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Planar maximal covering with ellipses

COMPUTERS & INDUSTRIAL ENGINEERING 2009年第1期57卷 201-208页

作者： Canbolat, Mustafa S. von Massow, Michael McMaster Univ DeGroote Sch Business Hamilton ON L8S 4M4 Canada

We consider a maximal covering location problem on the plane, where the objective is to provide maximal coverage of weighted demand points using a set of ellipses at minimum cost. The problem involves selecting k out of in ellipses. The problem occurs naturally in wireless telecommunications networks as coverage from some transmission towers takes an elliptical shape. A mixed integer nonlinear programming formulation (MINLP) for the problem is presented but MINLP solvers fail to solve it in a reasonable time. We suggest a Simulated Annealing heuristic as an alternate approach for solving the problem. Our computational results employing the heuristic show very good results with efficient processing times. We also discuss an extension to the problem where coverage occurs on a spherical surface and show that it can be solved with the same heuristic. (c) 2008 Elsevier Ltd. All rights reserved.

关键词： Facility location Maximal covering Simulated Annealing Elliptical covering Wireless telecommunications networks mixed integer nonlinear programming

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Power generation expansion planning with emission control: a nonlinear model and a GA-based heuristic approach

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INTERNATIONAL JOURNAL OF ENERGY RESEARCH 2006年第2期30卷 81-99页

作者： Sirikum, J Techanitisawad, A Asian Inst Technol Ind Engn & Management Sch Adv Technol Pathum Thani 12120 Thailand

This paper presents an application of genetic algorithms (GA) for solving the long-term power generation expansion planning (PGEP) problem, a highly constrained nonlinear discrete optimization problem. The problem is formulated into a mixed integer nonlinear programming (MINLP) program that determines the most economical investment plan for additional thermal power generating units over a planning horizon, subject to the requirements of power demands, power capacities, loss of load probability (LOLP) levels, locations, and environmental limitations. Computational results show that the GA-based heuristic method can solve the PGEP problem effectively and more efficiently at a significant saving in runtime, when compared with a commercial optimization package. Copyright (c) 2005 John Wiley & Sons, Ltd.

关键词： genetic algorithms mixed integer nonlinear programming power generation expansion planning emission modelling

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Properties, Extensions and Application of Piecewise Linearization for Euclidean Norm Optimization in R²

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2022年第2期195卷 418-448页

作者： Duguet, Alois Artigues, Christian Houssin, Laurent Ngueveu, Sandra Ulrich Univ Toulouse INP CNRS LAAS CNRS Toulouse France Univ Toulouse ISAE SUPAERO Toulouse France

This work considers nonconvex mixed integer nonlinear programming where nonlinearity comes from the presence of the two-dimensional euclidean norm in the objective or the constraints. We build from the euclidean norm piecewise linearization proposed by Camino et al. (Comput. Optim. Appl. https://***/10.1007/s10589-019-00083-z, 2019) that allows to solve such nonconvex problems via mixed-integer linear programming with an arbitrary approximation guarantee. Theoretical results are established that prove that this linearization is able to satisfy any given approximation level with the minimum number of pieces. An extension of the piecewise linearization approach is proposed. It shares the same theoretical properties for elliptic constraints and/or objective. An application shows the practical appeal of the elliptic linearization on a nonconvex beam layout mixed optimization problem coming from an industrial application.

关键词： mixed integer linear programming mixed integer nonlinear programming Euclidean norm linearization Approximation guarantee Multibeam satellites

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Learning to Branch: Accelerating Resource Allocation in Wireless Networks

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2020年第1期69卷 958-970页

作者： Lee, Mengyuan Yu, Guanding Li, Geoffrey Ye Zhejiang Univ Zhejiang Prov Key Lab Informat Proc Commun & Netw Hangzhou 310027 Peoples R China Georgia Inst Technol Sch ECE Atlanta GA 30332 USA

