Optimization for L1-Norm Error Fitting via Data Aggregation

We propose a data aggregation-based algorithm with monotonic convergence to a global optimum for a generalized version of the L1-norm error fitting model with an assumption of the fitting function. The proposed algorithm generalizes the recent algorithm in the literature, aggregate and iterative disaggregate (AID), which selectively solves three specific L1-norm error fitting problems. With the proposed algorithm, any L1-norm error fitting model can be solved optimally if it follows the form of the L1-norm error fitting problem and if the fitting function satisfies the assumption. The proposed algorithm can also solve multi-dimensional fitting problems with arbitrary constraints on the fitting coefficients matrix. The generalized problem includes popular models such as regression and the orthogonal Procrustes problem. The results of the computational experiment show that the proposed algorithms are faster than the state-of-the-art benchmarks for L1-norm regression subset selection and L1-norm regression over a sphere. Further, the relative performance of the proposed algorithm improves as data size increases

A flexible modeling framework to estimate interregional trade patterns and input-output accounts

This study implements and tests a mathematical programming model to estimate interregional, interindustry transaction flows in a national system of economic regions based on an interregional accounting framework and initial information of interregional shipments. A national input-output (IO) table, regional data on gross output, value-added, exports, imports and final demand at sector level are used as inputs to generate an interregional IO account that reconciles regional economic statistics and interregional transaction data. The model is tested using data from a multi-regional global input-output database and shows remarkable capacity to discover true interregional trade patterns from highly distorted initial estimates.Scientific Research&Science Parks,Information Technology,Environmental Economics&Policies,Statistical&Mathematical Sciences,ICT Policy and Strategies,Statistical&Mathematical Sciences,Information Technology,Scientific Research&Science Parks,Science Education,Geographical Information Systems

A Generalized Nash-Cournot Model for the North-Western European Natural Gas Markets with a Fuel SubstitutionDemand Function: The GaMMES Model

This article presents a dynamic Generalized Nash-Cournot model to describe the evolution of the natural gas markets. The aim of this work is to provide a theoretical framework that would allow us to analyze future infrastructure and policy developments, while trying to answer some of the main criticisms addressed to Cournot-based models of natural gas markets. The major gas chain players are depicted including: producers, consumers, storage and pipeline operators, as well as intermediate local traders. Our economic structure description takes into account market power and the demand representation tries to capture the possible fuel substitution that can be made between the consumption of oil, coal and natural gas in the overall fossil energy consumption. We also take into account the long-term aspects inherent to some markets, in an endogenous way. This particularity of our description makes the model a Generalized Nash Equilibrium problem that needs to be solved using specialized mathematical techniques. Our model has been applied to represent the European natural gas market and forecast, until 2030, after a calibration process, consumption, prices, production and natural gas dependence. A comparison between our model, a more standard one that does not take into account energy substitution, and the European Commission natural gas forecasts is carried out to analyze our results. Finally, in order to illustrate the possible use of fuel substitution, we studied the evolution of the natural gas price as compared to the coal and oil prices. This paper mostly focuses on the model description.Energy markets modeling, Game theory, Generalized Nash-Cournot equilibria, Quasi-Variational Inequality

Comparative model accuracy of a data-fitted generalized Aw-Rascle-Zhang model

The Aw-Rascle-Zhang (ARZ) model can be interpreted as a generalization of the Lighthill-Whitham-Richards (LWR) model, possessing a family of fundamental diagram curves, each of which represents a class of drivers with a different empty road velocity. A weakness of this approach is that different drivers possess vastly different densities at which traffic flow stagnates. This drawback can be overcome by modifying the pressure relation in the ARZ model, leading to the generalized Aw-Rascle-Zhang (GARZ) model. We present an approach to determine the parameter functions of the GARZ model from fundamental diagram measurement data. The predictive accuracy of the resulting data-fitted GARZ model is compared to other traffic models by means of a three-detector test setup, employing two types of data: vehicle trajectory data, and sensor data. This work also considers the extension of the ARZ and the GARZ models to models with a relaxation term, and conducts an investigation of the optimal relaxation time.Comment: 30 pages, 10 figures, 3 table

Approaches to integrated strategic/tactical forest planning

Traditionally forest planning is divided into a hierarchy of planning phases. Strategic planning is conducted to make decisions about sustainable harvest levels while taking into account legislation and policy issues. Within the frame of the strategic plan, the purpose of tactical planning is to schedule harvest operations to specific areas in the immediate few years and on a finer time scale than in the strategic plan. The operative phase focuses on scheduling harvest crews on a monthly or weekly basis, truck scheduling and choosing bucking instructions. Decisions at each level are to a varying degree supported by computerized tools. A problem that may arise when planning is divided into levels and that is noted in the literature focusing on decision support tools is that solutions at one level may be inconsistent with the results of another level. When moving from the strategic plan to the tactical plan, three sources of inconsistencies are often present; spatial discrepancies, temporal discrepancies and discrepancies due to different levels of constraint. The models used in the papers presented in this thesis approaches two of these discrepancies. To address the spatial discrepancies, the same spatial resolution has been used at both levels, i.e., stands. Temporal discrepancies are addressed by modelling the tactical and strategic issues simultaneously. Integrated approaches can yield large models. One way of circumventing this is to aggregate time and/or space. The first paper addresses the consequences of temporal aggregation in the strategic part of a mixed integer programming integrated strategic/tactical model. For reference, linear programming based strategic models are also used. The results of the first paper provide information on what temporal resolutions could be used and indicate that outputs from strategic and integrated plans are not particularly affected by the number of equal length strategic periods when more than five periods, i.e. about 20 year period length, are used. The approach used in the first paper could produce models that are very large, and the second paper provides a two-stage procedure that can reduce the number of variables and preserve the allocation of stands to the first 10 years provided by a linear programming based strategic plan, while concentrating tactical harvest activities using a penalty concept in a mixed integer programming formulation. Results show that it is possible to use the approach to concentrate harvest activities at the tactical level in a full scale forest management scenario. In the case study, the effects of concentration on strategic outputs were small, and the number of harvest tracts declined towards a minimum level. Furthermore, the discrepancies between the two planning levels were small