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Convex and network flow optimization for Structured Sparsity

JOURNAL OF MACHINE LEARNING RESEARCH 2011年第9期12卷 2681-2720页

作者： Mairal, Julien Jenatton, Rodolphe Obozinski, Guillaume Bach, Francis Univ Calif Berkeley Dept Stat Berkeley CA 94720 USA Ecole Normale Super INRIA ENS CNRS UMR 8548 Lab Informat INRIA SIERRA Project Team F-75214 Paris 13 France

We consider a class of learning problems regularized by a structured sparsity-inducing norm defined as the sum of l(2)- or l(infinity)-norms over groups of variables. Whereas much effort has been put in developing fast optimization techniques when the groups are disjoint or embedded in a hierarchy, we address here the case of general overlapping groups. To this end, we present two different strategies: On the one hand, we show that the proximal operator associated with a sum of l(infinity)-norms can be computed exactly in polynomial time by solving a quadratic min-cost flow problem, allowing the use of accelerated proximal gradient methods. On the other hand, we use proximal splitting techniques, and address an equivalent formulation with non-overlapping groups, but in higher dimension and with additional constraints. We propose efficient and scalable algorithms exploiting these two strategies, which are significantly faster than alternative approaches. We illustrate these methods with several problems such as CUR matrix factorization, multi-task learning of tree-structured dictionaries, background subtraction in video sequences, image denoising with wavelets, and topographic dictionary learning of natural image patches.

关键词： convex optimization proximal methods sparse coding structured sparsity matrix factorization network flow optimization alternating direction method of multipliers

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Mixed-integer programming models and heuristic algorithms for the maximum value dynamic network flow scheduling problem

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COMPUTERS & OPERATIONS RESEARCH 2025年 175卷

作者： Nixon, Tanner Curry, Robert M. Allaissem, B. Phanuel US Navy Arlington VA USA Univ Arkansas Coll Engn Dept Ind Engn 800 W Dickson St Fayetteville AR 72701 USA

Various applications in contested logistics and infrastructure restoration require dynamic flow solutions characterized by a schedule of network flows consecutively transmitted over a sequence of successive periods. For these schedules, we assume flows transmit via arcs during periods while flows reside at nodes from one period to the next. Within this context, we introduce the Maximum Value Dynamic network flow Problem (MVDFP) in which we seek to maximize the cumulative value of a non-simultaneous network flow schedule that accumulates node value whenever some minimum amount of flow resides at a node between periods. For solving the MVDFP, we first introduce a large mixed-integer program (MIP). As this MIP can become computationally-expensive for large networks, we present a trio of computationally-effective, easy to implement heuristic approaches that solve a series of smaller, more manageable MIPs. These heuristic approaches typically determine high-quality solutions significantly faster than the MIP obtains an optimal solution by dividing the full network flow schedule into a sequence of consecutive shorter network flow subschedules. In many cases, at least one of our heuristic approaches produces an optimal solution in a fraction of the MIP's computational time. We present extensive computational results to highlight our heuristics' efficacy, discuss for what instances each approach may be most applicable, and detail future research avenues.

关键词： network flow optimization Mixed-integer programming Heuristic methods

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network optimization model approach to the volume-to-point heat conduction problem

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optimization AND ENGINEERING 2025年第1期26卷 229-251页

作者： Ferreira, Ricardo Poley Martins Pinto, Ricardo Luiz Utsch de Freitas Mahey, Philippe Fed Univ Minas Gerais UFMG Grad Program Mech Engn Ave Antonio Carlos 6627 Belo Horizonte MG Brazil Univ Clermont Auvergne UCA Lab Informat Modelling & Optimizat Syst Campus Univ Cezeaux1 Rue Chebarde F-63178 Aubiere France

This paper gives the classical volume-to-point heat conduction optimization problem a fresh model and formulation. The new volume-to-point problem model is a minimization problem, whereas the original model is a minimax problem. We establish that both problems have the same solution. The new formulation optimizes the volume and distribution of high-conductive materials while solving the heat flow equations and respecting a maximum temperature constraint. It was inspired by direct methods in optimal control problems. The problem is formulated as a mathematical programming problem, a network optimization problem, and it can be solved using off-the-shelf nonlinear optimization solvers. The new network design formulation is versatile and efficient as it can solve different problems fast and with good results. Numerical experiments show that the obtained solutions with the new formulation are competitive with state-of-the-art literature solutions, which were obtained using heuristics or computationally expensive methods.

