Solving MPCC problem with the hyperbolic penalty function

The main goal of this work is to solve mathematical program with complementarity constraints (MPCC) using nonlinear programming techniques (NLP). An hyperbolic penalty function is used to solve MPCC problems by including the complementarity constraints in the penalty term. This penalty function [1] is twice continuously differentiable and combines features of both exterior and interior penalty methods. A set of AMPL problems from MacMPEC [2] are tested and a comparative study is performed.

Solving a signalized traffic intersection problem with an hyperbolic penalty function

Mathematical Program with Complementarity Constraints (MPCC) finds many applications in fields such as engineering design, economic equilibrium and mathematical programming theory itself. A queueing system model resulting from a single signalized intersection regulated by pre-timed control in traffic network is considered. The model is formulated as an MPCC problem. A MATLAB implementation based on an hyperbolic penalty function is used to solve this practical problem, computing the total average waiting time of the vehicles in all queues and the green split allocation. The problem was codified in AMPL.

Classification of some penalty methods

Optimization problems arise in science, engineering, economy, etc. and we need to find the best solutions for each reality. The methods used to solve these problems depend on several factors, including the amount and type of accessible information, the available algorithms for solving them, and, obviously, the intrinsic characteristics of the problem. There are many kinds of optimization problems and, consequently, many kinds of methods to solve them. When the involved functions are nonlinear and their derivatives are not known or are very difficult to calculate, these methods are more rare. These kinds of functions are frequently called black box functions. To solve such problems without constraints (unconstrained optimization), we can use direct search methods. These methods do not require any derivatives or approximations of them. But when the problem has constraints (nonlinear programming problems) and, additionally, the constraint functions are black box functions, it is much more difficult to find the most appropriate method. Penalty methods can then be used. They transform the original problem into a sequence of other problems, derived from the initial, all without constraints. Then this sequence of problems (without constraints) can be solved using the methods available for unconstrained optimization. In this chapter, we present a classification of some of the existing penalty methods and describe some of their assumptions and limitations. These methods allow the solving of optimization problems with continuous, discrete, and mixing constraints, without requiring continuity, differentiability, or convexity. Thus, penalty methods can be used as the first step in the resolution of constrained problems, by means of methods that typically are used by unconstrained problems. We also discuss a new class of penalty methods for nonlinear optimization, which adjust the penalty parameter dynamically.

Penalty fuzzy function for derivative-free optimization

Penalty and Barrier methods are normally used to solve Nonlinear Optimization Problems constrained problems. The problems appear in areas such as engineering and are often characterised by the fact that involved functions (objective and constraints) are non-smooth and/or their derivatives are not know. This means that optimization methods based on derivatives cannot net used. A Java based API was implemented, including only derivative-free optimizationmethods, to solve both constrained and unconstrained problems, which includes Penalty and Barriers methods. In this work a new penalty function, based on Fuzzy Logic, is presented. This function imposes a progressive penalization to solutions that violate the constraints. This means that the function imposes a low penalization when the violation of the constraints is low and a heavy penalisation when the violation is high. The value of the penalization is not known in beforehand, it is the outcome of a fuzzy inference engine. Numerical results comparing the proposed function with two of the classic penalty/barrier functions are presented. Regarding the presented results one can conclude that the prosed penalty function besides being very robust also exhibits a very good performance.

Direct-search penalty/barrier methods

In Nonlinear Optimization Penalty and Barrier Methods are normally used to solve Constrained Problems. There are several Penalty/Barrier Methods and they are used in several areas from Engineering to Economy, through Biology, Chemistry, Physics among others. In these areas it often appears Optimization Problems in which the involved functions (objective and constraints) are non-smooth and/or their derivatives are not know. In this work some Penalty/Barrier functions are tested and compared, using in the internal process, Derivative-free, namely Direct Search, methods. This work is a part of a bigger project involving the development of an Application Programming Interface, that implements several Optimization Methods, to be used in applications that need to solve constrained and/or unconstrained Nonlinear Optimization Problems. Besides the use of it in applied mathematics research it is also to be used in engineering software packages.

