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.

Stochastic short-term maintenance scheduling of GENCOs in an oligopolistic electricity market

In the proposed model, the independent system operator (ISO) provides the opportunity for maintenance outage rescheduling of generating units before each short-term (ST) time interval. Long-term (LT) scheduling for 1 or 2 years in advance is essential for the ISO and the generation companies (GENCOs) to decide their LT strategies; however, it is not possible to be exactly followed and requires slight adjustments. The Cournot-Nash equilibrium is used to characterize the decision-making procedure of an individual GENCO for ST intervals considering the effective coordination with LT plans. Random inputs, such as parameters of the demand function of loads, hourly demand during the following ST time interval and the expected generation pattern of the rivals, are included as scenarios in the stochastic mixed integer program defined to model the payoff-maximizing objective of a GENCO. Scenario reduction algorithms are used to deal with the computational burden. Two reliability test systems were chosen to illustrate the effectiveness of the proposed model for the ST decision-making process for future planned outages from the point of view of a GENCO.

Self-similarity principle: the reduced description of randomness

A new general fitting method based on the Self-Similar (SS) organization of random sequences is presented. The proposed analytical function helps to fit the response of many complex systems when their recorded data form a self-similar curve. The verified SS principle opens new possibilities for the fitting of economical, meteorological and other complex data when the mathematical model is absent but the reduced description in terms of some universal set of the fitting parameters is necessary. This fitting function is verified on economical (price of a commodity versus time) and weather (the Earth’s mean temperature surface data versus time) and for these nontrivial cases it becomes possible to receive a very good fit of initial data set. The general conditions of application of this fitting method describing the response of many complex systems and the forecast possibilities are discussed.

Memória de longo prazo nos retornos acionistas dos índices de referência da euronext, implicações para a hipótese de mercados eficientes e contributo fractal para aperfeiçoamento do capital asset pricing model

Não existe uma definição única de processo de memória de longo prazo. Esse processo é geralmente definido como uma série que possui um correlograma decaindo lentamente ou um espectro infinito de frequência zero. Também se refere que uma série com tal propriedade é caracterizada pela dependência a longo prazo e por não periódicos ciclos longos, ou que essa característica descreve a estrutura de correlação de uma série de longos desfasamentos ou que é convencionalmente expressa em termos do declínio da lei-potência da função auto-covariância. O interesse crescente da investigação internacional no aprofundamento do tema é justificado pela procura de um melhor entendimento da natureza dinâmica das séries temporais dos preços dos ativos financeiros. Em primeiro lugar, a falta de consistência entre os resultados reclama novos estudos e a utilização de várias metodologias complementares. Em segundo lugar, a confirmação de processos de memória longa tem implicações relevantes ao nível da (1) modelação teórica e econométrica (i.e., dos modelos martingale de preços e das regras técnicas de negociação), (2) dos testes estatísticos aos modelos de equilíbrio e avaliação, (3) das decisões ótimas de consumo / poupança e de portefólio e (4) da medição de eficiência e racionalidade. Em terceiro lugar, ainda permanecem questões científicas empíricas sobre a identificação do modelo geral teórico de mercado mais adequado para modelar a difusão das séries. Em quarto lugar, aos reguladores e gestores de risco importa saber se existem mercados persistentes e, por isso, ineficientes, que, portanto, possam produzir retornos anormais. O objetivo do trabalho de investigação da dissertação é duplo. Por um lado, pretende proporcionar conhecimento adicional para o debate da memória de longo prazo, debruçando-se sobre o comportamento das séries diárias de retornos dos principais índices acionistas da EURONEXT. Por outro lado, pretende contribuir para o aperfeiçoamento do capital asset pricing model CAPM, considerando uma medida de risco alternativa capaz de ultrapassar os constrangimentos da hipótese de mercado eficiente EMH na presença de séries financeiras com processos sem incrementos independentes e identicamente distribuídos (i.i.d.). O estudo empírico indica a possibilidade de utilização alternativa das obrigações do tesouro (OT’s) com maturidade de longo prazo no cálculo dos retornos do mercado, dado que o seu comportamento nos mercados de dívida soberana reflete a confiança dos investidores nas condições financeiras dos Estados e mede a forma como avaliam as respetiva economias com base no desempenho da generalidade dos seus ativos. Embora o modelo de difusão de preços definido pelo movimento Browniano geométrico gBm alegue proporcionar um bom ajustamento das séries temporais financeiras, os seus pressupostos de normalidade, estacionariedade e independência das inovações residuais são adulterados pelos dados empíricos analisados. Por isso, na procura de evidências sobre a propriedade de memória longa nos mercados recorre-se à rescaled-range analysis R/S e à detrended fluctuation analysis DFA, sob abordagem do movimento Browniano fracionário fBm, para estimar o expoente Hurst H em relação às séries de dados completas e para calcular o expoente Hurst “local” H t em janelas móveis. Complementarmente, são realizados testes estatísticos de hipóteses através do rescaled-range tests R/S , do modified rescaled-range test M - R/S e do fractional differencing test GPH. Em termos de uma conclusão única a partir de todos os métodos sobre a natureza da dependência para o mercado acionista em geral, os resultados empíricos são inconclusivos. Isso quer dizer que o grau de memória de longo prazo e, assim, qualquer classificação, depende de cada mercado particular. No entanto, os resultados gerais maioritariamente positivos suportam a presença de memória longa, sob a forma de persistência, nos retornos acionistas da Bélgica, Holanda e Portugal. Isto sugere que estes mercados estão mais sujeitos a maior previsibilidade (“efeito José”), mas também a tendências que podem ser inesperadamente interrompidas por descontinuidades (“efeito Noé”), e, por isso, tendem a ser mais arriscados para negociar. Apesar da evidência de dinâmica fractal ter suporte estatístico fraco, em sintonia com a maior parte dos estudos internacionais, refuta a hipótese de passeio aleatório com incrementos i.i.d., que é a base da EMH na sua forma fraca. Atendendo a isso, propõem-se contributos para aperfeiçoamento do CAPM, através da proposta de uma nova fractal capital market line FCML e de uma nova fractal security market line FSML. A nova proposta sugere que o elemento de risco (para o mercado e para um ativo) seja dado pelo expoente H de Hurst para desfasamentos de longo prazo dos retornos acionistas. O expoente H mede o grau de memória de longo prazo nos índices acionistas, quer quando as séries de retornos seguem um processo i.i.d. não correlacionado, descrito pelo gBm(em que H = 0,5 , confirmando- se a EMH e adequando-se o CAPM), quer quando seguem um processo com dependência estatística, descrito pelo fBm(em que H é diferente de 0,5, rejeitando-se a EMH e desadequando-se o CAPM). A vantagem da FCML e da FSML é que a medida de memória de longo prazo, definida por H, é a referência adequada para traduzir o risco em modelos que possam ser aplicados a séries de dados que sigam processos i.i.d. e processos com dependência não linear. Então, estas formulações contemplam a EMH como um caso particular possível.

