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.

Damage evaluation of drilled carbon/epoxy laminates based on area assessment methods

The characteristics of carbon fibre reinforced laminates had widened their use, from aerospace to domestic appliances. A common characteristic is the need of drilling for assembly purposes. It is known that a drilling process that reduces the drill thrust force can decrease the risk of delamination. In this work, delamination assessment methods based on radiographic data are compared and correlated with mechanical test results (bearing test).

A web-based tool to evaluate the iterative processes of direct search methods

Constrained and unconstrained Nonlinear Optimization Problems often appear in many engineering areas. In some of these cases it is not possible to use derivative based optimization methods because the objective function is not known or it is too complex or the objective function is non-smooth. In these cases derivative based methods cannot be used and Direct Search Methods might be the most suitable optimization methods. An Application Programming Interface (API) including some of these methods was implemented using Java Technology. This API can be accessed either by applications running in the same computer where it is installed or, it can be remotely accessed through a LAN or the Internet, using webservices. From the engineering point of view, the information needed from the API is the solution for the provided problem. On the other hand, from the optimization methods researchers’ point of view, not only the solution for the problem is needed. Also additional information about the iterative process is useful, such as: the number of iterations; the value of the solution at each iteration; the stopping criteria, etc. In this paper are presented the features added to the API to allow users to access to the iterative process data.

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.

Strength prediction and experimental validation of adhesive joints including polyethylene, carbon-epoxy and aluminium adherends

Polyolefins are especially difficult to bond due to their non-polar, non-porous and chemically inert surfaces. Acrylic adhesives used in industry are particularly suited to bond these materials, including many grades of polypropylene (PP) and polyethylene (PE), without special surface preparation. In this work, the tensile strength of single-lap PE and mixed joints bonded with an acrylic adhesive was investigated. The mixed joints included PE with aluminium (AL) or carbon fibre reinforced plastic (CFRP) substrates. The PE substrates were only cleaned with isopropanol, which assured cohesive failures. For the PE CFRP joints, three different surfaces preparations were employed for the CFRP substrates: cleaning with acetone, abrasion with 100 grit sand paper and peel-ply finishing. In the PE AL joints, the AL bonding surfaces were prepared by the following methods: cleaning with acetone, abrasion with 180 and 320 grit sand papers, grit blasting and chemical etching with chromic acid. After abrasion of the CFRP and AL substrates, the surfaces were always cleaned with acetone. The tensile strengths were compared with numerical results from ABAQUS® and a mixed mode (I+II) cohesive damage model. A good agreement was found between the experimental and numerical results, except for the PE AL joints, since the AL surface treatments were not found to be effective.

An embedded 1149.4 extension to support mixed-signal debugging

Debugging electronic circuits is traditionally done with bench equipment directly connected to the circuit under debug. In the digital domain, the difficulties associated with the direct physical access to circuit nodes led to the inclusion of resources providing support to that activity, first at the printed circuit level, and then at the integrated circuit level. The experience acquired with those solutions led to the emergence of dedicated infrastructures for debugging cores at the system-on-chip level. However, all these developments had a small impact in the analog and mixed-signal domain, where debugging still depends, to a large extent, on direct physical access to circuit nodes. As a consequence, when analog and mixed-signal circuits are integrated as cores inside a system-on-chip, the difficulties associated with debugging increase, which cause the time-to-market and the prototype verification costs to also increase. The present work considers the IEEE1149.4 infrastructure as a means to support the debugging of mixed-signal circuits, namely to access the circuit nodes and also an embedded debug mechanism named mixed-signal condition detector, necessary for watch-/breakpoints and real-time analysis operations. One of the main advantages associated with the proposed solution is the seamless migration to the system-on-chip level, as the access is done through electronic means, thus easing debugging operations at different hierarchical levels.

A comparative analysis of fault injection methods via enhanced on-chip debug infrastructures

On-chip debug (OCD) features are frequently available in modern microprocessors. Their contribution to shorten the time-to-market justifies the industry investment in this area, where a number of competing or complementary proposals are available or under development, e.g. NEXUS, CJTAG, IJTAG. The controllability and observability features provided by OCD infrastructures provide a valuable toolbox that can be used well beyond the debugging arena, improving the return on investment rate by diluting its cost across a wider spectrum of application areas. This paper discusses the use of OCD features for validating fault tolerant architectures, and in particular the efficiency of various fault injection methods provided by enhanced OCD infrastructures. The reference data for our comparative study was captured on a workbench comprising the 32-bit Freescale MPC-565 microprocessor, an iSYSTEM IC3000 debugger (iTracePro version) and the Winidea 2005 debugging package. All enhanced OCD infrastructures were implemented in VHDL and the results were obtained by simulation within the same fault injection environment. The focus of this paper is on the comparative analysis of the experimental results obtained for various OCD configurations and debugging scenarios.

