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Analytical Optimization Approach for Simultaneous Design and Operation of Water Distribution-Systems Optimization

JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT 2021年第3期147卷

作者： Qiu, Mengning Housh, Mashor Ostfeld, Avi Technion Israel Inst Technol Fac Civil & Environm Engn IL-32000 Haifa Israel Univ Haifa Fac Management Dept Nat Resource & Environm Management IL-3498838 Haifa Israel Technion Fac Civil & Environm Engn IL-32000 Haifa Israel

This paper presents an analytical algorithm for simultaneous least-cost design and operation of looped water distribution systems (WDSs). This method could be used to replace evolutionary methods (which are typically used to solve the design-operation problem), or it can be used in conjunction with evolutionary algorithms to enhance their performance (i.e., a hybrid approach). Unlike previous studies that propose analytical methods for split-pipe or continuous diameter design, the developed method addresses a more realistic case in which the pipe design is restricted to commercially available discrete diameters. The analytical approach consists of three stages. In the first stage, a reformulated linear programming (LP) method is used to find the least-cost design of a WDS for a given set of flow distribution while allowing a pipe-split in the solution. In the second stage, the equivalent pipe diameters of the split-pipe design are calculated and modified to discrete pipe diameters by applying a rounding-up strategy to the next commercially available pipe diameter. In the third stage, a nonlinear programming (NLP) method is used to find a new flow distribution that reduces the cost of the WDS operation given the design of the second stage. It is shown in this study that the results produced by the analytical method outperform the results of evolutionary methods when compared to previously published studies. Moreover, when a hybrid approach is adapted, the analytical method can be used to initialize the evolutionary algorithm to gain enhanced performance. The results of the hybrid approach fine-tune those obtained from the analytical method and demonstrate a substantial improvement when compared to a standard evolutionary algorithm initialized with a randomly generated initial population.

关键词： Water distribution system Water distribution system design Water distribution system operation Linear programming nonlinear programming Hybrid genetic algorithm (GA)

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A novel formalisation of the Markov-Dubins problem 18

A novel formalisation of the Markov-Dubins problem

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18th European Control Conference (ECC)

作者： Bevilacqua, P. Frego, M. Fontanelli, D. Palopoli, L. Univ Trento Dipartimento Ingn & Sci Informaz Trento Italy Univ Trento Dipartimento Ingn Ind Trento Italy

ISBN: (纸本)9783907144022

The Markov-Dubins problem requires to find the shortest path that connects an initial point and angle to a final point and angle with bounded turning radius. Formally, this is equivalent to solve an interpolation problem with continuity up to the first derivative and with bounded curvature. We propose a mathematical framework that models with a single equation the different cases that arise, i.e., we can represent with the same function an arc of circle or a line segment by smoothly blending from one to the other. This allows us to restate the problem as a standard Mixed Integer nonlinear programming (MINLP), which can be relaxed into a standard nonlinear programming (NLP) and therefore opens the way to solve it using off-the-shelf solvers. Moreover, our formalism captures the symmetries of the problem in a more intuitive way with respect to previous works, thanks to the considered conformal bipolar transform. This approach is suitable for an effective solution of the extended problem of connecting multiple points, that will be addressed in future research.

关键词： nonlinear programming

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A Nested Schur decomposition approach for multiperiod optimization of chemical processes

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COMPUTERS & CHEMICAL ENGINEERING 2021年 155卷

作者： Yoshio, Noriyuki Biegler, Lorenz T. Carnegie Mellon Univ Dept Chem Engn 5000 Forbes Ave Pittsburgh PA 15213 USA

