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Accelerating Generalized Benders Decomposition for Wireless Resource Allocation

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2021年第2期20卷 1233-1247页

作者： Lee, Mengyuan Ma, Ning Yu, Guanding Dai, Huaiyu Zhejiang Univ Coll Informat Sci & Elect Engn Hangzhou 310027 Peoples R China North Carolina State Univ Dept Elect & Comp Engn Raleigh NC 27606 USA Zhejiang Univ Coll Comp Sci & Technol Hangzhou 310027 Peoples R China

Generalized Benders decomposition (GBD) is a globally optimal algorithm for mixed integer nonlinear programming (MINLP) problems, which are NP-hard and can be widely found in the area of wireless resource allocation. The main idea of GBD is decomposing an MINLP problem into a primal problem and a master problem, which are iteratively solved until their solutions converge. However, a direct implementation of GBD is time- and memory-consuming. The main bottleneck is the high complexity of the master problem, which increases over the iterations. Therefore, we propose to leverage machine learning (ML) techniques to accelerate GBD aiming at decreasing the complexity of the master problem. Specifically, we utilize two different ML techniques, classification and regression, to deal with this acceleration task. In this way, a cut classifier and a cut regressor are learned, respectively, to distinguish between useful and useless cuts. Only useful cuts are added to the master problem and thus the complexity of the master problem is reduced. By using a resource allocation problem in device-to-device communication networks as an example, we validate that the proposed method can reduce the computational complexity of GBD without loss of optimality and has good generalization ability. The proposed method is applicable for solving various MINLP problems in wireless networks since the designs are invariant for different problems.

关键词： Resource management Acceleration Wireless networks Complexity theory programming Training Machine learning generalized Benders decomposition device-to-device communications resource allocation mixed integer nonlinear programming

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A note on solving DiDi's driver-order matching problem

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OPTIMIZATION LETTERS 2021年第1期15卷 109-125页

作者： Liu, Yanchao Wayne State Univ Dept Ind & Syst Engn 4815 4th StRm 2169 Detroit MI 48202 USA

This paper investigates the combinatorial nonlinear programming model that DiDi proposed for solving their driver-order matching problem. The model is reformulated to an equivalent continuous nonlinear program which is amenable to efficient commercial solvers. A backward induction procedure for computing the lower bound is also proposed. Computational experiments demonstrate that the local solution produced by the reformulation becomes increasingly close to the global solution, thereby suggesting a diminishing marginal benefit of pursing global optimality as the problem size increases.

关键词： Combinatorial optimization Submodular welfare problem mixed integer nonlinear programming Transportation applications

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Relax-tighten-round algorithm for optimal placement and control of valves and chlorine boosters in water networks

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2021年第2期295卷 690-698页

作者： Pecci, Filippo Stoianov, Ivan Ostfeld, Avi Imperial Coll London Dept Civil & Environm Engn InfraSense Labs London SW7 2BB England Israel Inst Technol Fac Civil & Environm Engn Technion IL-32000 Haifa Israel

In this paper, a new mixed integer nonlinear programming formulation is proposed for optimally placing and operating pressure reducing valves and chlorine booster stations in water distribution networks. The objective is the minimization of average zone pressure, while penalizing deviations from a target chlorine concentration. We propose a relax-tighten-round algorithm based on tightened polyhedral relaxations and a rounding scheme to compute feasible solutions, with bounds on their optimality gaps. This is because off-the-shelf global optimization solvers failed to compute feasible solutions for the considered non-convex mixed integer nonlinear program. The implemented algorithm is evaluated using three benchmarking water networks, and they are shown to outperform off-the-shelf solvers, for these case studies. The proposed heuristic has enabled the computation of good quality feasible solutions in most instances, with bounds on the optimality gaps that are comparable to the order of uncertainty observed in operational water network models. (c) 2021 Elsevier B.V. All rights reserved.

关键词： Global optimization mixed integer nonlinear programming Water networks Pressure management Water quality

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Optimal design and operation of an islanded water-energy network including a combined electrodialysis-reverse osmosis desalination unit

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RENEWABLE ENERGY 2021年 167卷 395-408页

作者： Moazeni, Faegheh Khazaei, Javad Penn State Harrisburg Civil & Environm Engn Dept Sch Sci Engn & Technol 777 W Harrisburg Pike Middletown PA 17057 USA Penn State Harrisburg Elect Engn Dept 777 W Harrisburg Pike Middletown PA 17057 USA Architectural Engn Dept Penn State Univ Pk State Coll PA 16801 USA

This paper proposes an optimization framework to simultaneously optimize the saline and freshwater water sources as well as decentralized renewable and conventional energy sources, which consequently results in an economic and efficient water-energy system operation. The inextricable links between water and energy systems are taken into considerations, and a mixed integer nonlinear programming formulation is used to solve the proposed optimization model. A hybrid electrodialysis-reverse osmosis is integrated in the water distribution system and its electricity consumption is minimized. Also, the dayahead economic dispatch problem of the energy system incorporates the random behavior of solar and wind generation units, along with charging and discharging modes of battery storage systems. The outcomes of the proposed models highlight: 1) integrating the hybrid desalination module in the waterenergy system will reduce peak demands by more than 30% if the water and energy systems are solely supplied by saline water and renewable energy sources, respectively;2) presence of an extra water storage tank also decreases peak demands by 13%. The impact of key elements of the combined system such as pumps' speeds, water tank constraints, and presence of renewable sources on the output cost, generated energy, and hydraulic parameters is investigated through case studies. (c) 2020 Elsevier Ltd. All rights reserved.