Adaptive Penalty and Barrier function based on Fuzzy Logic

Optimization methods have been used in many areas of knowledge, such as Engineering, Statistics, Chemistry, among others, to solve optimization problems. In many cases it is not possible to use derivative methods, due to the characteristics of the problem to be solved and/or its constraints, for example if the involved functions are non-smooth and/or their derivatives are not know. To solve this type of problems a Java based API has been implemented, which includes only derivative-free optimization methods, and that can be used to solve both constrained and unconstrained problems. For solving constrained problems, the classic Penalty and Barrier functions were included in the API. In this paper a new approach to Penalty and Barrier functions, based on Fuzzy Logic, is proposed. Two penalty functions, that impose a progressive penalization to solutions that violate the constraints, are discussed. The implemented functions impose a low penalization when the violation of the constraints is low and a heavy penalty when the violation is high. Numerical results, obtained using twenty-eight test problems, comparing the proposed Fuzzy Logic based functions to six of the classic Penalty and Barrier functions are presented. Considering the achieved results, it can be concluded that the proposed penalty functions besides being very robust also have a very good performance.

Impacto microeconómico da formação profissional e medida da discriminação sexual no mercado de trabalho português: uma abordagem semiparamétrica

A tese estrutura-se em dois ensaios versando temas distintos, se bem que entre eles se possam perceber algumas afinidades decorrentes do facto de ambos se subsumirem à análise de diferentes tipos de investimento em capital humano: a formação profissional e a formação académica superior. No primeiro ensaio, aborda-se a questão da avaliação do impacto de diferentes tipos de formação profissional sobre os salários, a estabilidade da relação contratual trabalhador-empregador e a empregabilidade, em Portugal, por recurso a uma metodologia de estimação semiparamétrica, mais especificamente, através de uma metodologia de enlaçamento baseado em índices de propensão aplicada aos dados do Inquérito ao Emprego do INE, relativos aos anos de 1998 a 2001. Quanto aos impactos salariais, conclui-se que a formação obtida nas empresas será a mais compensadora, mas os restantes tipos de formação também propiciarão ganhos salariais, sendo que a formação obtida nas escolas ou centros de formação profissional será aquela com efeitos menos expressivos. Quanto ao efeito sobre a empregabilidade, as estimativas obtidas apontam para a conclusão de que a formação profissional potenciará o abandono da inactividade, mas não garantidamente o emprego, verificando-se mesmo que a formação recebida nas escolas e centros de formação profissional conduzirá, mais provavelmente, ao desemprego, se bem que, para uma certa fracção de desempregados, o sentido da causalidade possa ser inverso. O segundo ensaio versa a decomposição, da média condicional e por quantis, do diferencial salarial entre homens e mulheres específico do universo dos diplomados do ensino superior, em Portugal (dados do 1.º Inquérito de Percurso aos Diplomados do Ensino Superior realizado em 2001), por forma a apurar o grau de discriminação por género nele indiciado. Usando a metodologia de Machado-Mata e, em alternativa, a metodologia de enlaçamento baseado em índices de propensão, dir-se-ia que, no sector público, a discriminação salarial por género, a existir, será reduzida, i.e. o diferencial salarial observado explicar se á quase integralmente pelas diferenças entre os atributos produtivos dos homens e das mulheres. Diferentemente, no sector empresarial, a discriminação é potencialmente ponderosa. Especial atenção é dedicada ao contributo da área de formação escolar para a explicação do diferencial salarial.

Os Crimes fiscais: em especial, o crime de abuso de confiança (fiscal)

Dissertação para obtenção do Grau de Mestre em Contabilidade e Finanças Orientador: Professor Dr. António da Costa Oliveira

Long-term price range forecast applied to risk management using regression models

Long-term contractual decisions are the basis of an efficient risk management. However those types of decisions have to be supported with a robust price forecast methodology. This paper reports a different approach for long-term price forecast which tries to give answers to that need. Making use of regression models, the proposed methodology has as main objective to find the maximum and a minimum Market Clearing Price (MCP) for a specific programming period, and with a desired confidence level α. Due to the problem complexity, the meta-heuristic Particle Swarm Optimization (PSO) was used to find the best regression parameters and the results compared with the obtained by using a Genetic Algorithm (GA). To validate these models, results from realistic data are presented and discussed in detail.