This work develops an algorithm for solving nonlinear multiperiod optimization (MPO) problems using a nested Schur decomposition (NSD) approach. The NSD approach decomposes MPO using a Schur complement and allows us to solve the decomposed nonlinear programming (NLP) problem in parallel. The NSD partitions the MPO into a two-level problem with individual NLPs at the lower level. In MPO problems for chemical processes, the upper problem generally has inventory, demand, and design constraints set over the entire period. The lower problem consists of a single process model for each period. The problem-level decomposition facilitates the flexible selection of the lower-level solver. For example, an efficient barrier solver such as IPOPT can be used when the problem is well-conditioned. Conversely, a robust active-set solver such as CONOPT can be selected when degeneracy exists in the problem. In this paper, the NSD approach is demonstrated with different process models for MPO under uncertain demand in both serial and parallel implementation. The solutions are also compared with the direct approach, which solves the entire MPO problem simultaneously. The demonstration shows the capability of the flexible inner solver selection with IPOPT and CONOPT. The result shows that NSD converges to the same optimum as the direct approach, regardless of the choice of the inner solver. Furthermore, IPOPT could be more efficient than CONOPT when the problem is well-conditioned. Moreover, it is noted that the NSD outperforms the direct approach when the size of the process model is large with CONOPT as the inner solver. From those results, we observe that NSD is well-suited to solve large MPO problems for chemical processes in an efficient, flexible, and robust manner. (c) 2021 Elsevier Ltd. All rights reserved.

关键词： Multiperiod optimization Parallel computing Schur-complement decomposition nonlinear programming Interior-point method Active set method

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Extension of Unified Trigonometrization Method to Enforce Inequality Boundary Conditions in Optimal Control Problems

Extension of Unified Trigonometrization Method to Enforce In...

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AIAA Aviation Forum

作者： Nolan, Sean M. Sparapany, Michael J. DeLaurentis, Daniel Purdue Univ Aeronaut & Astronaut Engn W Lafayette IN 47904 USA

ISBN: (数字)9781624105982

ISBN: (纸本)9781624105982

Solving optimal control problems with indirect methods is historically challenging, especially when problems contain complex features such as inequality constraints. For this reason in large part, direct methods have dominated trajectory optimization since the advent of sufficiently fast digital computers. Recently though, new methods and techniques have arisen to make indirect methods more accessible and reliable thus enabling the generation of high-quality solutions. One of these methods, the Unified Trigonometrization Method, aids solving problems with inequality path constraints on states and controls by modifying the optimal control problem. The work presented here extends the Unified Trigonometrization Method to handle inequality constraints on the initial and terminal boundaries as well. It does so by augmenting the initial and terminal cost with two-sided interior penalty functions mirroring the original method's handling of state path constraints. A variation of Zermelo's navigation problem verifies and illustrates the method, and a Space Shuttle re-entry problem demonstrates the new method's efficacy and applicability for more complex aerospace problems.

关键词： Zermelo's Navigation Problem Space Shuttle Digital Computers Flight Path Angle Terminal Velocity nonlinear programming Lagrange Multipliers Boundary Value Problems Angle of Attack Numerical Algorithms

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Duality relations for second-order programming problem under (G, αf)-bonvexity assumptions

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ASIAN-EUROPEAN JOURNAL OF MATHEMATICS 2020年第2期13卷

作者： Dubey, Ramu Mishra, Vishnu Narayan Tomar, Puneet YMCA Univ Sci & Technol Dept Math Faridabad 121006 Haryana India Indira Gandhi Natl Tribal Univ Dept Math Amarkantak 484887 Madhya Pradesh India L 1627 Awadh Puri Colony Beniganj Phase 3 Faizabad 224001 Uttar Pradesh India St Peterburg State Univ Fac Appl Math & Control Proc St Petersburg 198504 Russia

In this paper, we introduce the definition of (G, alpha(f))-bonvex/(G, alpha(f))-pseudobonvex functions and to show the existence of such functions, we construct nontrivial numerical examples. In the next section, we formulate a pair of second-order symmetric dual model in optimization problem and proved the duality results under (G, alpha(f))-bonvexity/(G, alpha(f))pseudobonvexity assumptions. Further, we also construct nontrivial concrete examples which justifying definitions as well as the weak duality theorem presented in the paper.

关键词： Symmetric duality second-order nonlinear programming (G, alpha(f))-bonvexity/(G, alpha(f))-pseudobonvexity

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Fast UAV Trajectory Optimization using Bilevel Optimization with Analytical Gradients

Fast UAV Trajectory Optimization using Bilevel Optimization ...

