Let's talk: public evaluation of large projects: variational inequialities, bilevel programming and complementarity. a survey

Large projects evaluation rises well known difficulties because -by definition- they modify the current price system; their public evaluation presents additional difficulties because they modify too existing shadow prices without the project. This paper analyzes -first- the basic methodologies applied until late 80s., based on the integration of projects in optimization models or, alternatively, based on iterative procedures with information exchange between two organizational levels. New methodologies applied afterwards are based on variational inequalities, bilevel programming and linear or nonlinear complementarity. Their foundations and different applications related with project evaluation are explored. As a matter of fact, these new tools are closely related among them and can treat more complex cases involving -for example- the reaction of agents to policies or the existence of multiple agents in an environment characterized by common functions representing demands or constraints on polluting emissions.

Bilevel approach for optimal location and contract pricing of distributed generation in radial distribution systems using mixed-integer linear programming

In this study, a novel approach for the optimal location and contract pricing of distributed generation (DG) is presented. Such an approach is designed for a market environment in which the distribution company (DisCo) can buy energy either from the wholesale energy market or from the DG units within its network. The location and contract pricing of DG is determined by the interaction between the DisCo and the owner of the distributed generators. The DisCo intends to minimise the payments incurred in meeting the expected demand, whereas the owner of the DG intends to maximise the profits obtained from the energy sold to the DisCo. This two-agent relationship is modelled in a bilevel scheme. The upper-level optimisation is for determining the allocation and contract prices of the DG units, whereas the lower-level optimisation is for modelling the reaction of the DisCo. The bilevel programming problem is turned into an equivalent single-level mixed-integer linear optimisation problem using duality properties, which is then solved using commercially available software. Results show the robustness and efficiency of the proposed model compared with other existing models. As regards to contract pricing, the proposed approach allowed to find better solutions than those reported in previous works. © The Institution of Engineering and Technology 2013.

Tarification logit dans un réseau

Le problème de tarification qui nous intéresse ici consiste à maximiser le revenu généré par les usagers d'un réseau de transport. Pour se rendre à leurs destinations, les usagers font un choix de route et utilisent des arcs sur lesquels nous imposons des tarifs. Chaque route est caractérisée (aux yeux de l'usager) par sa "désutilité", une mesure de longueur généralisée tenant compte à la fois des tarifs et des autres coûts associés à son utilisation. Ce problème a surtout été abordé sous une modélisation déterministe de la demande selon laquelle seules des routes de désutilité minimale se voient attribuer une mesure positive de flot. Le modèle déterministe se prête bien à une résolution globale, mais pèche par manque de réalisme. Nous considérons ici une extension probabiliste de ce modèle, selon laquelle les usagers d'un réseau sont alloués aux routes d'après un modèle de choix discret logit. Bien que le problème de tarification qui en résulte est non linéaire et non convexe, il conserve néanmoins une forte composante combinatoire que nous exploitons à des fins algorithmiques. Notre contribution se répartit en trois articles. Dans le premier, nous abordons le problème d'un point de vue théorique pour le cas avec une paire origine-destination. Nous développons une analyse de premier ordre qui exploite les propriétés analytiques de l'affectation logit et démontrons la validité de règles de simplification de la topologie du réseau qui permettent de réduire la dimension du problème sans en modifier la solution. Nous établissons ensuite l'unimodalité du problème pour une vaste gamme de topologies et nous généralisons certains de nos résultats au problème de la tarification d'une ligne de produits. Dans le deuxième article, nous abordons le problème d'un point de vue numérique pour le cas avec plusieurs paires origine-destination. Nous développons des algorithmes qui exploitent l'information locale et la parenté des formulations probabilistes et déterministes. Un des résultats de notre analyse est l'obtention de bornes sur l'erreur commise par les modèles combinatoires dans l'approximation du revenu logit. Nos essais numériques montrent qu'une approximation combinatoire rudimentaire permet souvent d'identifier des solutions quasi-optimales. Dans le troisième article, nous considérons l'extension du problème à une demande hétérogène. L'affectation de la demande y est donnée par un modèle de choix discret logit mixte où la sensibilité au prix d'un usager est aléatoire. Sous cette modélisation, l'expression du revenu n'est pas analytique et ne peut être évaluée de façon exacte. Cependant, nous démontrons que l'utilisation d'approximations non linéaires et combinatoires permet d'identifier des solutions quasi-optimales. Finalement, nous en profitons pour illustrer la richesse du modèle, par le biais d'une interprétation économique, et examinons plus particulièrement la contribution au revenu des différents groupes d'usagers.

Optimal Contract Pricing of Distributed Generation in Distribution Networks

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Location and contract pricing of distributed generation using a genetic algorithm

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Optimal contract pricing of distributed generation under a competitive framework

A bilevel programming approach for the optimal contract pricing of distributed generation (DG) in distribution networks is presented. The outer optimization problem corresponds to the owner of the DG who must decide the contract price that would maximize his profits. The inner optimization problem corresponds to the distribution company (DisCo), which procures the minimization of the payments incurred in attending the expected demand while satisfying network constraints. The meet the expected demand the DisCo can purchase energy either form the transmission network through the substations or form the DG units within its network. The inner optimization problem is substituted by its Karush- Kuhn-Tucker optimality conditions, turning the bilevel programming problem into an equivalent single-level nonlinear programming problem which is solved using commercially available software. © 2010 IEEE.