A short-term risk management tool applied to OMEL electricity market using particle swarm optimization

Short-term risk management is highly dependent on long-term contractual decisions previously established; risk aversion factor of the agent and short-term price forecast accuracy. Trying to give answers to that problem, this paper provides a different approach for short-term risk management on electricity markets. Based on long-term contractual decisions and making use of a price range forecast method developed by the authors, the short-term risk management tool presented here has as main concern to find the optimal spot market strategies that a producer should have for a specific day in function of his risk aversion factor, with the objective to maximize the profits and simultaneously to practice the hedge against price market volatility. Due to the complexity of the optimization problem, the authors make use of Particle Swarm Optimization (PSO) to find the optimal solution. Results from realistic data, namely from OMEL electricity market, are presented and discussed in detail.

Optimal dispatch with reactive power compensation by Genetic Algorithm

This paper presents a Unit Commitment model with reactive power compensation that has been solved by Genetic Algorithm (GA) optimization techniques. The GA has been developed a computational tools programmed/coded in MATLAB. The main objective is to find the best generations scheduling whose active power losses are minimal and the reactive power to be compensated, subjected to the power system technical constraints. Those are: full AC power flow equations, active and reactive power generation constraints. All constraints that have been represented in the objective function are weighted with a penalty factors. The IEEE 14-bus system has been used as test case to demonstrate the effectiveness of the proposed algorithm. Results and conclusions are dully drawn.

Derivative-free optimization and filter methods to solve nonlinear constrained problems

In real optimization problems, usually the analytical expression of the objective function is not known, nor its derivatives, or they are complex. In these cases it becomes essential to use optimization methods where the calculation of the derivatives, or the verification of their existence, is not necessary: the Direct Search Methods or Derivative-free Methods are one solution. When the problem has constraints, penalty functions are often used. Unfortunately the choice of the penalty parameters is, frequently, very difficult, because most strategies for choosing it are heuristics strategies. As an alternative to penalty function appeared the filter methods. A filter algorithm introduces a function that aggregates the constrained violations and constructs a biobjective problem. In this problem the step is accepted if it either reduces the objective function or the constrained violation. This implies that the filter methods are less parameter dependent than a penalty function. In this work, we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of the simplex method and filter methods. This method does not compute or approximate any derivatives, penalty constants or Lagrange multipliers. The basic idea of simplex filter algorithm is to construct an initial simplex and use the simplex to drive the search. We illustrate the behavior of our algorithm through some examples. The proposed methods were implemented in Java.

Derivative-free nonlinear optimization filter simplex

The filter method is a technique for solving nonlinear programming problems. The filter algorithm has two phases in each iteration. The first one reduces a measure of infeasibility, while in the second the objective function value is reduced. In real optimization problems, usually the objective function is not differentiable or its derivatives are unknown. In these cases it becomes essential to use optimization methods where the calculation of the derivatives or the verification of their existence is not necessary: direct search methods or derivative-free methods are examples of such techniques. In this work we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of simplex and filter methods. This method neither computes nor approximates derivatives, penalty constants or Lagrange multipliers.

Aferição do desempenho operacional de parques eólicos (Referência: D0708-047)

