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Optimal design of looped water supply network by GA-NLP hybrid approach

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Optimal design of looped water supply network by GA-NLP hybr...

International Conference on Recent Inventions and Innovations in Mathematical Sciences, ICRIIMS 2019

作者： Prasad, Srinivasa A. Krishna, Leela K. Dept. of Civil Engineering R.V.R. and J.C.College of Engineering Chowdavaram Andhra Pradesh Guntur India

Any Municipal distribution system consists of pipe network, valves and pressure generating facilities etc. Around 70% of total cost of any water distribution system is towards cost of pipe network only. Therefore, the cost of pipe network is to be reduced by selecting the appropriate lengths of candidate diameter pipes between the nodes in a pipe network. In the present study, a municipal looped water distribution network is designed for least cost by Genetic Algorithm - Non Linear programming (GA-NLP) hybrid approach. In the present study, optimal lengths of sub pipes of various discrete diameters (sizes) available in the market making the link between the nodes are obtained by minimising the total cost of pipe network. In order to obtain the optimal solution of a looped network, non - linear hydraulic analysis and optimization of network is to be performed. In this study, non - linear hydraulic analysis is made a part of optimization by adding loop head loss and node continuity equations as constraints to the objective function. The model developed is solved by GA-NLP hybrid approach in MATLAB. Near optimal solution obtained by GA is taken as initial solution of NLP for obtaining optimal solution. By adopting GA-NLP hybrid approach, convergence is faster when compared to GA avoiding the complexity in selection of suitable trial values of GA parameters. Many researchers applied different techniques like linear programming, integer linear programming, linear programming gradient method and branch & bound algorithm etc. and optimized the looped pipe network by minimizing the cost. The results obtained by proposed model are compared with that of other investigators and found to be superior. It is also concluded that the proposed model may be applied to any larger municipal looped pipe network through demonstration by applying proposed model to a case study of Rajiv Gandhi Nagar of Guntur Municipal Corporation. © Published under licence by IOP Publishing Ltd.

关键词： nonlinear programming

Local path-following property of inexact interior methods in nonlinear programming

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Local path-following property of inexact interior methods in...

24th International Federation for Information Processing-7th Technical Committee Conference on System Modeling and Optimization

作者： Armand, Paul Benoist, Joel Dussault, Jean-Pierre Univ Limoges Lab XLIM CNRS UMR 6172 Limoges France Univ Sherbrooke Dept Informat Sherbrooke PQ J1K 2R1 Canada

We study the local behavior of a primal-dual inexact interior point methods for solving nonlinear systems arising from the solution of nonlinear optimization problems or more generally from nonlinear complementarity problems. The algorithm is based on the Newton method applied to a sequence of perturbed systems that follows by perturbation of the complementarity equations of the original system. In case of an exact solution of the Newton system, it has been shown that the sequence of iterates is asymptotically tangent to the central path (Armand and Benoist in Math. Program. 115:199-222, 2008). The purpose of the present paper is to extend this result to an inexact solution of the Newton system. We give quite general conditions on the different parameters of the algorithm, so that this asymptotic property is satisfied. Some numerical tests are reported to illustrate our theoretical results.

关键词： Constrained optimization Interior methods nonlinear programming Primal-dual methods nonlinear complementarity problems Inexact Newton method

Reactive Power Optimization for Loss Reduction and Voltage Profile Improvement

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Reactive Power Optimization for Loss Reduction and Voltage P...

2019 IEEE PES Conference on Innovative Smart Grid Technologies, ISGT Latin America 2019

作者： Mazzini, Ana Paula Asada, Eduardo N. Lage, Guilherme G. Federal Institute of Education Science and Technology of São Paulo Campus Matão Rua Stéfano Dävassi 625 Nova Cidade Matão SP Brazil Department of Electrical and Computer Engineering São Carlos School of Engineering University of São Paulo São Carlos SP Brazil Department of Electrical Engineering Center for Exact Sciences and Technology Federal University of São Carlos São Carlos SP13565-905 Brazil

ISBN: (纸本)9781538695678

This paper proposes the resolution of the optimal reactive dispatch (ORD) problem for the combined objective of minimizing active power losses and voltage profile improvement on load buses considering discrete variables and limited the number of control adjustments. The problem is modeled as a multiobjective ORD problem, a resolution strategy which models discrete control variables by a polynomial discretization function and considers limited number of control adjustments is proposed. The proposed solution method is based on transformation of the original mixed integer nonlinear programming (MINLP) problem with mixed continuous, discrete and binary control variables into a nonlinear programming (NLP) problem with only continuous variables. The method has been tested with IEEE test systems with 118 and 300 buses and the success of the proposed strategy has been observed with the resulting high quality solutions with high speed computation. © 2019 IEEE.