Avaliação de Localizção e preço de contrato de geração distribuida em um ambiente competitivo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Localização e preço de contrato ótimo da geração distribuída em sistemas de distribuição radiais de energia elétrica

Pós-graduação em Engenharia Elétrica - FEIS

A Bilevel Approach to Transmission Expansion Planning Within a Market Environment

We present a bilevel model for transmission expansion planning within a market environment, where producers and consumers trade freely electric energy through a pool. The target of the transmission planner, modeled through the upper-level problem, is to minimize network investment cost while facilitating energy trading. This upper-level problem is constrained by a collection of lower-level market clearing problems representing pool trading, and whose individual objective functions correspond to social welfare. Using the duality theory the proposed bilevel model is recast as a mixed-integer linear programming problem, which is solvable using branch-and-cut solvers. Detailed results from an illustrative example and a case study are presented and discussed. Finally, some relevant conclusions are drawn.

New Rigorous Decomposition Methods for Mixed-integer Linear and Nonlinear Programming

Process systems design, operation and synthesis problems under uncertainty can readily be formulated as two-stage stochastic mixed-integer linear and nonlinear (nonconvex) programming (MILP and MINLP) problems. These problems, with a scenario based formulation, lead to large-scale MILPs/MINLPs that are well structured. The first part of the thesis proposes a new finitely convergent cross decomposition method (CD), where Benders decomposition (BD) and Dantzig-Wolfe decomposition (DWD) are combined in a unified framework to improve the solution of scenario based two-stage stochastic MILPs. This method alternates between DWD iterations and BD iterations, where DWD restricted master problems and BD primal problems yield a sequence of upper bounds, and BD relaxed master problems yield a sequence of lower bounds. A variant of CD, which includes multiple columns per iteration of DW restricted master problem and multiple cuts per iteration of BD relaxed master problem, called multicolumn-multicut CD is then developed to improve solution time. Finally, an extended cross decomposition method (ECD) for solving two-stage stochastic programs with risk constraints is proposed. In this approach, a CD approach at the first level and DWD at a second level is used to solve the original problem to optimality. ECD has a computational advantage over a bilevel decomposition strategy or solving the monolith problem using an MILP solver. The second part of the thesis develops a joint decomposition approach combining Lagrangian decomposition (LD) and generalized Benders decomposition (GBD), to efficiently solve stochastic mixed-integer nonlinear nonconvex programming problems to global optimality, without the need for explicit branch and bound search. In this approach, LD subproblems and GBD subproblems are systematically solved in a single framework. The relaxed master problem obtained from the reformulation of the original problem, is solved only when necessary. A convexification of the relaxed master problem and a domain reduction procedure are integrated into the decomposition framework to improve solution efficiency. Using case studies taken from renewable resource and fossil-fuel based application in process systems engineering, it can be seen that these novel decomposition approaches have significant benefit over classical decomposition methods and state-of-the-art MILP/MINLP global optimization solvers.

Minimizing total tardiness in a stochastic single machine scheduling problem using approximate dynamic programming

This paper addresses the non-preemptive single machine scheduling problem to minimize total tardiness. We are interested in the online version of this problem, where orders arrive at the system at random times. Jobs have to be scheduled without knowledge of what jobs will come afterwards. The processing times and the due dates become known when the order is placed. The order release date occurs only at the beginning of periodic intervals. A customized approximate dynamic programming method is introduced for this problem. The authors also present numerical experiments that assess the reliability of the new approach and show that it performs better than a myopic policy.

ECONOMICAL OCCUPATION OF AGRICULTURAL AREA OF PIRACICABA (SAO PAULO STATE, BRAZIL), INCLUDING RISK THROUGH LINEAR PROGRAMMING

The economic occupation of an area of 500 ha for Piracicaba was studied with the irrigated cultures of maize, tomato, sugarcane and beans, having used models of deterministic linear programming and linear programming including risk for the Target-Motad model, where two situations had been analyzed. In the deterministic model the area was the restrictive factor and the water was not restrictive for none of the tested situations. For the first situation the gotten maximum income was of R$ 1,883,372.87 and for the second situation it was of R$ 1,821,772.40. In the model including risk a producer that accepts risk can in the first situation get the maximum income of R$ 1,883,372. 87 with a minimum risk of R$ 350 year(-1), and in the second situation R$ 1,821,772.40 with a minimum risk of R$ 40 year(-1). Already a producer averse to the risk can get in the first situation a maximum income of R$ 1,775,974.81 with null risk and for the second situation R$ 1.707.706, 26 with null risk, both without water restriction. These results stand out the importance of the inclusion of the risk in supplying alternative occupations to the producer, allowing to a producer taking of decision considered the risk aversion and the pretension of income.

Rough Notes on Programming AVR Microcontrollers in C

These notes follow on from the material that you studied in CSSE1000 Introduction to Computer Systems. There you studied details of logic gates, binary numbers and instruction set architectures using the Atmel AVR microcontroller family as an example. In your present course (METR2800 Team Project I), you need to get on to designing and building an application which will include such a microcontroller. These notes focus on programming an AVR microcontroller in C and provide a number of example programs to illustrate the use of some of the AVR peripheral devices.