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3-D UAV Small Cell Base Station Positioning and Resource Allocation in Cellular Network: A stochastic Optimization Approach

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IEEE INTERNET OF THINGS JOURNAL 2024年第6期11卷 10951-10963页

作者： Rahimi, Zahra Ghanbari, Reza Mohajerzadeh, Amir Hossein Ahmadi, Hamed Ferdowsi Univ Mashhad Mashhad *** Iran Sohar Univ Fac Comp & Informat Technol Sohar 311 Oman Univ York York YO10 5DD England

Integrating unmanned aerial vehicles (UAVs) into wireless communication as aerial platforms to mount small cell base stations has grown rapidly in recent years. One of the main objectives of UAV integration into wireless networks is to optimize UAV deployment while meeting user expectations with the fewest UAVs. To ensure that users receive the requested data rate, management of UAV placement and user association is necessary due to the limited capacity of aerial base stations. Besides the user-base station distance, environmental conditions and propagation mode affect the data rate received by the users. When accounting for uncertain conditions, network management decisions become more realistic and productive. This article considers a random propagation mode for each link depending on the environmental conditions of the desired area. We exploit the stochastic programming framework to reflect propagation mode uncertainty in the optimization problem, which impacts the received data rate and path loss. The suggested mathematical formulation determines the minimum number of required UAVs, their 3-D positions, and the best user association strategy. The proposed model also includes interference-aware constraints for optimal radio resource allocation to base stations. The nonlinear path loss and line-of-sight (LoS) probability distribution functions in terms of the base station positions lead to a nonlinear formulation. We obtain a mixed-binary linear formulation by replacing nonlinear functions with their piecewise linear approximations and solve the model accurately using the CPLEX solver. The implementation results show that stochastic approaches provide more accurate diagnoses of the environment, as well as superior performance to deterministic optimization.

关键词： Channel assignment probability of line-of-sight (LoS) propagation stochastic programming unmanned aerial vehicle (UAV) positioning

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Coordinated Planning for Multiarea Wind-Solar-Energy Storage Systems That Considers Multiple Uncertainties

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ENERGIES 2024年第21期17卷 5242页

作者： Wu, Weijie Li, Yixin Wang, Shu Wang, Zheng Zhou, Shucan Zhang, Yining Zheng, Minjia Guangdong Power Grid Corp Guangdong Power Grid Planning Res Ctr Guangzhou 510062 Peoples R China China Elect Power Res Inst Natl Key Lab Renewable Energy Grid Integrat Beijing 100192 Peoples R China Peking Univ Sch Phys Beijing 100871 Peoples R China

As the scale of renewable energy sources (RESs) expands, it is essential to optimize the configuration of wind, solar, and storage resources across different areas. Nevertheless, the unavoidable uncertainties associated with both energy supply and demand present significant challenges for planners. This study aims to address the challenge of coordinated planning for multiarea wind-solar-energy storage systems considering multiple uncertainties. First, uncertainties related to future peak demand, thermal generation output boundaries, demand variability, and stochastic unit production are analyzed and modeled on the basis of robust optimization and stochastic programming techniques. Then, a hierarchical coordinated planning model that incorporates both system-wide (SW) and local area (LA) planning models is proposed. The SW planning model is designed to manage the optimal capacity configuration of RESs and energy storage systems (ESSs) within each LA, as well as the operational boundary of LAs. The LA planning models aim to further optimize the capacities of RESs and ESSs and minimize the economic cost within each LA on the basis of local resource characteristics. To achieve the optimal solution, the analytical target cascading (ATC) algorithm is integrated with the column-and-constraint generation (C&CG) algorithm. The simulation results validate the effectiveness and reasonableness of the proposed coordinated planning model, which not only outperforms independent planning approaches but also effectively manages the uncertainties.

