Otimização não linear aplicada à operação de sistemas com múltiplos reservatórios para abastecimento de água.

O presente estudo considera a aplicação do modelo SISAGUA de simulação matemática e de otimização para a operação de sistemas de reservatórios integrados em sistemas complexos para o abastecimento de água. O SISAGUA utiliza a programação não linear inteira mista (PNLIM) com os objetivos de evitar ou minimizar racionamentos, equilibrar a distribuição dos armazenamentos em sistemas com múltiplos reservatórios e minimizar os custos de operação. A metodologia de otimização foi aplicada para o sistema produtor de água da Região Metropolitana de São Paulo (RMSP), que enfrenta a crise hídrica diante de um cenário de estiagem em 2013-2015, o pior na série histórica dos últimos 85 anos. Trata-se de uma região com 20,4 milhões de habitantes. O sistema é formado por oito sistemas produtores parcialmente integrados e operados pela Sabesp (Companhia de Saneamento do Estado de São Paulo). A RMSP é uma região com alta densidade demográfica, localizada na Bacia Hidrográfica do Alto Tietê e caracterizada pela baixa disponibilidade hídrica per capita. Foi abordada a possibilidade de considerar a evaporação durante as simulações, e a aplicação de uma regra de racionamento contínua nos reservatórios, que transforma a formulação do problema em programação não linear (PNL). A evaporação se mostrou pouco representativa em relação a vazão de atendimento à demanda, com cerca de 1% da vazão. Se por um lado uma vazão desta magnitude pode contribuir em um cenário crítico, por outro essa ordem de grandeza pode ser comparada às incertezas de medições ou previsões de afluências. O teste de sensibilidade das diferentes taxas de racionamento em função do volume armazenado permite analisar o tempo de resposta de cada sistema. A variação do tempo de recuperação, porém, não se mostrou muito significativo.

Rigorous Design of Complex Distillation Columns Using Process Simulators and the Particle Swarm Optimization Algorithm

We present a derivative-free optimization algorithm coupled with a chemical process simulator for the optimal design of individual and complex distillation processes using a rigorous tray-by-tray model. The proposed approach serves as an alternative tool to the various models based on nonlinear programming (NLP) or mixed-integer nonlinear programming (MINLP) . This is accomplished by combining the advantages of using a commercial process simulator (Aspen Hysys), including especially suited numerical methods developed for the convergence of distillation columns, with the benefits of the particle swarm optimization (PSO) metaheuristic algorithm, which does not require gradient information and has the ability to escape from local optima. Our method inherits the superstructure developed in Yeomans, H.; Grossmann, I. E.Optimal design of complex distillation columns using rigorous tray-by-tray disjunctive programming models. Ind. Eng. Chem. Res.2000, 39 (11), 4326–4335, in which the nonexisting trays are considered as simple bypasses of liquid and vapor flows. The implemented tool provides the optimal configuration of distillation column systems, which includes continuous and discrete variables, through the minimization of the total annual cost (TAC). The robustness and flexibility of the method is proven through the successful design and synthesis of three distillation systems of increasing complexity.

Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform

The integrability of the nonlinear Schräodinger equation (NLSE) by the inverse scattering transform shown in a seminal work [1] gave an interesting opportunity to treat the corresponding nonlinear channel similar to a linear one by using the nonlinear Fourier transform. Integrability of the NLSE is in the background of the old idea of eigenvalue communications [2] that was resurrected in recent works [3{7]. In [6, 7] the new method for the coherent optical transmission employing the continuous nonlinear spectral data | nonlinear inverse synthesis was introduced. It assumes the modulation and detection of data using directly the continuous part of nonlinear spectrum associated with an integrable transmission channel (the NLSE in the case considered). Although such a transmission method is inherently free from nonlinear impairments, the noisy signal corruptions, arising due to the ampli¯er spontaneous emission, inevitably degrade the optical system performance. We study properties of the noise-corrupted channel model in the nonlinear spectral domain attributed to NLSE. We derive the general stochastic equations governing the signal evolution inside the nonlinear spectral domain and elucidate the properties of the emerging nonlinear spectral noise using well-established methods of perturbation theory based on inverse scattering transform [8]. It is shown that in the presence of small noise the communication channel in the nonlinear domain is the additive Gaussian channel with memory and signal-dependent correlation matrix. We demonstrate that the effective spectral noise acquires colouring", its autocorrelation function becomes slow decaying and non-diagonal as a function of \frequencies", and the noise loses its circular symmetry, becoming elliptically polarized. Then we derive a low bound for the spectral effiency for such a channel. Our main result is that by using the nonlinear spectral techniques one can significantly increase the achievable spectral effiency compared to the currently available methods [9]. REFERENCES 1. Zakharov, V. E. and A. B. Shabat, Sov. Phys. JETP, Vol. 34, 62{69, 1972. 2. Hasegawa, A. and T. Nyu, J. Lightwave Technol., Vol. 11, 395{399, 1993. 3. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4312{4328, 2014. 4. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4329{4345 2014. 5. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4346{4369, 2014. 6. Prilepsky, J. E., S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, Phys. Rev. Lett., Vol. 113, 013901, 2014. 7. Le, S. T., J. E. Prilepsky, and S. K. Turitsyn, Opt. Express, Vol. 22, 26720{26741, 2014. 8. Kaup, D. J. and A. C. Newell, Proc. R. Soc. Lond. A, Vol. 361, 413{446, 1978. 9. Essiambre, R.-J., G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol., Vol. 28, 662{701, 2010.

Interrupted searches in the BBMCSFilter context for MINLP problems

The BBMCSFilter method was developed to solve mixed integer nonlinear programming problems. This kind of problems have integer and continuous variables and they appear very frequently in process engineering problems. The objective of this work is to analyze the performance of the method when the coordinate searches are interrupted in the context of the multistart strategy. From the numerical experiments, we observed a reduction on the number of function evaluations and on the CPU time.

Planning of distribution networks for medium voltage and low voltage

Determination of the placement and rating of transformers and feeders are the main objective of the basic distribution network planning. The bus voltage and the feeder current are two constraints which should be maintained within their standard range. The distribution network planning is hardened when the planning area is located far from the sources of power generation and the infrastructure. This is mainly as a consequence of the voltage drop, line loss and system reliability. Long distance to supply loads causes a significant amount of voltage drop across the distribution lines. Capacitors and Voltage Regulators (VRs) can be installed to decrease the voltage drop. This long distance also increases the probability of occurrence of a failure. This high probability leads the network reliability to be low. Cross-Connections (CC) and Distributed Generators (DGs) are devices which can be employed for improving system reliability. Another main factor which should be considered in planning of distribution networks (in both rural and urban areas) is load growth. For supporting this factor, transformers and feeders are conventionally upgraded which applies a large cost. Installation of DGs and capacitors in a distribution network can alleviate this issue while the other benefits are gained. In this research, a comprehensive planning is presented for the distribution networks. Since the distribution network is composed of low and medium voltage networks, both are included in this procedure. However, the main focus of this research is on the medium voltage network planning. The main objective is to minimize the investment cost, the line loss, and the reliability indices for a study timeframe and to support load growth. The investment cost is related to the distribution network elements such as the transformers, feeders, capacitors, VRs, CCs, and DGs. The voltage drop and the feeder current as the constraints are maintained within their standard range. In addition to minimizing the reliability and line loss costs, the planned network should support a continual growth of loads, which is an essential concern in planning distribution networks. In this thesis, a novel segmentation-based strategy is proposed for including this factor. Using this strategy, the computation time is significantly reduced compared with the exhaustive search method as the accuracy is still acceptable. In addition to being applicable for considering the load growth, this strategy is appropriate for inclusion of practical load characteristic (dynamic), as demonstrated in this thesis. The allocation and sizing problem has a discrete nature with several local minima. This highlights the importance of selecting a proper optimization method. Modified discrete particle swarm optimization as a heuristic method is introduced in this research to solve this complex planning problem. Discrete nonlinear programming and genetic algorithm as an analytical and a heuristic method respectively are also applied to this problem to evaluate the proposed optimization method.