Resource allocation in wireless networks, such as device-to-device (D2D) communications, is usually formulated as mixed integer nonlinear programming (MINLP) problems, which are generally NP-hard and difficult to get the optimal solutions. Traditional methods to solve these MINLP problems are all based on mathematical optimization techniques, such as the branch-and-bound (B&B) algorithm that converges slowly and has forbidding complexity for real-time implementation. Therefore, machine leaning (ML) has been used recently to address the MINLP problems in wireless communications. In this paper, we use imitation learning method to accelerate the B&B algorithm. With invariant problem-independent features and appropriate problem-dependent feature selection for D2D communications, a good auxiliary prune policy can be learned in a supervised manner to speed up the most time-consuming branch process of the B&B algorithm. Moreover, we develop a mixed training strategy to further reinforce the generalization ability and a deep neural network (DNN) with a novel loss function to achieve better dynamic control over optimality and computational complexity. Extensive simulation demonstrates that the proposed method can achieve good optimality and reduce computational complexity simultaneously.

关键词： Machine learning device-to-device communicati-ons resource allocation mixed integer nonlinear programming imitation learning branch-and-bound algorithm

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Integration of oilfield planning problems: infrastructure design, development planning and production scheduling

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JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING 2017年 158卷 585-602页

作者： Redutskiy, Yury Molde Univ Coll POB 2110 N-6402 Molde Norway

The oil and gas industry faces considerable technological challenges nowadays, mainly associated with nonconventional reserves and offshore environments. To ensure the economic efficiency of operations under such complicated conditions, industrial solutions called "smart fields" were introduced. A vital part of these solutions is strategic planning which aims to coordinate field development and hydrocarbons production operations to optimize the entire field lifecycle, given the chosen planning criterion (e.g., net present value of the project). Still, in many cases engineering design is conducted with a conservative approach of solving one problem at a time. In this study, a multi-period mixed integer nonlinear problem (MINLP) covering the relevant issues of both development and production phases, is introduced. The contribution of the proposed model to the area of oilfield development planning is related to the model's simultaneously incorporating technological details regarding the infrastructure layout, pressures and flows in the gathering system, and artificial lift performance, all of which ultimately aims to provide realistic production scheduling results and cost evaluation. The composed model is used to study the benefits of joint development and production planning in comparison to planning these two phases of the project separately. This research is relevant to the engineering design departments and contractors for the preliminary design stage of the engineering project when the infrastructures layout and capacities are chosen, and rough estimates of costs and revenues are calculated.

关键词： Development and production planning Electrical submersible pump Integrated decision-making mixed integer nonlinear programming Oilfield infrastructure design Operational efficiency Production scheduling

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Models and solution techniques for production planning problems with increasing byproducts

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JOURNAL OF GLOBAL OPTIMIZATION 2014年第2-3期59卷 597-631页

作者： Sridhar, Srikrishna Linderoth, Jeffrey Luedtke, James Univ Wisconsin Sch Comp Sci Madison WI USA Univ Wisconsin Dept Ind & Syst Engn Madison WI 53706 USA

We consider a production planning problem where the production process creates a mixture of desirable products and undesirable byproducts. In this production process, at any point in time the fraction of the mixture that is an undesirable byproduct increases monotonically as a function of the cumulative mixture production up to that time. The mathematical formulation of this continuous-time problem is nonconvex. We present a discrete-time mixed-integer nonlinear programming (MINLP) formulation that exploits the increasing nature of the byproduct ratio function. We demonstrate that this new formulation is more accurate than a previously proposed MINLP formulation. We describe three different mixed-integer linear programming (MILP) approximation and relaxation models of this nonconvex MINLP, and we derive modifications that strengthen the linear programming relaxations of these models. We also introduce nonlinear programming formulations to choose piecewise-linear approximations and relaxations of multiple functions that share the same domain and use the same set of break points in the domain. We conclude with computational experiments that demonstrate that the proposed formulation is more accurate than the previous formulation, and that the strengthened MILP approximation and relaxation models can be used to obtain provably near-optimal solutions for large instances of this nonconvex MINLP. Experiments also illustrate the quality of the piecewise-linear approximations produced by our nonlinear programming formulations.

