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.

Inexact restoration approaches to solve mathematical program with complementarity constraints

Mathematical Program with Complementarity Constraints (MPCC) finds applica- tion in many fields. As the complementarity constraints fail the standard Linear In- dependence Constraint Qualification (LICQ) or the Mangasarian-Fromovitz constraint qualification (MFCQ), at any feasible point, the nonlinear programming theory may not be directly applied to MPCC. However, the MPCC can be reformulated as NLP problem and solved by nonlinear programming techniques. One of them, the Inexact Restoration (IR) approach, performs two independent phases in each iteration - the feasibility and the optimality phases. This work presents two versions of an IR algorithm to solve MPCC. In the feasibility phase two strategies were implemented, depending on the constraints features. One gives more importance to the complementarity constraints, while the other considers the priority of equality and inequality constraints neglecting the complementarity ones. The optimality phase uses the same approach for both algorithm versions. The algorithms were implemented in MATLAB and the test problems are from MACMPEC collection.

Mixed extractant systems for metal recovery

Hoje em dia, a prevenção dos resíduos de metais é uma questão muito importante para um grande número de empresas, pois necessitam optimizar o seu sistema de tratamento de águas residuais a fim de alcançarem os limites legais dos teores em iões metálicos e poderem efectuar a descarga das águas residuais no domínio hídrico público. Devido a esta problemática foram efectuados estudos inovadores relacionados com a remoção de iões metálicos de águas residuais, verificando-se que as tecnologias de membrana oferecem uma série de vantagens para o efeito. Uma dessas tecnologias, referida como Membrana Líquida de Suporte (SLM), é baseada num mecanismo de extracção. A membrana hidrofóbica, impregnada com uma solução extractora, funciona como barreira entre a água residual e uma solução, geralmente ácida. A diferença de pH entre a água residual e a solução actua como força motriz para o transporte de iões metálicos da água residual para a referida solução. Poderá ocorrer um problema de falta de estabilidade, resultante da possível fuga da solução extractora para fora dos poros das membranas. Estudos anteriores mostraram que os ácidos alquilfosfóricos ou ácidos fosfónicos, como os reagentes D2EHPA e CYANEX e hidroxioximas como o LIX 860-I podem ser muito úteis para a extração de iões metálicos como ferro, cobre, níquel, zinco e outros. A clássica extracção líquido-líquido também tem mostrado que a mistura de diferentes extractores pode ter um efeito sinergético. No entanto, não é claro que haja um efeito óptimo da razão de extractor ou que tipo de complexo é formado durante o processo de extracção. O objectivo deste projecto é investigar este comportamento sinergético e as complexas formações por meio de um método espectrofotométrico, o “Job’s method” e “Mole-ratio method”. Estes métodos são utilizados para estimar a estequiometria dos vários complexos entre dois solutos, a partir da variação de absorvância dos complexos quando comparado com a absorvância do soluto. Com este projecto, o Job’s method e mole-ratio method serão aplicados a um sistema de três componentes, para conseguir mais informações sobre a complexação de níquel (II) e a fim de determinar a razão extractor: metal dos complexos formados durante a aplicação de mistura de extractores D2EHPA e LIX 860-I. Segundo Job’s method a elavada absorvância situa-se na região de 0,015-0,040 M de LIX 860-I e uma baixa concentração de D2EHPA. Quando as diferentes experiências são encontradas num conjunto experimental foram avaliadas de acordo com o método de trabalho, o valor máximo do gráfico foi encontrado para uma baixa fração molar do ião metálico e uma maior concentração de D2EHPA. Esta mudança foi encontrado de 0,50 até 0,30, que poderia apontar para a direção da formação de diferentes complexos. Para o Mole-Ratio method, a estequiometria dos complexos metal pode ser determinada a partir do ponto de intersecção das linhas tangente do gráfico da absorbância versus a concentração do ligante. Em todos os casos, o máximo foi obtido em torno de uma concentração total de 0,010 M. Quando D2EHPA foi aplicado sozinho, absorvâncias muito baixos foram obtidas.

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.