Optimal coordination of overcurrent relays in distribution systems with distributed generators based on differential evolution algorithm

Distributed generators (DGs) are defined as generators that are connected to a distribution network. The direction of the power flow and short-circuit current in a network could be changed compared with one without DGs. The conventional protective relay scheme does not meet the requirement in this emerging situation. As the number and capacity of DGs in the distribution network increase, the problem of coordinating protective relays becomes more challenging. Given this background, the protective relay coordination problem in distribution systems is investigated, with directional overcurrent relays taken as an example, and formulated as a mixed integer nonlinear programming problem. A mathematical model describing this problem is first developed, and the well-developed differential evolution algorithm is then used to solve it. Finally, a sample system is used to demonstrate the feasiblity and efficiency of the developed method.

Reliability Optimization using SLUMT

This paper is concerned with the reliability optimization of a spatially redundant system, subject to various constraints, by using nonlinear programming. The constrained optimization problem is converted into a sequence of unconstrained optimization problems by using a penalty function. The new problem is then solved by the conjugate gradient method. The advantages of this method are highlighted.

A four-timescale algorithm for constrained stochastic optimization of RED

The overall performance of random early detection (RED) routers in the Internet is determined by the settings of their associated parameters. The non-availability of a functional relationship between the RED performance and its parameters makes it difficult to implement optimization techniques directly in order to optimize the RED parameters. In this paper, we formulate a generic optimization framework using a stochastically bounded delay metric to dynamically adapt the RED parameters. The constrained optimization problem thus formulated is solved using traditional nonlinear programming techniques. Here, we implement the barrier and penalty function approaches, respectively. We adopt a second-order nonlinear optimization framework and propose a novel four-timescale stochastic approximation algorithm to estimate the gradient and Hessian of the barrier and penalty objectives and update the RED parameters. A convergence analysis of the proposed algorithm is briefly sketched. We perform simulations to evaluate the performance of our algorithm with both barrier and penalty objectives and compare these with RED and a variant of it in the literature. We observe an improvement in performance using our proposed algorithm over RED, and the above variant of it.

Improved Inverted V-Notch or Chimney Weir

This paper is devoted to the improvement of the measuring range of inverted V-notch (IVN) weir, a practical linear sharp-crested weir, designed earlier by the writers. The range of linearity of IVN can be considerably enhanced (by more than 200%) by the addition of a retangular weir of width 0.265W (W = half crest width) at a depth of 0.735d (d = altitude of IVN), above the crest of the weir, which is equivalent to providing at this depth two vertical straight lines to the IVN, resulting in a chimney-shaped profile; hence, the modified weir is named chimney weir. The design parameters of the weir, that is, the linearity range, base flow depth, and datum constant, which fixes the reference plane of the weir, are estimated by solving the nonlinear programming problem using a numerical optimization procedure. For flows through this weir above a depth of 0.22d, the discharges are proportional to the depth of flow measured above a reference plane situated at 0.08d above the weir crest for all heads in the range 0.22d <= h <= 2.43d, within a maximum percentage deviation of ±1.5 from the theoretical discharge. A significant result of the analysis is that the same linear head-discharge relationship governing the flow through the IVN is also valid for the extended chimney weir. Experiments with three different chimney weirs show excellent agreement with the theory by giving a constant average coefficient of discharge for each weir.