关键词： nonlinear programming

An integral penalty-barrier direct transcription method for optimal control

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arXiv 2020年

作者： Neuenhofen, Martin Peter Kerrigan, Eric C. Deparment of Electrical & Electronic Engineering Imperial College London LondonSW7 2AZ United Kingdom Deparment of Electrical & Electronic Engineering Department of Aeronautics Imperial College London LondonSW7 2AZ United Kingdom

Some direct transcription methods can fail to converge, e.g. when there are singular arcs. We recently introduced a convergent direct transcription method for optimal control problems, called the penalty-barrier finite element method (PBF). PBF converges under very weak assumptions on the problem instance. PBF avoids the ringing between collocation points, for example, by avoiding collocation entirely. Instead, equality path constraint residuals are forced to zero everywhere by an integral quadratic penalty term. We highlight conceptual differences between collocation- and penalty-type direct transcription methods. Theoretical convergence results for both types of methods are reviewed and compared. Formulas for implementing PBF are presented, with details on the formulation as a nonlinear program (NLP), sparsity and solution. Numerical experiments compare PBF against several collocation methods with regard to robustness, accuracy, sparsity and computational cost. We show that the computational cost, sparsity and construction of the NLP functions are roughly the same as for orthogonal collocation methods of the same degree and mesh. As an advantage, PBF converges in cases where collocation methods fail. PBF also allows one to trade off computational cost, optimality and violation of differential and other equality equations against each *** Codes 49M25 Copyright © 2020, The Authors. All rights reserved.

关键词： nonlinear programming

An Interior Point Method Solving Motion Planning Problems with Narrow Passages

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arXiv 2020年

作者： Mainprice, Jim Ratliff, Nathan Toussaint, Marc Schaal, Stefan Machine Learning and Robotics Lab University of Stuttgart Germany Max Planck Institute for Intelligent Systems IS-MPITübingen & Stuttgart Germany Learning and Intelligent Systems Lab TU Berlin Berlin Germany

Algorithmic solutions for the motion planning problem have been investigated for five decades. Since the development of A* in 1969 many approaches have been investigated, traditionally classified as either grid decomposition, potential fields or sampling-based. In this work, we focus on using numerical optimization, which is understudied for solving motion planning problems. This lack of interest in the favor of sampling-based methods is largely due to the non-convexity introduced by narrow passages. We address this shortcoming by grounding the solution in differential geometry. We demonstrate through a series of experiments on 3 Dofs and 6 Dofs narrow passage problems, how modeling explicitly the underlying Riemannian manifold leads to an efficient interior point non-linear programming solution. 1. Copyright © 2020, The Authors. All rights reserved.

关键词： nonlinear programming

Relations between abs-normal NLPs and MPCCs. Part 2: Weak constraint qualifications

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arXiv 2020年

作者： Hegerhorst-Schultchen, Lisa C. Kirches, Christian Steinbach, Marc C. Leibniz Universität Hannover Institut für Angewandte Mathematik Welfengarten 1 Hannover30167 Germany Technische Universität Carolo-Wilhelmina zu Braunschweig Institut für Mathematische Optimierung Universitätsplatz 2 Braunschweig38106 Germany

This work continues an ongoing effort to compare non-smooth optimization problems in abs-normal form to Mathematical Programs with Complementarity Constraints (MPCCs). We study general nonlinear Programs with equality and inequality constraints in abs-normal form, so-called Abs-Normal NLPs, and their relation to equivalent MPCC reformulations. We introduce the concepts of Abadie's and Guignard's kink qualification and prove relations to MPCC-ACQ and MPCC-GCQ for the counterpart MPCC formulations. Due to non-uniqueness of a specific slack reformulation suggested in [10], the relations are non-trivial. It turns out that constraint qualifications of Abadie type are preserved. We also prove the weaker result that equivalence of Guginard's (and Abadie's) constraint qualifications for all branch problems hold, while the question of GCQ preservation remains open. Finally, we introduce M-stationarity and B-stationarity concepts for abs-normal NLPs and prove first order optimality conditions corresponding to MPCC counterpart *** Codes 90C30, 90C33, 90C46 © 2020, CC BY-SA.

