Codis no lineals en Magma: noves construccions

L'objectiu principal d'aquest projecte és ampliar la llibreria BinaryCodes, iniciada al 2007, que ens permet construir i manipular codis binaris lineals i no lineals. Per aquest motiu, s'han desenvolupat una sèrie de funcions, amb els seus corresponents tests i exemples, en l'entorn de programació matemàtica Magma. Aquestes funcions consisteixen bàsicament en la construcció de nous codis a partir d'altres ja existents.

Improving electricity market price scenarios by means of forecasting factor models

In liberalized electricity markets, generation Companies must build an hourly bidthat is sent to the market operator. The price at which the energy will be paid is unknown during the bidding process and has to be forecast. In this work we apply forecasting factor models to this framework and study its suitability.

Optimal management of microgrids

Desenvolupament dels models matemàtics necessaris per a controlar de forma òptima la microxarxa existent als laboratoris del Institut de Recerca en Energia de Catalunya. Els algoritmes s'implementaran per tal de simular el comportament i posteriorment es programaran directament sobre els elements de la microxarxa per verificar el seu correcte funcionament.. Desenvolupament dels models matemàtics necessaris per a controlar de forma òptima la microxarxa existent als laboratoris del Institut de Recerca en Energia de Catalunya. Els algoritmes s'implementaran per tal de simular el comportament i posteriorment es programaran directament sobre els elements de la microxarxa per verificar el seu correcte funcionament.

Spanish unemployment : normative versus analytical regionalisation procedures

In applied regional analysis, statistical information is usually published at different territorial levels with the aim providing inforamtion of interest for different potential users. When using this information, there are two different choices: first, to use normative regions ( towns, provinces, etc.) or, second, to design analytical regions directly related with the analysed phenomena. In this paper, privincial time series of unemployment rates in Spain are used in order to compare the results obtained by applying yoy analytical regionalisation models ( a two stages procedure based on cluster analysis and a procedure based on mathematical programming) with the normative regions available at two different scales: NUTS II and NUTS I. The results have shown that more homogeneous regions were designed when applying both analytical regionalisation tools. Two other obtained interesting results are related with the fact that analytical regions were also more estable along time and with the effects of scales in the regionalisation process

Spanish unemployment : normative versus analytical regionalisation procedures

In applied regional analysis, statistical information is usually published at different territorial levels with the aim providing inforamtion of interest for different potential users. When using this information, there are two different choices: first, to use normative regions ( towns, provinces, etc.) or, second, to design analytical regions directly related with the analysed phenomena. In this paper, privincial time series of unemployment rates in Spain are used in order to compare the results obtained by applying yoy analytical regionalisation models ( a two stages procedure based on cluster analysis and a procedure based on mathematical programming) with the normative regions available at two different scales: NUTS II and NUTS I. The results have shown that more homogeneous regions were designed when applying both analytical regionalisation tools. Two other obtained interesting results are related with the fact that analytical regions were also more estable along time and with the effects of scales in the regionalisation process

Line search multilevel optimization as computational methods for dense optical flow

We evaluate the performance of different optimization techniques developed in the context of optical flow computation with different variational models. In particular, based on truncated Newton methods (TN) that have been an effective approach for large-scale unconstrained optimization, we de- velop the use of efficient multilevel schemes for computing the optical flow. More precisely, we evaluate the performance of a standard unidirectional mul- tilevel algorithm - called multiresolution optimization (MR/OPT), to a bidrec- tional multilevel algorithm - called full multigrid optimization (FMG/OPT). The FMG/OPT algorithm treats the coarse grid correction as an optimiza- tion search direction and eventually scales it using a line search. Experimental results on different image sequences using four models of optical flow com- putation show that the FMG/OPT algorithm outperforms both the TN and MR/OPT algorithms in terms of the computational work and the quality of the optical flow estimation.

L'estadística i els nous mitjans de càlcul

Aquesta exposició vol presentar breument el ventall d'eines disponibles, la terminologia utilitzada i, en general, el marc metodològic de l'estadística exploratoria i de l'analisi de dades, el paradigma de la disciplina.En el decurs dels darrers anys, la disciplina no ha estat pas capgirada, però de tota manera sí que cal una actualització permanent.S'han forjat i provat algunes eines gairebé només esbossades, han aparegut nous dominis d'aplicació. Cal precisar la relació amb els competidors i dinamics veïns (intel·ligencia artificial, xarxes neurals, Data Mining). La perspectiva que presento dels mètodes d'anàlisi de dades emana evidentment d'un punt de vista particular; altres punts de vista poden ser igualment vàlids

Trust region versus line search for computing the optical flow

We consider the numerical treatment of the optical flow problem by evaluating the performance of the trust region method versus the line search method. To the best of our knowledge, the trust region method is studied here for the first time for variational optical flow computation. Four different optical flow models are used to test the performance of the proposed algorithm combining linear and nonlinear data terms with quadratic and TV regularization. We show that trust region often performs better than line search; especially in the presence of non-linearity and non-convexity in the model.