Metaheurística para o Problema de Planejamento de Redes de Transmissão de Energia Elétrica com Redimensionamento

Com o passar do tempo, a demanda elétrica de diversas áreas varia tornando necessária a construção de novos geradores elétricos e a expansão da rede de transmissão de energia elétrica. Nesta dissertação, focamos no problema de expansão da rede de transmissão, assumindo que novos geradores estão construídos para suprir as novas demandas. Essa expansão exige altos investimentos que precisam ser cuidadosamente planejados. O problema pode ser modelado como um problema de otimização não linear inteira mista e pertence à classe dos problemas NP-difíceis. Desta forma, uma abordagem heurística pode ser adequada para a sua solução pois pode vir a fornecer boas soluções em tempo computacional aceitável. Esta dissertação se propõe a apresentar um estudo do problema de planejamento da expansão de redes de transmissão de energia elétrica estático e multiestágio. Mostramos o que já existe na literatura para o que é chamado de problema sem redimensionamento e as inovações feitas por nós para o problema com redimensionamento. Quanto aos métodos de solução, utilizamos a metaheurística GRASP para o problema estático e combinamos o GRASP com o procedimento Backward-Forward quando falamos em problema multiestágio. Nesta dissertação comparamos os resultados computacionais obtidos com resultados encontrados na literatura.

Minimum maneuver time calculation using convex optimization

The problem of calculating the minimum lap or maneuver time of a nonlinear vehicle, which is linearized at each time step, is formulated as a convex optimization problem. The formulation provides an alternative to previously used quasi-steady-state analysis or nonlinear optimization. Key steps are: the use of model predictive control; expressing the minimum time problem as one of maximizing distance traveled along the track centerline; and linearizing the track and vehicle trajectories by expressing them as small displacements from a fixed reference. A consequence of linearizing the vehicle dynamics is that nonoptimal steering control action can be generated, but attention to the constraints and the cost function minimizes the effect. Optimal control actions and vehicle responses for a 90 deg bend are presented and compared to the nonconvex nonlinear programming solution. Copyright © 2013 by ASME.

双机械臂协调系统的一类最优轨迹规划方法

基于动力学约束的机械臂最优关节轨迹规划

本文提出了基于机械臂关节驱动力矩约束方程规划其关节最优运动轨迹的一种有效方法.该方法运用矩阵范数理论简化机械臂的动力学约束方程;在机械臂的关节空间内采用归一化的无因次量运用非线性规划法优化其运动轨迹.将所规划的无因次量轨迹方程作为机械臂产生实际运动轨迹的发生器,通过给定机械臂各运动段的起始和终止关节坐标,由系统的动力学约束方程计算出整个运动段所允许的最短运行时间,即生成所期望的运动轨迹.本文的轨迹规划方法计算效率高,可用于在线轨迹规划,文中通过算例证实了该方法的实用性.

Accurate and Efficient Gesture Spotting via Pruning and Subgesture Reasoning

Gesture spotting is the challenging task of locating the start and end frames of the video stream that correspond to a gesture of interest, while at the same time rejecting non-gesture motion patterns. This paper proposes a new gesture spotting and recognition algorithm that is based on the continuous dynamic programming (CDP) algorithm, and runs in real-time. To make gesture spotting efficient a pruning method is proposed that allows the system to evaluate a relatively small number of hypotheses compared to CDP. Pruning is implemented by a set of model-dependent classifiers, that are learned from training examples. To make gesture spotting more accurate a subgesture reasoning process is proposed that models the fact that some gesture models can falsely match parts of other longer gestures. In our experiments, the proposed method with pruning and subgesture modeling is an order of magnitude faster and 18% more accurate compared to the original CDP algorithm.

Kuznetsov independence for interval-valued expectations and sets of probability distributions: Properties and algorithms

Kuznetsov independence of variables X and Y means that, for any pair of bounded functions f(X) and g(Y), E[f(X)g(Y)]=E[f(X)] *times* E[g(Y)], where E[.] denotes interval-valued expectation and *times* denotes interval multiplication. We present properties of Kuznetsov independence for several variables, and connect it with other concepts of independence in the literature; in particular we show that strong extensions are always included in sets of probability distributions whose lower and upper expectations satisfy Kuznetsov independence. We introduce an algorithm that computes lower expectations subject to judgments of Kuznetsov independence by mixing column generation techniques with nonlinear programming. Finally, we define a concept of conditional Kuznetsov independence, and study its graphoid properties.