关键词： coordinated planning renewable energy source energy storage system robust optimization stochastic programming uncertainty

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A novel day-ahead scheduling model to unlock hydropower flexibility limited by vibration zones in hydropower-variable renewable energy hybrid system

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APPLIED ENERGY 2024年 356卷

作者： Han, Shuo Yuan, Yifan He, Mengjiao Zhao, Ziwen Xu, Beibei Chen, Diyi Jurasz, Jakub Northwest A&F Univ Key Lab Agr Soil & Water Engn Arid & Semiarid Area Minist Educ Yangling 712100 Shaanxi Peoples R China Northwest A&F Univ Inst Water Resources & Hydropower Res Yangling 712100 Shaanxi Peoples R China Wroclaw Univ Sci & Technol Fac Environm Engn PL-50370 Wroclaw Poland

Giving full play to the flexibility of hydropower and integrating more variable renewable energy (VRE) is of great significance for accelerating the transformation of China's power energy system. For middle- to large-sized hydropower units, its irregular vibration zone (VZ) is a major factor affecting its flexibility, because VZs limits the power output and adjustment range. In the existing studies on hydropower unit commitment and flexibility scheduling, VZs only limits the output of hydropower units, while the impact on the flexibility adjustment ability of units is ignored. The hydropower flexibility in day-ahead scheme is overestimated, which increases the risk of system flexibility shortage causing power curtailment and load loss. In this study, a novel day-ahead scheduling model considering the flexibility limited by the VZs and the probability of flexibility shortage is constructed for the day-ahead generation scheme of hydropower-VRE hybrid generation system (HVHGS) to optimize the target load, VRE output and hydropower unit commitments. The impaction of the VZs on hydropower flexibility is firstly modeled by chance constraints and stochastic programming method. Moreover, a data-driven model based on machine learning and an efficient solving approach based on successive linear programming is carry out to describe the uncertainty of VRE output more realistically and ensure the timeliness of optimization scheme, respectively. The proposed model is applied to a real hydropower station in the Hongshui River Basin in China. In 16 representative scenarios, the proposed model can complete the optimization in an acceptable time, with a maximum of 444.57 s. Compared with the traditional interval optimization model, the proposed model effectively improves the flexibility supply capacity of hydropower in the day-ahead scheme. The maximum reduction value of flexibility shortage probability and expectation reach 98.77% and 442.66 MW, respectively. In particular, the flex

关键词： Hydropower flexibility Renewable energy hybrid generation systems Day -ahead scheduling Hydropower vibration zones stochastic programming Scenario generation

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Genetic algorithm based fuzzy programming approach for multi-objective linear fractional stochastic transportation problem involving four-parameter Burr distribution

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INTERNATIONAL JOURNAL OF SYSTEM ASSURANCE ENGINEERING AND MANAGEMENT 2020年第1期11卷 93-109页

作者： Abebaw Gessesse, Adane Mishra, Rajashree Acharya, Mitali Madhumita Das, Kedar Nath Deemed be Univ Dept Math KIIT Bhubaneswar 751024 Odisha India Dept Math NIT Silchar Silchar 788010 Assam India

In real life situations, it is difficult to handle multi-objective linear fractional stochastic transportation problem. It can't be solved directly using mathematical programming approaches. In this paper, a solution procedure is proposed for the above problem using a genetic algorithm based fuzzy programming method. The supply and demand parameters of the said problem follow four-parameters Burr distribution. The proposed approach omits the derivation of deterministic equivalent form as required in case of classical approach. In the given methodology, initially the probabilistic constraints present in the problem are tackled using stochastic programming combining the strategy adopted in genetic algorithm. Throughout the problem, feasibility criteria is maintained. Then after, the non-dominated solution are obtained using genetic algorithm based fuzzy programming approach. In the proposed approach, the concept of fuzzy programming approach is inserted in the genetic algorithm cycle. The proposed algorithm has been compared with fuzzy programming approach and implemented on two examples. The result shows the efficacy of the proposed algorithm over fuzzy programming approach.