Using MILP to plan holidays and working hours under an annualised hours agreement

Annualising work hours (AH) is a means of achievement flexibility in the use of human resources to face the seasonal nature of demand. In Corominas et al. (1) two MILP models are used to solve the problem of planning staff working hours with annual horizon. The costs due to overtime and to the employment of temporary workers are minimised, and the distribution of working time over the course of the year for each worker and the distribution of working time provided by temporary workers are regularised.In the aforementioned paper, the following is assumed: (i) the holiday weeks are fixed a priori and (ii) the workers are from different categories who are able to perform specific type of task have se same efficiency; moreover, the values of the binary variables (and others) in the second model are fixed to those in the first model (thus, in the second model these will intervene as constants and not as variables, resulting in an LP model).In the present paper, these assumptions are relaxed and a more general problem is solved. The computational experiment leads to the conclusion that MILP is a technique suited to dealing with the problem.

Studies on integrating kinematic design method with mechanical systems simulation techniques

Theultimate goal of any research in the mechanism/kinematic/design area may be called predictive design, ie the optimisation of mechanism proportions in the design stage without requiring extensive life and wear testing. This is an ambitious goal and can be realised through development and refinement of numerical (computational) technology in order to facilitate the design analysis and optimisation of complex mechanisms, mechanical components and systems. As a part of the systematic design methodology this thesis concentrates on kinematic synthesis (kinematic design and analysis) methods in the mechanism synthesis process. The main task of kinematic design is to find all possible solutions in the form of structural parameters to accomplish the desired requirements of motion. Main formulations of kinematic design can be broadly divided to exact synthesis and approximate synthesis formulations. The exact synthesis formulation is based in solving n linear or nonlinear equations in n variables and the solutions for the problem areget by adopting closed form classical or modern algebraic solution methods or using numerical solution methods based on the polynomial continuation or homotopy. The approximate synthesis formulations is based on minimising the approximation error by direct optimisation The main drawbacks of exact synthesis formulationare: (ia) limitations of number of design specifications and (iia) failure in handling design constraints- especially inequality constraints. The main drawbacks of approximate synthesis formulations are: (ib) it is difficult to choose a proper initial linkage and (iib) it is hard to find more than one solution. Recentformulations in solving the approximate synthesis problem adopts polynomial continuation providing several solutions, but it can not handle inequality const-raints. Based on the practical design needs the mixed exact-approximate position synthesis with two exact and an unlimited number of approximate positions has also been developed. The solutions space is presented as a ground pivot map but thepole between the exact positions cannot be selected as a ground pivot. In this thesis the exact synthesis problem of planar mechanism is solved by generating all possible solutions for the optimisation process ¿ including solutions in positive dimensional solution sets - within inequality constraints of structural parameters. Through the literature research it is first shown that the algebraic and numerical solution methods ¿ used in the research area of computational kinematics ¿ are capable of solving non-parametric algebraic systems of n equations inn variables and cannot handle the singularities associated with positive-dimensional solution sets. In this thesis the problem of positive-dimensional solutionsets is solved adopting the main principles from mathematical research area of algebraic geometry in solving parametric ( in the mathematical sense that all parameter values are considered ¿ including the degenerate cases ¿ for which the system is solvable ) algebraic systems of n equations and at least n+1 variables.Adopting the developed solution method in solving the dyadic equations in direct polynomial form in two- to three-precision-points it has been algebraically proved and numerically demonstrated that the map of the ground pivots is ambiguousand that the singularities associated with positive-dimensional solution sets can be solved. The positive-dimensional solution sets associated with the poles might contain physically meaningful solutions in the form of optimal defectfree mechanisms. Traditionally the mechanism optimisation of hydraulically driven boommechanisms is done at early state of the design process. This will result in optimal component design rather than optimal system level design. Modern mechanismoptimisation at system level demands integration of kinematic design methods with mechanical system simulation techniques. In this thesis a new kinematic design method for hydraulically driven boom mechanism is developed and integrated in mechanical system simulation techniques. The developed kinematic design method is based on the combinations of two-precision-point formulation and on optimisation ( with mathematical programming techniques or adopting optimisation methods based on probability and statistics ) of substructures using calculated criteria from the system level response of multidegree-of-freedom mechanisms. Eg. by adopting the mixed exact-approximate position synthesis in direct optimisation (using mathematical programming techniques) with two exact positions and an unlimitednumber of approximate positions the drawbacks of (ia)-(iib) has been cancelled.The design principles of the developed method are based on the design-tree -approach of the mechanical systems and the design method ¿ in principle ¿ is capable of capturing the interrelationship between kinematic and dynamic synthesis simultaneously when the developed kinematic design method is integrated with the mechanical system simulation techniques.