Environmental policies in an international mixed duopoly

The purpose of this paper is to study the effects of environmental and trade policies in an international mixed duopoly serving two markets. We suppose that the firm in the home country is a welfare-maximizing public firm, while the firm in the foreign country is its own profit-maximizing private firm. We find that the environmental tax can be a strategic instrument for the home government to distribute production from the foreign private firm to the home public firm. An additional effect of the home environmental tax is the reduction of the foreign private firm's output for local consumption, thereby expanding the foreign market for the home public firm.

Modified particle swarm optimization for day-ahead distributed energy resources scheduling including vehicle-to-grid

Mestrado em Engenharia Electrotécnica – Sistemas Eléctricos de Energia

Escalonamento de geradores térmicos com integração de produção eólica: uma abordagem baseada em programação inteira mista

A alta e crescente participação da energia eólica na matriz da produção traz grandes desafios aos operadores do sistema na gestão da rede e planeamento da produção. A incerteza associada à produção eólica condiciona os processos de escalonamento e despacho económico dos geradores térmicos, uma vez que a produção eólica efetiva pode ser muito diferente da produção prevista. O presente trabalho propõe duas metodologias de otimização do escalonamento de geradores térmicos baseadas em Programação Inteira Mista. Pretende-se encontrar soluções de escalonamento que minimizem as influências negativas da integração de energia eólica no sistema elétrico. Inicialmente o problema de escalonamento de geradores é formulado sem considerar a integração da energia eólica. Posteriormente foi considerada a penetração da energia eólica no sistema elétrico. No primeiro modelo proposto, o problema é formulado como um problema de otimização estocástico. Nesta formulação todos os cenários de produção eólica são levados em consideração no processo de otimização. No segundo modelo, o problema é formulado como um problema de otimização determinística. Nesta formulação, o escalonamento é feito para cada cenário de produção eólica e no fim determina-se a melhor solução por meio de indicadores de avaliação. Foram feitas simulações para diferentes níveis de reserva girante e os resultados obtidos mostraram que a alta participação da energia eólica na matriz da produção põe em causa a segurança e garantia de produção devido às características volátil e intermitente da produção eólica e para manter os mesmos níveis de segurança é preciso dispor no sistema de capacidade reserva girante suficiente capaz de compensar os erros de previsão.

Uncertainty in a mixed duopoly with quadratic costs

In this paper, we consider a mixed market with uncertain demand, involving one private firm and one public firm with quadratic costs. The model is a two-stage game in which players choose to make their output decisions either in stage 1 or stage 2. We assume that the demand is unknown until the end of the first stage. We compute the output levels at equilibrium in each possible role. We also determine ex-ante and ex-post firms’ payoff functions.

Desirable role in a price-setting international mixed duopoly

In this paper, we study the order of moves in a mixed international duopoly for differentiated goods, where firms choose whether to set prices sequentially or simultaneously. We discuss the desirable role of the public firm by comparing welfare among three games. We find that, in the three possible roles, the domestic public firm put a lower price, and then produces more than the foreign private firm.

Environmental and international tariffs in a mixed duopoly

In this paper, we study the effects of environmental and trade policies in an international mixed duopoly serving two markets, in which the public firm maximizes the sum of consumer surplus and its profit. We also analyse the effects of privatization. The model has two stages. In the first stage, governments choose environmental taxes and import tariffs, simultaneously. Then, the firms engage in a Cournot competition, choosing output levels for the domestic market and to export. We compare the results obtained in the three different ways of moving on the decision make of the firms.

Privatization and government preferences in a mixed duopoly: Stackelberg versus Cournot

We analyse the relationship between the privatization of a public firm and government preferences for tax revenue, by considering a (sequential) Stackelberg duopoly with the public firm as the leader. We assume that the government payoff is given by a weighted sum of tax revenue and the sum of consumer and producer surplus. We get that if the government puts a sufficiently larger weight on tax revenue than on the sum of both surpluses, it will not privatize the public firm. In contrast, if the government puts a moderately larger weight on tax revenue than on the sum of both surpluses, it will privatize the public firm. Furthermore, we compare our results with the ones previously published by an other author obtained in a (simultaneous) Cournot duopoly.

Privatization in a mixed duopoly with environmental taxes

In this paper, we study the effects of environmental and privatization in a mixed duopoly, in which the public firm aims to maximize the social welfare. The model has two stages. In the first stage, the government sets the environmental tax. Then, the firms engage in a Cournot competition, choosing output and pollution abatement levels.