关键词： Multi-objective programming stochastic programming Fractional transportation problem Fuzzy programming Genetic algorithm

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Asymptotic Consistency for Nonconvex Risk-Averse stochastic Optimization with Infinite-Dimensional Decision Spaces

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MATHEMATICS OF OPERATIONS RESEARCH 2024年第3期49卷 1403-1418页

作者： Milz, Johannes Surowiec, Thomas M. Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA Simula Res Lab Dept Numer Anal & Sci Comp N-0164 Oslo Norway

Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these estimators as the sample size goes to infinity. This area of study has a long tradition in stochastic programming. However, the literature is lacking consistency analysis for problems in which the decision variables are taken from an infinite-dimensional space, which arise in optimal control, scientific machine learning, and statistical estimation. By exploiting the typical problem structures found in these applications that give rise to hidden norm compactness properties for solution sets, we prove consistency results for nonconvex risk-averse stochastic optimization problems formulated in infinite-dimensional space. The proof is based on several crucial results from the theory of variational convergence. The theoretical results are demonstrated for several important problem classes arising in the literature.

关键词： asymptotic consistency empirical approximation sample average approximation Monte Carlo sampling risk-averse optimization PDE-constrained optimization uncertainty quantification stochastic programming

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Geographical relevance-based multi-period optimization for e-commerce supply chain resilience strategies under disruption risks

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2024年第7期62卷 2455-2482页

作者： Pu, Wei Ma, Shuang Yan, Xiangbin Univ Sci & Technol Beijing Sch Econ & Management Beijing 100083 Peoples R China

With the fierce competition in e-commerce, e-tailers are required to rapid responses to a variety of customised orders with multiple frequencies and strict delivery times. The delay or insufficient supply caused by disruptions might result in lost sales during long-term processes. To address this problem, a two-stage stochastic programming model considering profits, consumer service level (CSL) as well as market priorities is developed to manage long-term disruptions. We analyse multi-period consumer transaction data and formulate geographical relevance (GR) to link each marketplace with historical data in related regions and then prioritise market segments. A GR-based two-stage stochastic programming with multi-period is proposed, which (1) considers both proactive mitigation decisions before disruption and reactive recovery plans after disruption;(2) collaborates three resilience strategies;(3) optimises the e-tailer's profits considering market priorities during long-term disruptions. Using a real case of Chinese e-commerce under the COVID-19 pandemic, it is illustrated (1) the applicability and performance of the proposed GR-based model for multi-period resilience optimisation improving both the CSL and the total profit;(2) the efficiency and robustness of the developed sequential particle swarm optimisation with social structures algorithm. The proposed method could optimise e-tailers' response strategies for managing long-term disruptions in practice.

关键词： E-commerce supply chain long-term disruptions hybrid resilience strategies geographical relevance stochastic programming

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Optimal Bidding Strategies of a Mixed RES Portfolio by stochastic programming

Optimal Bidding Strategies of a Mixed RES Portfolio by Stoch...

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5th IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT Europe)

作者： Kardakos, Evaggelos G. Simoglou, Christos K. Bakirtzis, Anastasios G. Aristotle Univ Thessaloniki Dept Elect & Comp Engn Thessaloniki 54124 Greece

ISBN: (纸本)9781479977208

Wind energy is one of the most growing renewable energy resources. However, its integration into the power systems has posed many challenges due to its uncertain and variable nature. To deal with these challenges, the coordinated operation of a pumped storage plant and a wind farm in order to yield a dispatchable generating unit has been widely proposed lately in the literature. In this paper, a stochastic bi-level optimization model for the development of optimal bidding strategies for a mixed RES portfolio comprising wind and hydro resources is proposed. This bi-level optimization problem is converted into a Mixed-Integer Linear programming (MILP) model using the Karush-Kuhn-Tucker (KKT) optimality conditions and the strong duality theory. Extensive simulations on the IEEE Reliability Test System demonstrate the applicability and effectiveness of the proposed model.

关键词： Day-ahead offering strategy distributed energy generation mathematical program with equilibrium constraints wind-hydro coordination stochastic programming

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Solving Product Line Design Optimization Problems Using stochastic programming 36th

Solving Product Line Design Optimization Problems Using Stoc...