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American Control Conference (ACC)

作者： Sun, Weidong Tang, Gao Hauser, Kris XYZ Robot Shanghai Peoples R China Univ Illinois Dept Comp Sci Urbana IL USA

ISBN: (纸本)9781538682661

We present an efficient optimization framework that solves trajectory optimization problems by decoupling state variables from timing variables, thereby decomposing a challenging nonlinear programming (NLP) problem into two easier subproblems. With timing fixed, the state variables can be optimized efficiently using convex optimization, and the timing variables can be optimized in a separate NLP, which forms a bilevel optimization problem. The challenge is to obtain the gradient of the objective function which itself needs an optimization to compute. Whereas finite differences must solve many optimization problems to compute the gradient, our method is based on sensitivity analysis of parametric programming: the dual solution (Lagrange multipliers) of the lower-level optimization is used to compute analytical gradients. Since the dual solution is a by-product of the optimization, the exact gradients can be obtained "for free". The framework is demonstrated on generating trajectories in safe corridors for an unmanned aerial vehicle. Experiments demonstrate that bilevel optimization converges significantly more reliably than a standard NLP solver, and analytical gradients outperform finite differences in terms of computation speed and accuracy. With a 25 ms cutoff time, our approach achieves over 8 times better suboptimality than the current state-of-the-art.

关键词： nonlinear programming

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Learning-based Optimal Control for Planetary Entry, Powered Descent and Landing Guidance

Learning-based Optimal Control for Planetary Entry, Powered ...

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AIAA Science and Technology Forum and Exposition (AIAA SciTech)

作者： You, Sixiong Wan, Changhuang Dai, Ran Lu, Ping Rea, Jeremy R. Ohio State Univ Dept Mech & Aerosp 201 W 19th Ave Columbus OH 43210 USA San Diego State Univ Dept Aerosp Engn 5500 Campanile Dr San Diego CA 92182 USA NASA Johnson Space Ctr Flight Mech & Trajectory Design Branch 2001 NASA Pkwy EG5 Houston TX 77058 USA

ISBN: (数字)9781624105951

ISBN: (纸本)9781624105951

This paper investigates the Mars entry and powered-descent guidance problems by developing a learning-based real-time optimal control method to achieve precise and fuel-efficient planetary landing in the future Mars mission. Specifically, in the entry phase, the goal is to find an optimal trajectory to minimize the terminal kinematic energy/velocity. While in the powered-descent phase for pinpoint landing, we aim to search for an optimal trajectory to minimize the fuel consumption subject to control and state constraints. By formulating the Hamiltonian function, the necessary conditions of optimality for both optimal control problems are obtained, which leads to two-point-boundary-value-problems (TPBVPs). We then identify critical parameters, that can determine the complete solution of the TPBVPs. To find the implicit relationship between the problem inputs and these critical parameters, deep neural networks are constructed to learn values of these variables in real-time given sufficient training data. Finally, the learning-based optimal control method is implemented and compared with the nonlinear programming solver in simulation cases for both entry and powered-descent phases to verify the effectiveness and accuracy of the proposed method.

关键词： Time Optimal Control Powered Descent Guidance nonlinear programming Recurrent Neural Network Fuel Consumption Mars Missions Boundary Value Problems Planetary Landing Hamiltonian Functions Flight Path Angle

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Optimal Power Management Considering Attitude Control and Battery Deterioration Control for Spacecraft with VSCMG/IPACS

Optimal Power Management Considering Attitude Control and Ba...

