04-28T15:17:03ZBenveniste Pérez, GabrielaCorchero García, CristinaCruz Zambrano, MiguelThis work focuses on the analysis developed in order to demonstrate how smart charging, using tailored control algorithms, contributes to minimize the environmental impact and economic costs associated to the electric vehicles under an LCA perspective. The analysis considers the Spanish grid mix profile and specific charging patterns.The LCA methodology adopted implies a comprehensive assessment of the impacts and costs occurring upstream and downstream the charging event. For the environmental analysis, the LCA impact categories are considered, while for the economic assessment, data regarding the costs associated to the electricity price and the pollutants generation have been adopted.European electric vehicle fleet: driving and charging behaviors
http://hdl.handle.net/2117/86393
European electric vehicle fleet: driving and charging behaviors
Corchero García, Cristina
The electrification of vehicles would be a reality in the coming decades. Statistical results on real electric vehicle usage data is a key point in the development of the electro mobility. A large collection of electric vehicles and charging points have been monitored during three years and the results about the driving and charging patterns are shown in this work. These results may help to develop future policies on, for instance, charging infrastructure location, end-users incentives, or to allow different type of economic analysis such as an evaluation of the electric vehicle integration in the grid, smart-charge impact…
2016-04-28T15:10:46ZCorchero García, CristinaThe electrification of vehicles would be a reality in the coming decades. Statistical results on real electric vehicle usage data is a key point in the development of the electro mobility. A large collection of electric vehicles and charging points have been monitored during three years and the results about the driving and charging patterns are shown in this work. These results may help to develop future policies on, for instance, charging infrastructure location, end-users incentives, or to allow different type of economic analysis such as an evaluation of the electric vehicle integration in the grid, smart-charge impact…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.
2016-04-15T15:03:14ZNasini, StefanoCastro Pérez, JordiFonseca Casas, PauThe 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 p-valor, 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.
2016-04-01T10:51:58ZCortés Martínez, JordiCasals, MartíLangohr, KlausGonzález Alastrué, José AntonioLos 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 p-valor, 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 multi-period services
http://hdl.handle.net/2117/84649
Scheduling policies for multi-period services
Núñez del Toro, Alma Cristina; Fernández Aréizaga, Elena; Kalcsics, Jörg; Nickel, Stefan
This paper discusses a multi-period 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.
2016-03-17T15:09:08ZNúñez del Toro, Alma CristinaFernández Aréizaga, ElenaKalcsics, JörgNickel, StefanThis paper discusses a multi-period 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.