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discrete-continuous optimization of heat network operating conditions in parallel operation of similar pumps at pumping stations

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JOURNAL OF GLOBAL optimization 2016年第1期66卷 83-94页

作者： Novitsky, N. N. Lutsenko, A. V. Russian Acad Sci Lab Pipeline & Hydraul Syst Dept Pipeline Syst Energet Melentiev Energy Syst InstSiberian Branch Lermontov St 130 Irkutsk Russia

The paper addresses an optimization problem of hydraulic conditions of heat supply systems. The research shows that when the main methods of operation control, including the control of the number of connected pumps at pumping stations, are used this problem is reduced to a mixed discrete-continuous programming problem which involves a nonlinear objective function, nonlinear equality constraints and simple inequalities. The paper presents the basic principles of the methods for calculation of feasible and optimal conditions on the basis of continuous variables as a constituent of the suggested technique for solving the general problem. Consideration is given to four possible strategies to fraction and cut the variants while searching for solutions on the basis of discrete variables. The results of computational experiments illustrating the comparative efficiency of different strategies are presented.

关键词： discrete-continuous optimization Strategies for problem solving on the basis of continuous and integer-valued variables Hydraulic conditions Heat supply systems

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LAGRANGE THEORY OF discrete-continuous NONLINEAR optimization

JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS

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JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS 2018年第3期2卷 317-342页

作者： Jahn, Johannes Knossalla, Martin Univ Erlangen Nurnberg Dept Math Cauerstr 11 D-91058 Erlangen Germany

This paper presents a new Lagrange theory of discrete-continuous conic optimization in an infinite dimensional setting. The following questions are answered for discrete-continuous optimization problems: how to define a Lagrange functional, how Karush-Kuhn-Tucker conditions look like, and which duality results can be obtained? This approach is based on new separation theorems for discrete sets, which are also given in this paper. The developed theory is finally applied to problems of discrete-continuous semidefinite and copositive optimization.

关键词： discrete-continuous optimization Lagrange theory Optimality conditions Duality

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Extensions to generalized disjunctive programming: hierarchical structures and first-order logic

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optimization AND ENGINEERING 2024年第2期25卷 605-+页

作者： Perez, Hector D. Grossmann, Ignacio E. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

optimization problems with discrete-continuous decisions are traditionally modeled in algebraic form via (non)linear mixed-integer programming. A more systematic approach to modeling such systems is to use generalized disjunctive programming (GDP), which extends the disjunctive programming paradigm proposed by Egon Balas to allow modeling systems from a logic-based level of abstraction that captures the fundamental rules governing such systems via algebraic constraints and logic. Although GDP provides a more general way of modeling systems, it warrants further generalization to encompass systems presenting a hierarchical structure. This work extends the GDP literature to address two major alternatives for modeling and solving systems with nested (hierarchical) disjunctions: explicit nested disjunctions and equivalent single-level disjunctions. We also provide theoretical proofs on the relaxation tightness of such alternatives, showing that explicitly modeling nested disjunctions is superior to the traditional approach discussed in literature for dealing with nested disjunctions.

关键词： Generalized disjunctive programming Hierarchical systems discrete-continuous optimization

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Asymptotic Bayesian optimization: A Markov sampling-based framework for design optimization

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PROBABILISTIC ENGINEERING MECHANICS 2022年 67卷 1页

作者： Jerez, D. J. Jensen, H. A. Beer, M. Chen, J. Leibniz Univ Hannover Inst Risk & Reliabil D-30167 Hannover Germany Univ Tecn Federico Santa Maria Dept Obras Civiles Valparaiso 2390302 Chile Tongji Univ Int Joint Res Ctr Engn Reliabil & Stochast Mech Shanghai 200092 Peoples R China Univ Liverpool Inst Risk & Uncertainty Liverpool L69 7ZF Merseyside England Univ Liverpool Sch Engn Liverpool L69 7ZF Merseyside England Tongji Univ State Key Lab Disaster Reduct Civil Engn Shanghai 200092 Peoples R China Tongji Univ Coll Civil Engn Shanghai 200092 Peoples R China

This paper presents a Markov sampling-based framework, called Asymptotic Bayesian optimization, for solving a class of constrained design optimization problems. The optimization problem is converted into a unified two-phase sample generation problem which is solved by an effective Markov chain Monte Carlo simulation scheme. First, an exploration phase generates designs distributed over the feasible design space. Based on this information, an exploitation phase obtains a set of designs lying in the vicinity of the optimal solution set. The proposed formulation can handle continuous, discrete, or mixed discrete-continuous design variables. Appropriate adaptive proposal distributions for the continuous and discrete design variables are suggested. The set of optimal solutions provides valuable sensitivity information of the different quantities involved in the problem with respect to the design variables. Representative examples including an analytical problem involving nonlinear benchmark functions, a classical engineering design problem, and a performance-based design optimization problem of a structural system under stochastic excitation are presented to show the effectiveness and potentiality of the proposed optimization scheme. Validation calculations show that the scheme is a flexible, efficient and competitive choice for solving a wide range of classical and complex engineering design problems.

