An application of semi-infinite programming to air pollution control

Environment issues are more then ever important in a modern society. Complying with stricter legal thresholds on pollution emissions raises an important economic issue. This talk presents some ideas in the use of optimization tools to help in the planning and control of non mobile pollution sources. We assume a Gaussian plume model where a plume rise and weather stabilities classes are considered. Three main semi-infinite programming formulations are described and numerical results are shown

Optimal control of fed-batch processes with particle swarm optimization

Optimal control problems appear in several engineering fields. These problems are often described by sets of nonlinear differential and algebraic equations, usually subject to constraints in the state and control variables. Some bioprocess optimal control problems are revisited and a numerical approach to its solution is introduced. The numerical procedure used to solve the problems takes advantage of the well know modeling AMPL language, providing an external dynamic library that solve the nonlinear differential equations. The optimal control problem as generally presented belongs to the class of semi-infinite programming (SIP) problems. A transformation of the SIP problem results in a nonlinear optimization problem (NLP) that can be address by off-the-shelf optimization software. The NLP formulation results in nondifferentiable optimization problems were the global solution is mostly desirable. We apply a particle swarm optimization strategy implemented in the MLOCPSOA [13] solver. Particle swarm optimization (PSO) is a stochastic technique that mimics the social behavior of a swarm

Optimização e controlo da poluição atmosférica

Alguns problemas de controlo da poluição atmosférica podem ser formulados como problemas de programação semi-infinita (PSI). Estas formulações, das quais descrevemos três abordagens, permitem que as instalações fabris cumpram a legislação da poluição atmosférica enquanto que o impacto económico é minimizado. As mesmas ferramentas da programação matemática podem também ser usadas pelas autoridades competentes no sentido de verificar que os limites impostos por lei são cumpridos, através do planeamento da localização dos postos de amostragem/controlo. A primeira das formulações consiste em optimizar um determinado objectivo enquanto que o nível de poluição atmosférica é mantido abaixo de um valor de referência. A segunda consiste no cálculo da poluição atmosférica máxima atingida numa determinada região e a terceira considera um problemas de redução da poluição. Estas formulações permitem obter os melhores parâmetros de controlo e as posições onde os valores máximos da poluição são atingidos, posições essas que correspondem ao melhor posicionamento dos postos de amostragem/controlo. As abordagens propostas são ilustradas com quatro problemas académicos. As ferramentas actualmente existentes apoiam a PSI desde a modelação do problema até à sua resolução. A linguagem de modelação (SIP)AMPL foi usada para codificar os problemas propostos e o solver NSIPS foi empregue na resolução dos mesmos

Semi-infinite air pollution control problems

Semi-infinite programming (SIP) problems arise in many engineering areas. Robot trajectory planning and optimal signal sets are two fine examples. Air pollution abatement problems, which are linear SIP problems, were proposed in the seventies by Gustafson and Kortanek [Analytical properties of some multiple-source urban diffusion models, Environment and Planning 4, pp. 31- 41, 1972]. Recent available tools for non-linear SIP allow the formulation of more general air control problems, namely the optimum stack design. In the air control SIP problem an objective function is to be optimised (minimum stack height or minimum cleaning costs), where the air pollution, at ground level, is kept bellow a given threshold. A Gaussian model is used to provide estimates of air pollution in a region where mean weather conditions are assumed. In this talk, we present three formulated air pollution control problems coded in the (SIP)AMPL modelling language and numerical results obtained with the discretization method of the NSIPS solver

Air pollution control with semi-infinite programming

Air pollution control problems can be formulated as a semi-infinite programming (SIP) problem and we describe three main approaches. The first consists in optimizing an objective function while the pollution level in a given region is kept bellow a given threshold. In the second approach the maximum pollution level in a given region is computed and in the third an air pollution abatement problem is considered. These formulation allow to obtain the best control parameters and the maxima pollution positions, where the sampling stations should be placed. To illustrate this idea, the (SIP)AMPL modeling language was used to code three academic problems. The SIPAMPL software package includes an interface to connect AMPL to any SIP solver, in particular to the NSIPS solver. Numerical results are shown with the discretization method, implemented in the NSIPS solver and it proved to be efficient in solving the proposed problems