关键词： Water-energy system mixed integer nonlinear programming Desalination process Electrodialysis Reverse osmosis Optimization

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Demand Response for Industrial Micro-Grid Considering Photovoltaic Power Uncertainty and Battery Operational Cost

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IEEE TRANSACTIONS ON SMART GRID 2021年第4期12卷 3043-3055页

作者： Huang, Chao Zhang, Hongcai Song, Yonghua Wang, Long Ahmad, Tanveer Luo, Xiong Univ Macau State Key Lab Internet Things Smart City Macau Peoples R China Univ Macau Dept Elect & Comp Engn Macau Peoples R China Univ Sci & Technol Beijing Sch Comp & Commun Engn Beijing 10083 Peoples R China Univ Sci & Technol Beijing Shunde Grad Sch Guangzhou 528399 Guangdong Peoples R China Jinan Univ Energy & Elect Res Ctr Int Energy Coll Guangzhou 519070 Guangdong Peoples R China

An intelligent demand response (DR) program is developed for multi-energy industrial micro-grid consisting of manufacturing facilities, photovoltaic (PV) panels, and battery energy storage system (BESS). The proposed DR program tackles the practical challenges of components in the micro-grid including industrial process represented by a discrete manufacturing production model, uncertainty of PV generation, and operational cost of the BESS. The proposed DR program optimizes day-ahead production scheduling for manufacturing facilities and operation regime for the BESS in response to time of use electricity price and probabilistic forecasting of PV power. To capture the uncertainty of PV power, a data-driven PV power probabilistic forecasting model is developed and a copula-based approach is deployed for the sampling of temporally correlated scenarios of PV power over the scheduling horizon from probabilistic forecasts. The multi-energy management optimization problem is formulated as a scenario-based stochastic nonconvex mixed integer nonlinear programming (MINLP). A hybrid optimization method integrating the evolutionary algorithm and the branch-and-bound algorithm for mixed integer liner programming is proposed to solve the nonconvex MINLP. Simulation studies illustrate that the proposed DR program efficiently reduces the operational cost for manufacturing production and releases the stress of the main grid by making full use of flexibility of all the components in the micro-grid.

关键词： Optimization Forecasting Production Uncertainty Manufacturing Probabilistic logic Optimization methods Demand response industrial micro-grid multi-energy mixed integer nonlinear programming

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Hybrid Genetic Algorithms and Heuristics for nonlinear Short-Term Hydropower Optimization: A Comparative Analysis

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Procedia Computer Science 2024年 246卷 282-291页

作者： M. Jafari Aminabadi S. Séguin I. Fofana Department of applied sciences Université du Québec à Chicoutimi Saguenay (Qc) Canada G7H 2B1 GERAD Montréal (Qc) Canada H3T 1J4 Department of computer science and mathematics Université du Québec à Chicoutimi Saguenay (Qc) Canada G7H 2B1 Canada Research Chair tier 1 in Aging of Oil-Filled Equipment on High Voltage Lines (ViAHT)

In this paper, a mixed integer nonlinear programming (MINLP) for the short-term hydropower optimization problem considering operational constraints such as demand and startup costs, is presented. Since solving the MINLP is complicated and, in many cases, impossible, three methods are proposed based on reducing the complexity, which is hybridized with the exact solver. Method A, a binary genetic algorithm; method B, an iterative heuristic method; and method C, using the iterative heuristic method in the genetic algorithm. Based on computational results in a case study, method B converges to a solution very quickly and with few iterations, whereas methods A and C perform more efficiently. A comparison between methods A and C indicates that method C not only reduces the computational burden for convergence but also yields better results. The proposed methods are evaluated by comparing them with optimal solutions. The results indicate that the proposed methods are highly effective in achieving favorable results.