Trust region versus line search for computing the optical flow

We consider the numerical treatment of the optical flow problem by evaluating the performance of the trust region method versus the line search method. To the best of our knowledge, the trust region method is studied here for the first time for variational optical flow computation. Four different optical flow models are used to test the performance of the proposed algorithm combining linear and nonlinear data terms with quadratic and TV regularization. We show that trust region often performs better than line search; especially in the presence of non-linearity and non-convexity in the model.

Structural and operational optimisation : applications in energy systems

In this work mathematical programming models for structural and operational optimisation of energy systems are developed and applied to a selection of energy technology problems. The studied cases are taken from industrial processes and from large regional energy distribution systems. The models are based on Mixed Integer Linear Programming (MILP), Mixed Integer Non-Linear Programming (MINLP) and on a hybrid approach of a combination of Non-Linear Programming (NLP) and Genetic Algorithms (GA). The optimisation of the structure and operation of energy systems in urban regions is treated in the work. Firstly, distributed energy systems (DES) with different energy conversion units and annual variations of consumer heating and electricity demands are considered. Secondly, district cooling systems (DCS) with cooling demands for a large number of consumers are studied, with respect to a long term planning perspective regarding to given predictions of the consumer cooling demand development in a region. The work comprises also the development of applications for heat recovery systems (HRS), where paper machine dryer section HRS is taken as an illustrative example. The heat sources in these systems are moist air streams. Models are developed for different types of equipment price functions. The approach is based on partitioning of the overall temperature range of the system into a number of temperature intervals in order to take into account the strong nonlinearities due to condensation in the heat recovery exchangers. The influence of parameter variations on the solutions of heat recovery systems is analysed firstly by varying cost factors and secondly by varying process parameters. Point-optimal solutions by a fixed parameter approach are compared to robust solutions with given parameter variation ranges. In the work enhanced utilisation of excess heat in heat recovery systems with impingement drying, electricity generation with low grade excess heat and the use of absorption heat transformers to elevate a stream temperature above the excess heat temperature are also studied.

Contact with friction using the augmented Lagrangian Method: a conditional constrained minimization problem

This work presents a formulation of the contact with friction between elastic bodies. This is a non linear problem due to unilateral constraints (inter-penetration of bodies) and friction. The solution of this problem can be found using optimization concepts, modelling the problem as a constrained minimization problem. The Finite Element Method is used to construct approximation spaces. The minimization problem has the total potential energy of the elastic bodies as the objective function, the non-inter-penetration conditions are represented by inequality constraints, and equality constraints are used to deal with the friction. Due to the presence of two friction conditions (stick and slip), specific equality constraints are present or not according to the current condition. Since the Coulomb friction condition depends on the normal and tangential contact stresses related to the constraints of the problem, it is devised a conditional dependent constrained minimization problem. An Augmented Lagrangian Method for constrained minimization is employed to solve this problem. This method, when applied to a contact problem, presents Lagrange Multipliers which have the physical meaning of contact forces. This fact allows to check the friction condition at each iteration. These concepts make possible to devise a computational scheme which lead to good numerical results.

The theory of constraints in manufacturing

In this paper, a systematic and quantitative view is presented for the application of the theory of constraints in manufacturing. This is done employing the operational research technique of mathematical programming. The potential of the theory of constraints in automated manufacturing is demonstrated.

Heuristics for the Critical Node Detection Problem in Large Complex Networks

Complex networks have recently attracted a significant amount of research attention due to their ability to model real world phenomena. One important problem often encountered is to limit diffusive processes spread over the network, for example mitigating pandemic disease or computer virus spread. A number of problem formulations have been proposed that aim to solve such problems based on desired network characteristics, such as maintaining the largest network component after node removal. The recently formulated critical node detection problem aims to remove a small subset of vertices from the network such that the residual network has minimum pairwise connectivity. Unfortunately, the problem is NP-hard and also the number of constraints is cubic in number of vertices, making very large scale problems impossible to solve with traditional mathematical programming techniques. Even many approximation algorithm strategies such as dynamic programming, evolutionary algorithms, etc. all are unusable for networks that contain thousands to millions of vertices. A computationally efficient and simple approach is required in such circumstances, but none currently exist. In this thesis, such an algorithm is proposed. The methodology is based on a depth-first search traversal of the network, and a specially designed ranking function that considers information local to each vertex. Due to the variety of network structures, a number of characteristics must be taken into consideration and combined into a single rank that measures the utility of removing each vertex. Since removing a vertex in sequential fashion impacts the network structure, an efficient post-processing algorithm is also proposed to quickly re-rank vertices. Experiments on a range of common complex network models with varying number of vertices are considered, in addition to real world networks. The proposed algorithm, DFSH, is shown to be highly competitive and often outperforms existing strategies such as Google PageRank for minimizing pairwise connectivity.