关键词： network flow optimization Volume-to-point problem Heat transfer Minimization problem

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Multiobjective real-time reservoir operation with a network flow algorithm

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JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION 2001年第4期37卷 837-852页

作者： Braga, B Barbosa, PSF Univ Sao Paulo Escola Politecn BR-05508900 Sao Paulo Brazil UNICAMP Dept Civil Engn BR-13083970 Campinas SP Brazil

A network flow algorithm has been developed for the optimization of real-time operation of a multiple reservoir system. Two purposes have been considered in the operation: flood control and hydropower generation. A special network structure was developed which allows the consideration of river routing. A multiobjective formulation is utilized thus allowing generation of a non-dominated curve. The effect of imperfect forecast on the performance of the real-time operation model is also evaluated. An application is made to a subsystem of the Brazilian hydroelectric system, located in the Paranapanema river basin. In this case study, the model showed good performance under the largest flood of the historical records.

关键词： flood control hydroelectric power optimal operation of hydrosystems multipurpose development of water resources network flow optimization reservoir operation water management

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Optimizing the supply chain of biomass and biogas for a single plant considering mass and energy losses

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第2期262卷 744-758页

作者： Jensen, Ida Graested Munster, Marie Pisinger, David Tech Univ Denmark DTU Management Engn Prod TorvetBldg 426 DK-2800 Lyngby Denmark

The share of renewable energy in the Danish energy sector is increasing and the goal is that biogas production should reach a production level of 17 petajoules (PJ) in 2020 according to the Danish Energy Agency. However, this goal is currently not reachable due to lack of investments in biogas plants. In this paper, a mixed integer programming (MIP) model for finding the optimal production and investment plan for a biogas supply chain is presented to ensure better economy for the full chain hopefully stimulating future investments in biogas. The model makes "use of step-wise linear functions to represent capital and operational expenditures at the biogas plant;considers the chain from the farmer to the end market;and includes changes of mass and energy content along the chain by modeling the losses and gains for all processes in the chain. Biomass inputs are scheduled on a weekly basis whereas energy outputs are scheduled on an hourly basis to better capture the changes of energy prices and potentially take advantage of these changes. The model is tested on a case study with co-digestion of straw, sugar beet and manure, considering natural gas, heat, and electricity as end products. The model finds a production and investment plan for a predefined location of the plant within half an hour of central processing unit (CPU) time. The resulting project turns out to be profitable and gives a production plan for each process, which underlines the possibilities of optimizing the processes in a biogas project. (C) 2017 Elsevier B.V. All rights reserved.

关键词： OR in energy Supply chain optimization Biomass and bioenergy supply chains network flow optimization

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Energy-efficient and delay-sensitive-based data gathering technique for multi-hop WSN using path-constraint mobile element

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WIRELESS networkS 2024年第1期30卷 77-95页

作者： Kumar, Naween Edla, D. Reddy Dash, Dinesh Swain, Gandharba Shankar, T. N. Bennett Univ Sch Comp Sci Engn & Technol Greater Noida 201310 UP India Natl Inst Technol Goa Dept CSE Ponda 403401 Goa India Natl Inst Technol Patna Dept CSE Patna Univ Campus Patna 800005 India Koneru Lakshmaiah Educ Fdn Dept CSE Guntur 522502 AP India