A Java expression evaluator for nonlinear programming

Finding the optimal value for a problem is usual in many areas of knowledge where in many cases it is needed to solve Nonlinear Optimization Problems. For some of those problems it is not possible to determine the expression for its objective function and/or its constraints, they are the result of experimental procedures, might be non-smooth, among other reasons. To solve such problems it was implemented an API contained methods to solve both constrained and unconstrained problems. This API was developed to be used either locally on the computer where the application is being executed or remotely on a server. To obtain the maximum flexibility both from the programmers’ and users’ points of view, problems can be defined as a Java class (because this API was developed in Java) or as a simple text input that is sent to the API. For this last one to be possible it was also implemented on the API an expression evaluator. One of the drawbacks of this expression evaluator is that it is slower than the Java native code. In this paper it is presented a solution that combines both options: the problem can be expressed at run-time as a string of chars that are converted to Java code, compiled and loaded dynamically. To wide the target audience of the API, this new expression evaluator is also compatible with the AMPL format.

Analysis of the domain of applicability of an algorithm for a resources system selection problem for Distributed/Agile/Virtual Enterprises integration

The process of resources systems selection takes an important part in Distributed/Agile/Virtual Enterprises (D/A/V Es) integration. However, the resources systems selection is still a difficult matter to solve in a D/A/VE, as it is pointed out in this paper. Globally, we can say that the selection problem has been equated from different aspects, originating different kinds of models/algorithms to solve it. In order to assist the development of a web prototype tool (broker tool), intelligent and flexible, that integrates all the selection model activities and tools, and with the capacity to adequate to each D/A/V E project or instance (this is the major goal of our final project), we intend in this paper to show: a formulation of a kind of resources selection problem and the limitations of the algorithms proposed to solve it. We formulate a particular case of the problem as an integer programming, which is solved using simplex and branch and bound algorithms, and identify their performance limitations (in terms of processing time) based on simulation results. These limitations depend on the number of processing tasks and on the number of pre-selected resources per processing tasks, defining the domain of applicability of the algorithms for the problem studied. The limitations detected open the necessity of the application of other kind of algorithms (approximate solution algorithms) outside the domain of applicability founded for the algorithms simulated. However, for a broker tool it is very important the knowledge of algorithms limitations, in order to, based on problem features, develop and select the most suitable algorithm that guarantees a good performance.

Reverse problem-based learning - a case study with a Braille machine

Engineering Education includes not only teaching theoretical fundamental concepts but also its verification during practical lessons in laboratories. The usual strategies to carry out this action are frequently based on Problem Based Learning, starting from a given state and proceeding forward to a target state. The possibility or the effectiveness of this procedure depends on previous states and if the present state was caused or resulted from earlier ones. This often happens in engineering education when the achieved results do not match the desired ones, e.g. when programming code is being developed or when the cause of the wrong behavior of an electronic circuit is being identified. It is thus important to also prepare students to proceed in the reverse way, i.e. given a start state generate the explanation or even the principles that underlie it. Later on, this sort of skills will be important. For instance, to a doctor making a patient?s story or to an engineer discovering the source of a malfunction. This learning methodology presents pedagogical advantages besides the enhanced preparation of students to their future work. The work presented on his document describes an automation project developed by a group of students in an engineering polytechnic school laboratory. The main objective was to improve the performance of a Braille machine. However, in a scenario of Reverse Problem-Based learning, students had first to discover and characterize the entire machine's function before being allowed (and being able) to propose a solution for the existing problem.

Problema de atribuição de vigilâncias de exames a docentes

O presente trabalho foi realizado com o intuito de resolver o problema de alocação de vigilantes a exames do Instituto Superior de Engenharia do Porto, no departamento de Engenharia Mecânica. O modelo apresentado faz a atribuição das vigilâncias de uma forma hierárquica, utilizando vários critérios, desde a regência da unidade curricular até à simples vigilância. Devido ao facto de estar implementado informaticamente, apresenta reduzidos tempos na formulação e obtenção de uma solução, o que o torna uma boa ferramenta para a criação de cenários alternativos. Em suma, o modelo proposto neste trabalho apresenta soluções de melhor qualidade, em que a distribuição de afetações é proporcional entre os docentes, e o seu tempo de obtenção é muito reduzido em comparação com a alternativa atual.

Environmental taxes in a public Stackelberg leader duopoly

We study whether privatization of a public firm improves (or deteriorates) the environment in a mixed Stackelberg duopoly with the public firm as the leader. We assume that each firm can prevent pollution by undertaking abatement measures. We get that, since in the mixed market the industry output is higher than in the private market, the abatement levels are also higher in the mixed market, and, thus, environmental tax rate in the mixed duopoly is higher than that in the privatized duopoly. Furthermore, the environment is more damaged in the mixed than in the private market. The overall effect on the social welfare is that it will becomes higher in the private than in the mixed market.

