Métodos de Pesquisa Direta: Otimização não Linear

Os Problemas de Optimização aparecem frequentemente em diversas áreas tais como a Engenharia, Economia, Química, entre outras. Nestas áreas aparecem usualmente Problemas onde as funções envolvidas (função objectivo e restrições) podem ser não suaves, as suas derivadas não são conhecidas, têm expressões complexas ou até casos em que as suas expressões analíticas não podem ser determinadas, seja pela sua complexidade ou pelo seu custo (monetário, computacional, temporal,...). Nestes casos os métodos que usam derivadas não são os mais apropriados para os resolver e os métodos que usam modelos para aproximar as funções mostram-se muitas vezes ineficazes. Neste trabalho estudam-se, implementam-se e comparam-se Métodos de Pesquisa Directa, isto é, métodos que usam apenas informação sobre os valores das funções, progredindo em direcção à solução óptima, comparando estes valores em determinados pontos, sem recorrer ao uso de derivadas, suas aproximações ou modelos que aproximem as funções envolvidas. Inicialmente será feita a apresentação de uma síntese sobre os métodos propostos na literatura da especialidade. Estes métodos serão posteriormente implementados e testadas algumas modificações, tendo em vista à melhoria da sua eficiência. No que respeita à Optimização sem Restrições foram estudados os métodos clássicos de Pesquisa Directa e apresentam-se novas metodologias, adoptadas de desenvolvimentos recentes nesta área, tendo os correspondentes algoritmos sido implementados, analisados e comparados. O mesmo sucedeu para os Métodos de Optimização de Problemas com Restrições, para os quais se adaptaram e apresentam alternativas de melhoria de métodos já usados na Optimização por Pesquisa Directa, como é o caso dos Métodos de Penalidade e Barreira. São também desenvolvidas técnicas que se consideram como possíveis alternativas de resolução deste tipo de problemas, como é o caso do Método dos Filtros, que dispensando a criação e uso de uma função de Penalidade/Barreira, bem como a escolha de parâmetros de penalidade, se mostrou como uma alternativa válida. A implementação destes algoritmos, com recurso à Tecnologia Java, correspondeu ao desenvolvimento de uma API que foi usada para realizar os testes numéricos e onde se encontram implementados os algoritmos e variantes aqui propostos.N/

Métodos de penalidade exacta para resolução de problemas de optimização não linear

In this work we present a classification of some of the existing Penalty Methods (denominated the Exact Penalty Methods) and describe some of its limitations and estimated. With these methods we can solve problems of optimization with continuous, discrete and mixing constrains, without requiring continuity, differentiability or convexity. The boarding consists of transforming the original problem, in a sequence of problems without constrains, derivate of the initial, making possible its resolution for the methods known for this type of problems. Thus, the Penalty Methods can be used as the first step for the resolution of constrained problems for methods typically used in by unconstrained problems. The work finishes discussing a new class of Penalty Methods, for nonlinear optimization, that adjust the penalty parameter dynamically.Neste trabalho pretende apresentar-se uma classificação dos Métodos de Penalidade existentes (salientando os Métodos de Penalidade Exacta) e descrever algumas das suas limitações e pressupostos. Esses métodos permitem resolver problemas de optimização com restrições contínuas, discretas e mistas, sem requerer continuidade, diferenciabilidade ou convexidade. A abordagem consiste em transformar o problema original, numa sequência de problemas sem restrições, derivados do inicial, possibilitando a sua resolução pelos métodos conhecidos para este tipo de problemas. Assim, os Métodos de Penalidade podem ser usados como o primeiro passo para a resolução de problemas de optimização permitindo a resolução de problemas com restrições por métodos tipicamente utilizados em problemas sem restrições. O trabalho termina com a discussão de uma nova classe de Métodos de Penalidade, para optimização não linear, que ajustam o parâmetro de penalidade dinamicamente

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

The Dynamics between Structural Conditions and Entrepreneurship in Europe: Feature Extraction and System GMM Approaches