关键词： nonlinear programming

A sigmoidal approximation for chance-constrained nonlinear programs

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arXiv 2020年

作者： Cao, Yankai Zavala, Victor M. Department of Chemical and Biological Engineering University of British Columbia 2360 East Mall VancouverBCV6T1Z3 Canada Department of Chemical and Biological Engineering University of Wisconsin-Madison 1415 Engineering Dr MadisonWI53706 United States

We propose a sigmoidal approximation for the value-at-risk (that we call SigVaR) and we use this approximation to tackle nonlinear programs (NLPs) with chance constraints. We prove that the approximation is conservative and that the level of conservatism can be made arbitrarily small for limiting parameter values. The SigVar approximation brings scalability benefits over exact mixed-integer reformulations because its sample average approximation can be cast as a standard NLP. We also establish explicit connections between SigVaR and other smooth sigmoidal approximations recently reported in the literature. We show that a key benefit of SigVaR over such approximations is that one can establish an explicit connection with the conditional value at risk (CVaR) approximation and exploit this connection to obtain initial guesses for the approximation parameters. We present small- and large-scale numerical studies to illustrate the developments. Copyright © 2020, The Authors. All rights reserved.

关键词： nonlinear programming

A sequential optimality condition for Mathematical Programs with Cardinality Constraints

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arXiv 2020年

作者： Krulikovski, Evelin H.M. Ribeiro, Ademir Alves Sachine, Mael Graduate Program in Mathematics Federal University of Paraná Brazil Department of Mathematics Federal University of Paraná Brazil

In this paper we propose an Approximate Weak stationarity (AW-stationarity) concept designed to deal with Mathematical Programs with Cardinality Constraints (MPCaC), and we proved that it is a legitimate optimality condition independently of any constraint qualification. Such a sequential optimality condition improves weaker stationarity conditions, presented in a previous work. Many research on sequential optimality conditions has been addressed for nonlinear constrained optimization in the last few years, some works in the context of MPCC and, as far as we know, no sequential optimality condition has been proposed for MPCaC problems. We also establish some relationships between our AW-stationarity and other usual sequential optimality conditions, such as AKKT, CAKKT and PAKKT. We point out that, despite the computational appeal of the sequential optimality conditions, in this work we are not concerned with algorithmic consequences. Our aim is purely to discuss theoretical aspects of such conditions for MPCaC *** Codes 90C30, 90C33, 90C46. Copyright © 2020, The Authors. All rights reserved.

关键词： nonlinear programming

Joint Optimisation of Privacy and Cost of in-App Mobile User Profiling and Targeted Ads

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arXiv 2020年

作者： Ullah, Imdad Binbusayyis, Adel College of Computer Engineering and Sciences Prince Sattam Bin Abdulaziz University Al-Kharj 11942 Saudi Arabia

Online mobile advertising ecosystems provide advertising and analytics services that collect, aggregate, process, and trade a rich amount of consumers' personal data and carry out interest-based ad targeting, which raised serious privacy risks and growing trends of users feeling uncomfortable while using the internet services. In this paper, we address users' privacy concerns by developing an optimal dynamic optimisation cost-effective framework for preserving user privacy for profiling, ads-based inferencing, temporal apps usage behavioral patterns, and interest-based ad targeting. A major challenge in solving this dynamic model is the lack of knowledge of time-varying updates during the profiling process. We formulate a mixed-integer optimisation problem and develop an equivalent problem to show that the proposed algorithm does not require knowledge of time-varying updates in user behavior. Following, we develop an online control algorithm to solve the equivalent problem and overcome the difficulty of solving nonlinear programming by decomposing it into various cases and to achieve a trade-off between user privacy, cost, and targeted ads. We carry out extensive experimentations and demonstrate the proposed framework's applicability by implementing its critical components using POC (Proof Of Concept) 'System App'. We compare the proposed framework with other privacy-protecting approaches and investigate whether it achieves better privacy and functionality for various performance parameters. Copyright © 2020, The Authors. All rights reserved.

关键词： nonlinear programming