In path-constrained multi-hop sensor networks (M-WSNs), maximizing data collection with minimal energy consumption is critical, especially for delay-sensitive applications. Because a mobile element (ME) moving at a constant speed along a constrained-path must receive data from sensor nodes (SNs) within a given time bound. This issue can be addressed by efficiently scheduling the SNs' data transmission. The shortest path data transmission (SPT) or its variations are a simple and energy-efficient technique for scheduling data transmission from SNs. Although this method considerably minimizes total energy spent, it does not enhance data collection efficiency due to uneven data forwarding load. To solve this issue, this paper proposes a novel efficient heuristic method. The proposed method first computes a set of discrete sub-paths on a given path based on the start and end distance points of nearby SNs, the speed of ME, and the given time delay. Then, for each sub-path and SN-communication model, a network flow graph is used to schedule and optimize SN data transmission to ME. Finally, a sub-path is chosen among those which return maximum data with minimum energy consumption. The network flow graphs are created by considering two distinct SN-communication models: (1) energy-unrestricted SN-model and (2) energy-restricted SN-model. Finally, the simulation reports demonstrate the proposed method's efficacy over baseline schemes in terms of data collected, energy usage efficiency, and success-delivery ratio.

关键词： Constrained-path Mobile element network flow optimization Maximum data Time period Energy efficient sub-path Wireless sensor networks

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An open-source Python implementation of California's hydroeconomic optimization model

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ENVIRONMENTAL MODELLING & SOFTWARE 2018年 108卷 8-13页

作者： Dogan, Mustafa S. Fefer, Max A. Herman, Jonathan D. Hart, Quinn J. Merz, Justin R. Medellin-Azuara, Josue Lund, Jay R. Univ Calif Davis Dept Civil & Environm Engn Davis CA 95616 USA Univ Calif Davis Ctr Watershed Sci Davis CA 95616 USA Univ Calif Davis Dept Land Air & Water Resources Davis CA 95616 USA Univ Calif Merced Sch Engn Merced CA USA

This short communication describes a new open-source implementation of the CALVIN model (CALifornia Value Integrated network), a large-scale network flow optimization model of California's water supply system. The model is cross-platform, uses common data formats, and connects to several freely available linear programming solvers. Given inputs including hydrology, urban/agricultural demand curves, and variable operating costs, the model minimizes the systemwide cost of water scarcity and operations including surface and groundwater reservoirs, wastewater reuse, desalination, environmental flow requirements, and hydropower. Key outputs include water shortage costs and marginal economic values of water and infrastructure capacity. We benchmark the scalability of different solvers up to roughly 5 million decision variables, using shared-memory parallelization on a high performance computing cluster. Runtimes are reduced by two orders of magnitude relative to the original model when no initial solution is provided, in addition to the benefits such as accessibility and transparency that come with an open-source platform. While this model is specific to California, the data and model structure are separated, so a similar framework could be used in any system where water allocation has been formulated as a network flow problem.

关键词： Hydroeconomic modeling network flow optimization Multi-reservoir operations

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Hierarchical Multilabel Classification with Optimal Path Prediction

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NEURAL PROCESSING LETTERS 2017年第1期45卷 263-277页

作者： Sun, Zhengya Zhao, Yangyang Cao, Dong Hao, Hongwei Chinese Acad Sci Inst Automat Beijing Peoples R China

We consider multilabel classification problems where the labels are arranged hierarchically in a tree or directed acyclic graph (DAG). In this context, it is of much interest to select a well-connected subset of nodes which best preserve the label dependencies according to the learned models. Top-down or bottom-up procedures for labelling the nodes in the hierarchy have recently been proposed, but they rely largely on pairwise interactions, thus susceptible to get stuck in local optima. In this paper, we remedy this problem by directly finding a small number of label paths that can cover the desired subgraph in a tree/DAG. To estimate the high-dimensional label vector, we adopt the advantages of partial least squares techniques which perform simultaneous projections of the feature and label space, while constructing sound linear models between them. We then show that the optimal label prediction problem with hierarchy constraints can be reasonably transformed into the optimal path prediction problem with the structured sparsity penalties. The introduction of path selection models further allows us to leverage the efficient network flow solvers with polynomial time complexity. The experimental results validate the promising performance of the proposed algorithm in comparison to the state-of-the-art algorithms on both tree- and DAG-structured data sets.