Bridging between programming exercises formats with BabeLO

Assessment plays a vital role in learning. This is certainly the case with assessment of computer programs, both in curricular and competitive learning. The lack of a standard – or at least a widely used format – creates a modern Ba- bel tower made of Learning Objects, of assessment items that cannot be shared among automatic assessment systems. These systems whose interoperability is hindered by the lack of a common format include contest management systems, evaluation engines, repositories of learning objects and authoring tools. A prag- matical approach to remedy this problem is to create a service to convert among existing formats. A kind of translation service specialized in programming prob- lems formats. To convert programming exercises on-the-fly among the most used formats is the purpose of the BabeLO – a service to cope with the existing Babel of Learning Object formats for programming exercises. BabeLO was designed as a service to act as a middleware in a network of systems typically used in auto- matic assessment of programs. It provides support for multiple exercise formats and can be used by: evaluation engines to assess exercises regardless of its format; repositories to import exercises from various sources; authoring systems to create exercises in multiple formats or based on exercises from other sources. This paper analyses several of existing formats to highlight both their differ- ences and their similar features. Based on this analysis it presents an approach to extensible format conversion. It presents also the features of PExIL, the pivotal format in which the conversion is based; and the function definitions of the proposed service – BabeLO. Details on the design and implementation of BabeLO, including the service API and the interfaces required to extend the conversion to a new format, are also provided. To evaluate the effectiveness and efficiency of this approach this paper reports on two actual uses of BabeLO: to relocate exercises to a different repository; and to use an evaluation engine in a network of heterogeneous systems.

Day-ahead Resource Scheduling Including Demand Response for Electric Vehicles

The energy resource scheduling is becoming increasingly important, as the use of distributed resources is intensified and massive gridable vehicle (V2G) use is envisaged. This paper presents a methodology for day-ahead energy resource scheduling for smart grids considering the intensive use of distributed generation and V2G. The main focus is the comparison of different EV management approaches in the day-ahead energy resources management, namely uncontrolled charging, smart charging, V2G and Demand Response (DR) programs i n the V2G approach. Three different DR programs are designed and tested (trip reduce, shifting reduce and reduce+shifting). Othe r important contribution of the paper is the comparison between deterministic and computational intelligence techniques to reduce the execution time. The proposed scheduling is solved with a modified particle swarm optimization. Mixed integer non-linear programming is also used for comparison purposes. Full ac power flow calculation is included to allow taking into account the network constraints. A case study with a 33-bus distribution network and 2000 V2G resources is used to illustrate the performance of the proposed method.

Dynamic programming for a Markov-switching jump–diffusion

We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump–diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman’s optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton–Jacobi–Belman equation, which turns out to be a partial integro-differential equation due to the extra terms arising from the Lévy process and the Markov process. As an application of our results, we study a finite horizon consumption– investment problem for a jump–diffusion financial market consisting of one risk-free asset and one risky asset whose coefficients are assumed to depend on the state of a continuous time finite state Markov process. We provide a detailed study of the optimal strategies for this problem, for the economically relevant families of power utilities and logarithmic utilities.

Provably Good Task Assignment for Two-Type Heterogeneous Multiprocessors Using Cutting Planes

Consider scheduling of real-time tasks on a multiprocessor where migration is forbidden. Specifically, consider the problem of determining a task-to-processor assignment for a given collection of implicit-deadline sporadic tasks upon a multiprocessor platform in which there are two distinct types of processors. For this problem, we propose a new algorithm, LPC (task assignment based on solving a Linear Program with Cutting planes). The algorithm offers the following guarantee: for a given task set and a platform, if there exists a feasible task-to-processor assignment, then LPC succeeds in finding such a feasible task-to-processor assignment as well but on a platform in which each processor is 1.5 × faster and has three additional processors. For systems with a large number of processors, LPC has a better approximation ratio than state-of-the-art algorithms. To the best of our knowledge, this is the first work that develops a provably good real-time task assignment algorithm using cutting planes.

Using interval graphs in an order processing optimization problem

In this paper we address an order processing optimization problem known as minimization of open stacks (MOSP). We present an integer pro gramming model, based on the existence of a perfect elimination scheme in interval graphs, which finds an optimal sequence for the costumers orders.