关键词： mixed integer nonlinear programming Piecewise linear approximation Production planning

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Minimum energy adaptive structures - All-In-One problem formulation

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COMPUTERS & STRUCTURES 2020年 236卷 106266-106266页

作者： Wang, Yafeng Senatore, Gennaro Swiss Fed Inst Technol EPFL Sch Architecture Civil & Environm Engn ENAC Appl Comp & Mech Lab IMAC CH-1015 Lausanne Switzerland

This paper presents a new All-In-One (AIO) implementation of an existing formulation to design adaptive structures through Total Energy Optimization (TEO). The method implemented in previous work is a nested optimization process, here named TEO-Nested. Numerical simulations and experimental testing have shown that the TEO-Nested method produces structures that embody and use significantly lower energy compared to passive designs. However, TEO-Nested does not guarantee solution optimality. The formulation presented in this paper is an ADD optimization based on mixed integer nonlinear programming (MINLP), here named TEO-MINLP. Element cross-section areas, internal forces, nodal displacements and control commands are treated as continuous variables while the actuator positions as binary variables. Stress and displacement limits are included in the optimization constraints. Case studies of reticular structures are employed to benchmark the solutions with those produced by the TEO-Nested method. Results have shown that both formulations produce similar solutions which are only marginally different in energy terms thus proving that the TEO-Nested method tends to converge to optimal (local) solutions. However, the computation time required by TEO-Nested is only a fraction of that required by TEO-MINLP, which makes the former more suitable for structures of complex layout that are made of many elements. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Adaptive structures Minimum whole-life energy mixed integer nonlinear programming Structural optimization Active structural control

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The Robust Cold Standby Redundancy Allocation in Series-Parallel Systems With Budgeted Uncertainty

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IEEE TRANSACTIONS ON RELIABILITY 2015年第2期64卷 799-806页

作者： Feizollahi, Mohammad Javad Soltani, Roya Feyzollahi, Hadi Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA Islamic Azad Univ Dept Ind Engn Sci & Res Branch Tehran Iran SUNY Buffalo Dept Ind & Syst Engn Buffalo NY 14260 USA

This paper studies a redundancy allocation problem (RAP) with cold standby strategy in non-repairable series-parallel systems. We assume that the components' reliabilities are uncertain values in a budgeted uncertainty set, with unknown probability distributions. Because the system reliability is a nonlinear function of the components' reliabilities, classical robust optimization approaches cannot be directly applied to construct the robust counterpart of this problem. Therefore, this paper for the first time proposes linear mixed integer programming (MIP) and binary equivalent models for the cold standby RAP;and by exploiting the problem structure, robust counterparts are developed to deal with budgeted uncertainty in this problem. Then, two exact solution methods are proposed: one of them solves a MIP model iteratively in a Benders' decomposition framework, and the other one solves a single binary linear model. The validity and the performance of the proposed approach are tested through a Monte Carlo simulation, and computational results.

关键词： Budgeted uncertainty cold standby redundancy allocation mixed integer nonlinear programming robust optimization series-parallel system

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Optimization and analysis of the profitability of tariff structures with two-part tariffs

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第3期206卷 691-701页

作者： Schlereth, Christian Stepanchuk, Tanja Skiera, Bernd Goethe Univ Frankfurt Fac Business & Econ Dept Mkt D-60323 Frankfurt Germany

Service providers often offer tariff structures with several two-part tariffs that consist of a fixed fee and a usage price, such that consumers may pick the tariff they prefer. Prices of tariffs have significant impacts on service providers' profit, because they simultaneously influence consumers' tariff choices and their usage. The number of tariffs also plays an important role, because more tariffs segment the market better but also increase the administrative burden and require more marketing effort. This article presents a mixed-integer nonlinear programming optimization problem to determine profit-maximizing tariffs;compares several heuristic search methods, in particular, the gradient method, stochastic search, and simulated annealing, to solve this problem;analyses the profitability of different tariff structures;and outlines the factors that drive differences in profitability across various tariff structures. The results show that especially for large samples of more than 100 consumers, simulated annealing performs best and deviates only 0.2% from the optimum. Structures with fewer two-part tariffs are generally sufficient, because additional two-part tariffs only negligibly increase service providers' profit. (C) 2010 Published by Elsevier B.V.

关键词： Marketing Pricing Two-part tariffs mixed integer nonlinear programming

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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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