关键词： Hierarchical classification Multilabel classification network flow optimization

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Minimum-cost flow problems having arc-activation costs

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NAVAL RESEARCH LOGISTICS 2022年第2期69卷 320-335页

作者： Curry, Robert M. Smith, J. Cole US Naval Acad Math Dept Annapolis MD 21401 USA Syracuse Univ Dept Elect Engn & Comp Sci Syracuse NY USA

Time-dependent network applications, such as wireless sensor network and infrastructure optimization settings, may require dynamic flows to be transmitted according to a nonsimultaneous schedule of path-flows. We study a dynamic network flow optimization problem considering the presence of activation costs required to begin transmitting flow on an arc. This problem can be modeled as a dynamic version of the minimum-cost flow problem having arc-activation costs (MCFA). The MCFA is related but not equivalent to the fixed-charge network flow problem. We first discuss the relationship between these two problems, and show how MCFA is unique in the network flow literature. We present a mixed-integer programming (MIP) model along with a series of symmetry-breaking inequalities for solving the MCFA. As an alternative, we employ a relaxation-based algorithm that iteratively obtains upper and lower bounds via the solution of a series of smaller, more tractable MIPs. We show that this algorithm finitely terminates with an optimal MCFA solution. Finally, computational results demonstrate the efficacy of our approach compared to solving a MIP using a state-of-the-art commercial solver.

关键词： consecutive flows fixed-charge network flow problems integer programming minimum-cost flow problems network flow optimization

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Bioenergy production to improve value-creation potential of strategic forest management plans in mixed-wood forests of Eastern Canada

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APPLIED ENERGY 2019年 247卷 171-181页

作者： Cantegril, Pierre Paradis, Gregory LeBel, Luc Raulier, Frederic Univ Laval Fac Foresterie Geog & Geomat Pavillon Abitibi Price2405 Rue Terrasse Quebec City PQ G1V 0A6 Canada Univ Laval Consortium Rech FORAC Pavillon Adrien Pouliot1065 Ave Med Quebec City PQ G1K 7P4 Canada Univ British Columbia Dept Forest Resources Management 2424 Main Mall Vancouver BC V6T 1Z4 Canada

The relationship between forest management and biomass sourcing is fundamental to the achievement of sustainable bioenergy production. Few biomass-sourcing studies have directly addressed the complex interactions between sustainable forest management and additional demand created by bioenergy production. The first objective of this research was to provide a method for estimating profits for a value chain that harvests volumes scheduled in a sustainable forest management plan. The second objective was to measure the financial and sustainable benefits generated by integrating bioenergy production into this value chain. Using data from a large management unit, a forest management plan was developed to generate an annual flow of timber that can be produced sustainably. We then proposed a network flow optimization model that links the optimal solution of a long-term wood supply optimization model with the processing capacity of an industrial network. Results revealed that the weak demand for lower-quality trees could be a serious impediment to achieving full value creation potential. Simulations of the implementation of a hardwood pellet mill improved the value-creation potential for hardwood pulp (direct effect) and also for other wood products by providing access to otherwise unprofitable mixed-wood forest strata (synergistic effect). Our experiment showed that integrating a lower quality timber user, such as a bioenergy production unit, could lead to higher financial profits (up to three-fold), and improve alignment between the sustainable forest management objectives and the industrial network capacity (harvested scheduled area increased from 79% to 98%). Implementing a bioenergy mill also grants a higher return on capital employed compared to historical values for the manufacturing sector. Strengthening the link between strategic planning and industrial processing capacity provides new insights into the impact on value-creation of bioenergy production from forest bi

关键词： Forest value chain network flow optimization Wood pellets Strategic forest planning Price volatility

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