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AIAA Science and Technology Forum and Exposition (AIAA SciTech)

作者： Yoshihara, Hiroyuki Takahashi, Masaki Keio Univ Sch Sci Open & Environm Syst 3-14-1 HiyoshiKohoku Ku Yokohama Kanagawa 2238522 Japan Keio Univ Dept Syst Design Engn 3-14-1 HiyoshiKohoku Ku Yokohama Kanagawa 2238522 Japan

ISBN: (数字)9781624105951

ISBN: (纸本)9781624105951

Earth observation satellites repeatedly charge and discharge their batteries in harsh environments, where sunlight illumination and shade occur repetitively;thus, battery power deteriorates rapidly. In this study, variable speed control moment gyro (VSCMG) / integrated power and attitude control system (IPACS), which has both an attitude control function and an energy storage function, was used for a lithium-ion battery and a hybrid. We propose a control law that suppresses the chemical deterioration factor of the battery while achieving attitude control by cooperatively charging and discharging the required power. The proposed method calculates the commands of VSCMG/IPACS and the power distribution ratio of the battery and VSCMG/IPACS at the same time, for power distribution that accounts for the reference torque. The proposed method considers the torque error, the wheel angular velocity variation, and the wheel angular acceleration variation, to ensure attitude control performance. In addition, to suppress the deterioration factor of the battery, an evaluation function considering the SOC and C rate of the battery is designed. While constraints on the output power, motor, and battery are satisfied, we obtain the optimal solution that minimizes the evaluation function. Using the above algorithm, the proposed method can yield optimal power distribution and commands of VSCMG/IPACS.

关键词： Attitude Control System Batteries Spacecrafts Power Distribution Energy Storage Earth Observation Satellite Small Satellites Synthetic Aperture Radar Nickel Hydrogen Batteries nonlinear programming

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Smooth Gradation of Anisotropic Mesh Based on Log-Euclidean Metrics

Smooth Gradation of Anisotropic Mesh Based on Log-Euclidean ...

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AIAA Science and Technology Forum and Exposition (AIAA SciTech)

作者： Xiaol, Zhoufang Olivier-Gooch, Carl Hangzhou Dianzi Univ Coll Comp Sci & Technol Hangzhou 310018 Peoples R China Univ British Columbia Adv Numer Simulat Lab Vancouver BC V6T 1Z4 Canada Univ British Columbia Dept Mech Engn Vancouver BC Canada

ISBN: (数字)9781624105951

ISBN: (纸本)9781624105951

The anisotropic mesh size function represented by metric tensors includes two features: mesh sizes and mesh orientation. Such metrics are widely used in scientific computing for adaptation, but the solution metrics are not smooth, which adversely affects adaptation. A novel algorithm is proposed in this paper to smooth the metric as a whole and to improve anisotropic mesh size gradation. First, the concept of Log-Euclidean metrics is used to convert the metric tensors from the Riemannian space into a Euclidean space. Then, the variations of metric tensors are limited by constraining the gradients of metric tensors in this space over the region of each background mesh element. Finally, a convex nonlinear optimization problem is formulated to smooth the metric tensors over the entire meshing domain. Theoretical analysis reveals the existence of a globally optimal smoothed sizing function. Numerical experiments on anisotropic meshes are presented to demonstrate the effectiveness of the proposed method.

关键词： Scientific Computing nonlinear programming Mesh Generation Aspect Ratio Triangular Element Fluid Flow

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Supporting Education in Algorithms of Computational Mathematics by Dynamic Visualizations Using Computer Algebra System 20th

Supporting Education in Algorithms of Computational Mathemat...

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20th Annual International Conference on Computational Science (ICCS)

作者： Wojas, Wlodzimierz Krupa, Jan Warsaw Univ Life Sci SGGW Dept Appl Math Ul Nowoursynowska 159 PL-02776 Warsaw Poland

ISBN: (纸本)9783030504366;9783030504359

Computer algebra systems (CAS) are often used programs in universities to support calculations and visualization in teaching mathematical subjects. In this paper we present some examples of dynamic visualizations which we prepared for students of Warsaw University of Life Sciences using Mathematica. Visualizations for simplex algorithm and Karush-Kuhn-Tucker algorithm are presented. We also describe a didactic experiment for students of the Production Engineering Faculty of Warsaw University of Life Sciences using dynamic visualization of the network flow problem.

关键词： Computational mathematics Symbolic calculations Mathematical didactics Linear programming nonlinear programming Network flows CAS

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