关键词： discrete-continuous optimization Dynamic systems Markov sampling method Metropolis-Hastings algorithm Performance-based design Proposal distributions Stochastic optimization

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Curriculum Learning: From Human Strategies to Learning Dynamics

Curriculum Learning: From Human Strategies to Learning Dynam...

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作者： Zhou, Tianyi University of Washington

学位级别：Ph.D., Doctor of Philosophy

The recent success of machine learning (ML), or "the third wave of artificial intelligence (AI)", is built upon computational methods from the fields of optimization and statistics, the availability of large-scale training data and computational power, and partial imitation of human cognitive functions such as convolutional networks. However, current ML techniques can be critically inefficient and prone to imperfect data in practical applications, e.g., when the data are noisy, unlabeled, imbalanced, or contain redundancy, biases, covariate shift, etc. On the other hand, human learning is more strategic and adaptive in planning and selecting training content for different learning stages. Comparing to ML techniques that repeat training on random mini-batches of the same data over all stages, human learning exhibits great advantages in efficiency and robustness when addressing those practical challenges. Therefore, how to develop a strategic ``curriculum'' for ML becomes an important challenge for bridging the gap between human intelligence and machine intelligence. Curriculum learning has been first introduced as a data selection method applied to different learning stages based on human-learning strategies, e.g., selecting easier samples at first and gradually adding more and harder ones later. However, the properties of training materials that humans utilize to design a curriculum are not limited to hardness but can also cover diversity, consistency, representativeness, incentives, impact or utility to future training, etc. In ML, it is challenging to develop efficient and accurate score functions measuring these properties and their contributions to the final/later learning goal. Moreover, given the score functions, it is still an open challenge for a curriculum strategy to plan multiple training stages and adjust the selection criterion adaptive to each stage. Another primary challenge in curriculum learning is the deficiency of principle and theoretically motiv

关键词： Curriculum learning discrete-continuous optimization Learning dynamics Machine learning Neural networks Time consistency

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Structural synthesis considering mixed discrete-continuous design variables: A Bayesian framework

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2022年 162卷 108042-108042页

作者： Jensen, H. A. Jerez, D. J. Beer, M. Univ Tecn Federico Santa Maria Dept Civil Engn Valparaiso Chile Leibniz Univ Hannover Inst Risk & Reliabil D-30167 Hannover Germany Tongji Univ Int Joint Res Ctr Engn Reliabil & Stochast Mech Shanghai 200092 Peoples R China Univ Liverpool Inst Risk & Uncertainty Liverpool L69 7ZF Merseyside England Univ Liverpool Sch Engn Liverpool L69 7ZF Merseyside England

In this work attention is directed to general structural optimization problems considering discrete-continuous design variables. The optimization problem is formulated as the minimization of an objective function subject to multiple design requirements. The mathematical programming statement is set into the framework of a Bayesian model updating problem. Constraints are handled directly within the proposed scheme, generating designs distributed over the feasible design space. Based on these samples, a set of designs lying in the vicinity of the optimal solution set is obtained. The Bayesian model updating problem is solved by an effective Markov chain Monte Carlo simulation scheme, where appropriate proposal distributions are introduced for the continuous and discrete design variables. The approach can efficiently estimate the sensitivity of the final design and constraints with respect to the design variables. In addition, the numerical implementation of the optimization algorithm depends on few control parameters. For illustration purposes, the general formulation is applied to an important class of problems, specifically, reliability-based design optimization of structural systems under stochastic excitation. Three numerical examples showing the effectiveness and potentiality of the approach reported herein are presented.

关键词： Bayesian updating discrete-continuous optimization Feasible design space Markov sampling method Reliability-based optimization Stochastic optimization

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A methodological approach to the determination of optimal parameters of district heating systems with several heat sources

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ENERGY 2019年 185卷 350-360页

作者： Stennikov, Valery A. Barakhtenko, Evgeny A. Sokolov, Dmitry V. RAS SB ESI Melentiev Energy Syst Inst Lermontov Str 130 Irkutsk 664033 Russia

The determination of optimal parameters is of great importance to ensure the operability of a district heating system. Solving this problem entails providing the necessary network transmission capacity by determining pipe diameters, sites and parameters of pumping stations. The Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of Sciences has proposed methods to solve problem. A significant feature of these methods lies in that they make it possible to use complex mathematical models of the equipment used and flexibly adjust the computational procedure to the specific features of the system to be modelled. Normally, district heating systems have several heat sources. The practical problems for such systems have been solved by a technique based on the decomposition of the model of a district heating system according to heat source service areas. The decomposition breaks the unity of the computational process. As a result, the solution obtained is not optimal for the original district heating system model. The paper presents a methodological approach to determining optimal parameters of district heating systems with several heat sources. The approach employs a modified dynamic programming optimization method that provides an optimal solution without decomposition into the heat source service areas. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： District heating systems Pipeline diameters Pumping station discrete-continuous optimization Algorithm Dynamic programming