Optimization models to support sustainable electricity planning decisions

Over the last decades, models and concepts related to sustainable electricity planning decisions have been changed according to the society, energy policy objectives and concerns. New and clean energy technologies are emerging as major contributors for the achievement of a set of imposed goals, being the energy efficiency combined with renewable energy sources (RES) a key strategy for a sustainable future. Power planning based on optimization models plays an important role for, not only electricity industry decision making process, but also for all processes where complex decision must be made. Following the idea of sustainability combined with the emergence of RES, this study aims to present an on-going research project that involves the development of a set of mathematical models to be used on the electricity planning. Assuming a time period of 10 years and through scenario analysis, the expected impacts in terms of costs and CO2 emissions were evaluated. The behaviour of system when coal and gas fuel price varies is observed. The results put evidence the significant wind power and hydro power impacts on the electricity sector performance and demonstrate importance of these technologies to achieve the European Union goals for the sector.This work was financed by: the QREN – Operational Programme for Competitiveness Factors, the European Union – European Regional Development Fund and National Funds- Portuguese Foundation for Science and Technology, under Project FCOMP-01- 0124-FEDER-011377 and Project Pest-OE/EME/UI0252/2011

Optimal trajectory approximation by cubic splines on fed-batch control problems

Optimal control problems appear in several engineering fields and in particular on the control of fedbatch fermentation processes. These problems are often described by sets of nonlinear differential and algebraic equations, usually subject to constraints in the state and control variables. Tradicional approaches to the optimal feed trajectory computation consists in getting a linear spline that approximates the trajectory, which optimizes a given performance of the fed-batch fermentation process. This approach leads to non-differentiable trajectories that can pose some problems to implement in practice, resulting in a possible discrepancy of the simulated and real performances. In this paper we develop a technique to obtain a cubic spline for the approximate trajectory, leading to a smooth approximation function. We provide numerical results for a set of case studies where the AMPL modeling language, CVODE ordinary differential equations solver and a particle swarm algorithm were used.Algoritmi Research Center.Fundação para a Ciência e a Tecnologia (FCT)

Determinação de trajectória óptima em processos de fermentação semi-contínua

Uma grande parte de produtos valiosos são produzidos usando processos de fermentação e consequentemente a optimização destes processos reveste-se de uma grande importância económica. Em geral a modelação dos processos de fermentação envolvem equações diferenciais não lineares e complexas para as quais frequentemente não é possível obter uma solução analítica. Neste trabalho propõe-se uma resolução do problema de determinação da trajectória de alimentação óptima num processo de fermentação semi-contínuo, através do uso de splines cúbicas para a sua aproximação. É apresentada uma reformulação do problema de controlo óptimo através do uso de conceitos de programação semiinfinita no tratamento das restrições. É apresentada uma formulação do problema na linguagem de modelação AMPL, permitindo o uso de software específico para a sua resolução

Short-term scheduling model for a wind-hydro-thermal electricity system

This study addresses the problem of the self-scheduling of an electricity system mainly based on hydro, fossil fuel thermal and wind power plants. A binary mixed integer non-linear optimization model is described and applied to short-term electricity planning of a system close to the expected Portuguese one on the year 2020. The model is written in a GAMS code and a global optimization solver is used to obtain the numerical results. The objective function encompasses the minimization of total system production costs through a centralized unit commitment. Different constraints, essentially related to operating parameters that characterize the power plants available for dispatch, are included in the model. The obtained results show the importance of the renewable energy sources seasonality on the thermal power plants operating conditions and on the total cost of the system.QREN, COMPETE, FCT, under Project FCOMP-01-0124-FEDER-01137