A verificação das Características Garantidas associadas aos equipamentos, em especial dos aerogeradores, incluídos no fornecimento de Parques Eólicos, reveste-se de particular importância devido, principalmente, ao grande volume de investimento em jogo, ao longo período necessário ao retorno do mesmo, à incerteza quanto à manutenção futura das actuais condições de remuneração da energia eléctrica produzida e ainda à falta de dados históricos sobre o período de vida útil esperado para os aerogeradores. Em face do exposto, é usual serem exigidas aos fornecedores, garantias do bom desempenho dos equipamentos, associadas a eventuais penalidades, quer para o período de garantia, quer para o restante período de vida útil, de modo a minimizar o risco associado ao investimento. No fornecimento de Parques Eólicos existem usualmente três tipos de garantias, nomeadamente, garantia de Curva de Potência dos aerogeradores, garantia de Disponibilidade dos equipamentos ou garantia de Produção de Energia. Estas poderão existir isoladamente ou em combinação, dependendo das condições contratuais acordadas entre o Adjudicatário e o Fornecedor. O grau de complexidade e/ou trabalho na implementação das mesmas é variável, não sendo possível afirmar qual delas é a mais conveniente para o Adjudicatário, nem qual a mais exacta em termos de resultados. Estas dúvidas surgem em consequência das dificuldades inerentes à recolha dos próprios dados e também da relativamente ampla margem de rearranjo dos resultados permitido pelas normas existentes, possibilitando a introdução de certo tipo de manipulações nos dados (rejeições e correlações), as quais podem afectar de forma considerável as incertezas dos resultados finais dos ensaios. Este trabalho, consistiu no desenvolvimento, execução, ensaio e implementação de uma ferramenta informática capaz de detectar de uma forma simples e expedita eventuais desvios à capacidade de produção esperada para os aerogeradores, em função do recurso verificado num dado período. Pretende ser uma ferramenta manuseável por qualquer operador de supervisão, com utilização para efeitos de reparações e correcção de defeitos, não constituindo contudo uma alternativa a outros processos abrangidos por normas, no caso de aplicação de penalidades. Para o seu funcionamento, são utilizados os dados mensais recolhidos pela torre meteorológica permanente instalada no parque e os dados de funcionamento dos aerogeradores, recolhidos pelo sistema SCADA. Estes são recolhidos remotamente sob a forma de tabelas e colocados numa directoria própria, na qual serão posteriormente lidos pela ferramenta.

Energy resource management in smart grids considering an Intensive use of electric vehicles

The introduction of electricity markets and integration of Distributed Generation (DG) have been influencing the power system’s structure change. Recently, the smart grid concept has been introduced, to guarantee a more efficient operation of the power system using the advantages of this new paradigm. Basically, a smart grid is a structure that integrates different players, considering constant communication between them to improve power system operation and management. One of the players revealing a big importance in this context is the Virtual Power Player (VPP). In the transportation sector the Electric Vehicle (EV) is arising as an alternative to conventional vehicles propel by fossil fuels. The power system can benefit from this massive introduction of EVs, taking advantage on EVs’ ability to connect to the electric network to charge, and on the future expectation of EVs ability to discharge to the network using the Vehicle-to-Grid (V2G) capacity. This thesis proposes alternative strategies to control these two EV modes with the objective of enhancing the management of the power system. Moreover, power system must ensure the trips of EVs that will be connected to the electric network. The EV user specifies a certain amount of energy that will be necessary to charge, in order to ensure the distance to travel. The introduction of EVs in the power system turns the Energy Resource Management (ERM) under a smart grid environment, into a complex problem that can take several minutes or hours to reach the optimal solution. Adequate optimization techniques are required to accommodate this kind of complexity while solving the ERM problem in a reasonable execution time. This thesis presents a tool that solves the ERM considering the intensive use of EVs in the smart grid context. The objective is to obtain the minimum cost of ERM considering: the operation cost of DG, the cost of the energy acquired to external suppliers, the EV users payments and remuneration and penalty costs. This tool is directed to VPPs that manage specific network areas, where a high penetration level of EVs is expected to be connected in these areas. The ERM is solved using two methodologies: the adaptation of a deterministic technique proposed in a previous work, and the adaptation of the Simulated Annealing (SA) technique. With the purpose of improving the SA performance for this case, three heuristics are additionally proposed, taking advantage on the particularities and specificities of an ERM with these characteristics. A set of case studies are presented in this thesis, considering a 32 bus distribution network and up to 3000 EVs. The first case study solves the scheduling without considering EVs, to be used as a reference case for comparisons with the proposed approaches. The second case study evaluates the complexity of the ERM with the integration of EVs. The third case study evaluates the performance of scheduling with different control modes for EVs. These control modes, combined with the proposed SA approach and with the developed heuristics, aim at improving the quality of the ERM, while reducing drastically its execution time. The proposed control modes are: uncoordinated charging, smart charging and V2G capability. The fourth and final case study presents the ERM approach applied to consecutive days.