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Algorithm for solving the discrete-continuous Inspection Problem

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ARCHIVES OF CONTROL SCIENCES 2020年第4期30卷 653-666页

作者： Grymin, R. Bozejko, W. Chaczko, Z. Pempera, J. Wodecki, M. Wroclaw Univ Sci & Technol Dept Control Syst & Mechatron Wyb Wyspianskiego 27 PL-50370 Wroclaw Poland Univ Technol Sydney UTS Fac Engn & Informat Technol FEIT Sydney NSW Australia Wroclaw Univ Sci & Technol Dept Telecommun & Teleinformat Wyb Wyspianskiego 27 PL-50370 Wroclaw Poland

The article introduces an innovative approch for the inspection challenge that represents a generalization of the classical Traveling Salesman Problem. Its priciple idea is to visit continuous areas (circles) in a way, that minimizes travelled distance. In practice, the problem can be defined as an issue of scheduling unmanned aerial vehicle which has discrete-continuous nature. In order to solve this problem the use of local search algorithms is proposed.

关键词： discrete-continuous optimization UAV VTOL autonomous drone zero emission

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continuous 3D Label Stereo Matching Using Local Expansion Moves

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2018年第11期40卷 2725-2739页

作者： Taniai, Tatsunori Matsushita, Yasuyuki Sato, Yoichi Naemura, Takeshi Univ Tokyo Bunkyo Ku Tokyo 1138654 Japan RIKEN AIP Chuo Ku Tokyo 1030027 Japan Osaka Univ 2-2 Yamadaoka Suita Osaka 5650871 Japan

We present an accurate stereo matching method using local expansion moves based on graph cuts. This new move-making scheme is used to efficiently infer per-pixel 3D plane labels on a pairwise Markov random field (MRF) that effectively combines recently proposed slanted patch matching and curvature regularization terms. The local expansion moves are presented as many a-expansions defined for small grid regions. The local expansion moves extend traditional expansion moves by two ways: localization and spatial propagation. By localization, we use different candidate a-labels according to the locations of local a-expansions. By spatial propagation, we design our local a-expansions to propagate currently assigned labels for nearby regions. With this localization and spatial propagation, our method can efficiently infer MRF models with a continuous label space using randomized search. Our method has several advantages over previous approaches that are based on fusion moves or belief propagation;it produces submodular moves deriving a subproblem optimality, it helps find good, smooth, piecewise linear disparity maps;it is suitable for parallelization;it can use cost-volume filtering techniques for accelerating the matching cost computations. Even using a simple pairwise MRF, our method is shown to have best performance in the Middlebury stereo benchmark V2 and V3.

关键词： Stereo vision 3D reconstruction graph cuts Markov random fields discrete-continuous optimization

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Multi-Target Tracking by discrete-continuous Energy Minimization

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2016年第10期38卷 2054-2068页

作者： Milan, Anton Schindler, Konrad Roth, Stefan Univ Adelaide Sch Comp Sci Adelaide SA 5005 Australia Swiss Fed Inst Technol Photogrammetry & Remote Sensing Grp Wolfgang Pauli Str 15 CH-8093 Zurich Switzerland Tech Univ Darmstadt Dept Comp Sci Hsch Str 10 D-64289 Darmstadt Germany

The task of tracking multiple targets is often addressed with the so-called tracking-by-detection paradigm, where the first step is to obtain a set of target hypotheses for each frame independently. Tracking can then be regarded as solving two separate, but tightly coupled problems. The first is to carry out data association, i.e., to determine the origin of each of the available observations. The second problem is to reconstruct the actual trajectories that describe the spatio-temporal motion pattern of each individual target. The former is inherently a discrete problem, while the latter should intuitively be modeled in continuous space. Having to deal with an unknown number of targets, complex dependencies, and physical constraints, both are challenging tasks on their own and thus most previous work focuses on one of these subproblems. Here, we present a multi-target tracking approach that explicitly models both tasks as minimization of a unified discrete-continuous energy function. Trajectory properties are captured through global label costs, a recent concept from multi-model fitting, which we introduce to tracking. Specifically, label costs describe physical properties of individual tracks, e.g., linear and angular dynamics, or entry and exit points. We further introduce pairwise label costs to describe mutual interactions between targets in order to avoid collisions. By choosing appropriate forms for the individual energy components, powerful discrete optimization techniques can be leveraged to address data association, while the shapes of individual trajectories are updated by gradient-based continuous energy minimization. The proposed method achieves state-of-the-art results on diverse benchmark sequences.

关键词： Multi-object tracking tracking-by-detection visual surveillance discrete-continuous optimization

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