Structural conditions and population characteristics of countries have been identified in the literature as factors for an individual to become, or to have intentions of becoming, an entrepreneur. However, this is still a subject under research, which has become increasingly relevant and could be crucial in the current challenges of European countries. In this work, the factors for entrepreneurial intentions and entrepreneurship activity are studied. More precisely, the structural conditions of European countries, which has changed over the last two decades, is analysed. The aim is to describe this behaviour and to state the main conditions for developing entrepreneurship activities and the intentions to become an entrepreneur. To achieve this purpose, feature extraction, namely, principal component analysis and dynamic longitudinal approaches are used. In particular, we propose that the system-generalised method of moments (GMM) model is adequate in this situation. The results suggest that the structure of the European framework conditions for entrepreneurship, obtained using the Factor Analysis year by year, is quite diversified until 2008, while after 2008, it is more stable. Moreover, it is concluded that the conditions associated with entrepreneurial intentions and entrepreneurial activity differ between these two time periods. Hence, the dynamic aspect of the structural conditions that affect entrepreneurial activities or intentions should be acknowledged.info:eu-repo/semantics/publishedVersio

Inventory models with reverse logistics for assets acquisition in a liquefied petroleum gas company

This paper addresses a case study regarding inventory models for acquiring liquefied petroleum gas (LPG) cylinders. This is an industrial challenge that was proposed at an European Study Group with Industry, by a Portuguese energy company, for which the LPG cylinder is the main asset of its LPG business. Due to the importance of this asset, an acquisition plan must be defined in order to determine the amount of LPG cylinders to acquire, and when to acquire them, in order to optimize the investment. As cylinders are returned and refilled, the reverse logistic flows of these assets must be considered. As the classical inventory models are not suitable for this case study, three new inventory models, which account for the return of LPG cylinders, are proposed in this work. The first proposed model considers deterministic constant demand and continuous returns of LPG cylinders, with discrete replenishment from the supplier. The second model is similar, but for the case when the returned cylinders cover for the demand. A third model is also proposed considering that both the demand and the returns are stochastic in nature and the replenishment from the supplier is discrete. The three models address different scenarios that the company is either currently facing or is expecting to occur in the near future.publishe

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

Linking corporate social responsibility, cooperation and innovation: the triple bottom line perspective

Purpose – Drawing on the resource-based view (RBV) and knowledge-based view (KBV) theories, this studycontributes to deepen the knowledge that corporate social responsibility (CSR) exerts on firms’ innovation,considering the role played by cooperation. The research also seeks to ascertain the factors that influence thedevelopment of business cooperation. Design/methodology/approach – The database used is the Community Innovation Survey (CIS, 2014)applied in the European Union (EU) during the time period 2012–2014. A sample of 7083 Portuguese firms wereanalyzed through the partial least squares structural equation modeling (PLS-SEM). Findings – The results suggest that CSR positively relates with firms’ innovation, and business cooperationpartially mediates this relationship. The outcomes also reveal that investing in certain types of innovationactivities increases the firms’ willingness to cooperate. Originality/value – The findings contribute to encourage an open innovation strategy as an easy andeffective way to cope with rapid trends and changes, since it demonstrates the complementary betweeninnovation and cooperation, as sources of value creation. From a triple bottom line (TBL) perspective, it alsohighlights that CSR must include social, economic and environmental initiatives, and should be a part of thefirms’ innovation strategy. As a result, managers who intend to contribute for society in the long term shouldplan, monitor and manage all CSR dimensions

MANOVA for Distinguishing Experts’ Perceptions about Entrepreneurship using NES Data from GEM

Global Entrepreneurship Monitor is a large scale database for internationally comparative entrepreneurship that includes information about many aspects of entrepreneurship activities, perceptions, conditions, national and regional policy, among others, of a large number of countries. This project has two main sources of primary data: the Adult Population Survey and the National Expert Survey. In this work the 2011 and 2012 National Expert Survey datasets are studied. Our goal is to analyze the effects of the different type of entrepreneurship expert specialization on the perceptions about the Entrepreneurial Framework Conditions. For this purpose the multivariate analysis of variance is used. Some similarities between the results obtained for the 2011 and 2012 datasets were found, however the differences between experts still exist.info:eu-repo/semantics/publishedVersio

Consumer Default Risk Assessment in a Banking Institution

Credit scoring is an application of financial risk forecasting to consumer lending. In this study, statistical analysis is applied to credit scoring data from a financial institution to evaluate the default risk of consumer loans. The default risk was found to be influenced by the spread, the age of the consumer, the number of credit cards owned by the consumer. A lower spread, a higher number of credit cards and a younger age of the borrower are factors that decrease the risk of default. Clients receiving the salary in the same banking institution of the loan have less chances of default than clients receiving their salary in another institution. We also found that clients in the lowest income tax echelon have more propensity to default.info:eu-repo/semantics/publishedVersio