关键词： nonlinear Short-term Hydropower Optimization mixed integer nonlinear programming Genetic algorithm Heuristic algorithm Meta-heuristic algorithm

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Groundwater Pollution Sources Identification Based on Hybrid Homotopy-Genetic Algorithm and Simulation Optimization

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ENVIRONMENTAL ENGINEERING SCIENCE 2021年第8期38卷 777-788页

作者： Li, Jiuhui Lu, Wenxi Fan, Yue Jilin Univ Key Lab Groundwater Resources & Environm Minist Educ 2519 Xiefang RdPhys Chem Bldg Changchun 130012 Peoples R China Jilin Univ Jilin Prov Key Lab Water Resources & Environm Changchun Peoples R China Jilin Univ Coll New Energy & Environm Changchun Peoples R China

Genetic algorithm (GA) is often used to solve the optimization model of groundwater pollution source identification. However, GA is prone to premature convergence and fall into local optimum. Thus, homotopy algorithm and GA are used in combination to improve the disadvantage. Then hybrid homotopy-genetic algorithm (HGA) was applied to solve the optimization model. A 0-1 mixed integer nonlinear optimization model (0-1MINLP) based on kriging surrogate model was used to simultaneously identify hydraulic conductivity, location, and release history of pollution sources. The results showed that the 0-1MINLP based on a kriging surrogate model could simultaneously identify the hydraulic conductivity and information of pollution sources, while maintaining a certain level of precision and reducing calculation load. The combination of homotopy algorithm and GA can improve the shortcomings of GA that is easy to fall into premature convergence. The identification results obtained by the HGA were closer to the true values of the pollution source characteristics compared with GA.

关键词： groundwater pollution hybrid homotopy-genetic algorithm mixed integer nonlinear programming surrogate model

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Mathematical optimization for time series decomposition

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OR SPECTRUM 2021年第3期43卷 733-758页

作者： Gozuyilmaz, Seyma Kundakcioglu, O. Erhun Ozyegin Univ Dept Ind Engn Istanbul Turkey

Decomposing time series into trend and seasonality components reveals insights used in forecasting and anomaly detection. This study proposes a mathematical optimization approach that addresses several data-related issues in time series decomposition. Our approach does not only handle longer and multiple seasons but also identifies outliers and trend shifts. Numerical experiments on real-world and synthetic problem sets present the effectiveness of the proposed approach.

关键词： Time series Seasonal trend decomposition mixed integer nonlinear programming

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Joint client selection and contract design for a risk-averse commodity broker in a two-echelon supply chain

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ANNALS OF OPERATIONS RESEARCH 2021年第1-2期307卷 111-138页

作者： Fontem, Belleh Price, Megan Univ Massachusetts Lowell Manning Sch Business Lowell MA 01854 USA Univ Mary Washington Coll Business 1301 Coll Ave Fredericksburg VA 22401 USA

We study an expected payoff maximization problem for a risk-sensitive broker aiming to evaluate the merits of designing and underwriting an option contract on a traded commodity with geometric Brownian motion (GBM) spot price trajectories. Candidate firms for whom the contract would mitigate the commodity's price risk, each face Poisson demands that are currently the broker's responsibility to satisfy. Subject to a variance risk budget and a robustness requirement, the broker's objective is jointly to (1) choose a so-called trigger price function that will fundamentally define the option contract, and (2) select a value-maximizing set of client firms to whom the broker will offer the contract. We reformulate the problem as a bilevel program whose continuous relaxation we transform into a single-level, univariate problem with a convenient property that makes it amenable to line search methods. The optimal solution for that single-level problem is then raw material for constructing the optimal solution for the original problem. Our theoretical and experimental findings indicate that the contract's optimal value, and optimal trigger price function are both strictly monotone increasing in a cost parameter in the model, as well as in the GBM's volatility coefficient. The findings also show that those two quantities are strictly monotone decreasing in the GBM's drift coefficient. We conclude with a benchmarking sensitivity study which uses real-world data to study the implications of violating a certain constraint which implicitly bounds the optimal trigger price.

关键词： Supply chain management mixed integer nonlinear programming Commodity brokerage Contract design Bilevel programming Risk management

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Optimal policies for finite horizon model with time-varying demand rate, non-instantaneous deterioration and backlogging

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE-OPERATIONS & LOGISTICS 2023年第1期10卷 Article: 2041128页

作者： Almathkour, Fatmah Benkherouf, Lakdere Kuwait Univ Coll Sci Dept Stat & Operat Res POB 5969 Kuwait 13060 Kuwait

This paper is concerned with the problem of finding an optimal replenishment policy for a finite planning horizon inventory model with time-varying demand, non-instantaneous deteriorating items and backlogging. This is formulated as a problem of solving some mixed integer non-linear program whose optimal solution delivers the frequency of orders as well as the timing of orders. The phenomena of non-instantaneous deterioration introduce a non-smoothness in the objective function which makes direct application of existing results, in the literature, not possible to the present model. A complete mathematical analysis of the problem is undertaken to overcome the non-smoothness of the objective and derive the optimal inventory policy. Uniqueness of the policy is shown under some technical conditions. Numerical results are presented for illustration.

关键词： Inventory model finite time horizon optimal schedule mixed integer nonlinear programming submodular function

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