Uncertainty propagation in inverse reliability-based design of composite structures

An approach for the analysis of uncertainty propagation in reliability-based design optimization of composite laminate structures is presented. Using the Uniform Design Method (UDM), a set of design points is generated over a domain centered on the mean reference values of the random variables. A methodology based on inverse optimal design of composite structures to achieve a specified reliability level is proposed, and the corresponding maximum load is outlined as a function of ply angle. Using the generated UDM design points as input/output patterns, an Artificial Neural Network (ANN) is developed based on an evolutionary learning process. Then, a Monte Carlo simulation using ANN development is performed to simulate the behavior of the critical Tsai number, structural reliability index, and their relative sensitivities as a function of the ply angle of laminates. The results are generated for uniformly distributed random variables on a domain centered on mean values. The statistical analysis of the results enables the study of the variability of the reliability index and its sensitivity relative to the ply angle. Numerical examples showing the utility of the approach for robust design of angle-ply laminates are presented.

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.

Fitness function evaluation through fractional algorithms

This paper proposes a Genetic Algorithm (GA) for the design of combinational logic circuits. The fitness function evaluation is calculated using Fractional Calculus. This approach extends the classical fitness function by including a fractional-order dynamical evaluation. The experiments reveal superior results when comparing with the classical method.

A biased random-key genetic algorithm with forward-backward improvement for the resource constrained project scheduling problem

This paper presents a biased random-key genetic algorithm for the resource constrained project scheduling problem. The chromosome representation of the problem is based on random keys. Active schedules are constructed using a priority-rule heuristic in which the priorities of the activities are defined by the genetic algorithm. A forward-backward improvement procedure is applied to all solutions. The chromosomes supplied by the genetic algorithm are adjusted to reflect the solutions obtained by the improvement procedure. The heuristic is tested on a set of standard problems taken from the literature and compared with other approaches. The computational results validate the effectiveness of the proposed algorithm.

Fractional describing function of systems with nonlinear friction

This paper studies the describing function (DF) of systems consisting in a mass subjected to nonlinear friction. The friction force is composed in three components namely, the viscous, the Coulomb and the static forces. The system dynamics is analyzed in the DF perspective revealing a fractional-order behaviour. The reliability of the DF method is evaluated through the signal harmonic content and the limit cycle prediction.

A random key based genetic algorithm for the resource constrained project scheduling problem

This paper presents a genetic algorithm for the Resource Constrained Project Scheduling Problem (RCPSP). The chromosome representation of the problem is based on random keys. The schedule is constructed using a heuristic priority rule in which the priorities of the activities are defined by the genetic algorithm. The heuristic generates parameterized active schedules. The approach was tested on a set of standard problems taken from the literature and compared with other approaches. The computational results validate the effectiveness of the proposed algorithm.

Describing function of two masses with backlash

This paper analyzes the dynamical properties of systems with backlash and impact phenomena based on the describing function method. It is shown that this type of nonlinearity can be analyzed in the perspective of the fractional calculus theory. The fractional dynamics is compared with that of standard models.

Fractional describing function of systems with Coulomb friction

This paper studies the describing function (DF) of systems constituted by a mass subjected to nonlinear friction. The friction force is decomposed into two components, namely, the viscous and the Coulomb friction. The system dynamics is analyzed in the DF perspective revealing a fractional-order behavior. The reliability of the DF method is evaluated through the signal harmonic contents.