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36th Annual Conference of the German-Classification-Society (GfKl)

作者： Voekler, Sascha Baier, Daniel Brandenburg Tech Univ Cottbus Inst Business Adm & Econ Postbox 101344 D-03013 Cottbus Germany

ISBN: (纸本)9783319015958;9783319015941

In this paper, we try to apply stochastic programming methods to product line design optimization problems. Because of the estimated part-worths of the product attributes in conjoint analysis, there is a need to deal with the uncertainty caused by the underlying statistical data (Kall and Mayer, 2011, stochastic linear programming: models, theory, and computation. International series in operations research & management science, vol. 156. New York, London: Springer). Inspired by the work of Georg B. Dantzig (1955, Linear programming under uncertainty. Management Science, 1, 197-206), we developed an approach to use the methods of stochastic programming for product line design issues. Therefore, three different approaches will be compared by using notional data of a yogurt market from Gaul and Baier (2009, Simulations-und optimierungsrechnungen auf basis der conjointanalyse. In D. Baier, & M. Brusch (Eds.), Conjointanalyse: methoden-anwendungen-praxisbeispiele (pp. 163-182). Berlin, Heidelberg: Springer). stochastic programming methods like chance constrained programming are applied on Kohli and Sukumar (1990, Heuristics for product-line design using conjoint analyses. Management Science, 36, 1464-1478) and will be compared to its original approach and to the one of Gaul, Aust and Baier (1995, Gewinnorientierte Produktliniengestaltung unter Beruecksichtigung des Kundennutzens. Zeitschrift fuer Betriebswirtschaftslehre, 65, 835-855). Besides the theoretical work, these methods will be realized by a self- written code with the help of the statistical software package R.

关键词： stochastic programming

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A Fuzzy programming Approach for Bilevel stochastic programming 2

A Fuzzy Programming Approach for Bilevel Stochastic Programm...

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2nd International Conference on Soft Computing for Problem Solving (SocProS)

作者： Modak, Nilkanta Biswas, Animesh Univ Kalyani Dept Math Kalyani 741235 W Bengal India

ISBN: (纸本)9788132216025;9788132216018

This article presents a fuzzy programming (FP) method for modeling and solving bilevel stochastic decision-making problems involving fuzzy random variables (FRVs) associated with the parameters of the objectives at different hierarchical decision-making units as well as system constraints. In model formulation process, an expectation model is generated first on the basis of the fuzzy random variables involved with the objectives at each level. The problem is then converted into a FP model by considering the fuzzily described chance constraints with the aid of applying chance constrained methodology in a fuzzy context. After that, the model is decomposed on the basis of tolerance ranges of fuzzy numbers associated with the parameters of the problem. To construct the fuzzy goals of the decomposed objectives of both decision-making levels under the extended feasible region defined by the decomposed system constraints, the individual optimal values of each objective at each level are calculated in isolation. Then, the membership functions are formulated to measure the degree of satisfaction of each decomposed objectives in both the levels. In the solution process, the membership functions are converted into membership goals by assigning unity as the aspiration level to each of them. Finally, a fuzzy goal programming model is developed to achieving the highest membership degree to the extent possible by minimizing the under deviational variables of the membership goals of the objectives of the decision makers (DMs) in a hierarchical decision-making environment. To expound the application potentiality of the approach, a numerical example is solved.

关键词： Bilevel programming stochastic programming Fuzzy random variable Fuzzy goal programming

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Capacity planning with uncertainty on contract fulfillment

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第1期314卷 152-175页

作者： Crainic, Teodor Gabriel Perboli, Guido Rei, Walter Rosano, Mariangela Lerma, Veronica Univ Quebec Montreal UQAM Sch Management Sci CP 8888 Succ Ctr ville Montreal PQ H3C 3P8 Canada Univ Montreal CIRRELT Interuniv Res Ctr Enterprise Networks PO 6120 Succ Ctr Ville Montreal PQ H3C 3J7 Canada DIGEP Politecn Torino Corso Duca Abruzzi 24 I-10129 Turin Italy

This paper focuses on the tactical planning problem faced by a shipper which seeks to secure transportation and warehousing capacity, such as containers, vehicles or space in a warehouse, of different sizes, costs, and characteristics, from a carrier or logistics provider, while facing different sources of uncertainty. The uncertainty can be related to the loads to be transported or stored, the cost and availability of ad-hoc capacity on the spot market in the future, and the availability of the contracted capacity in the future when the shipper needs it. This last source of uncertainty on the capacity loss on the contracted capacity is particularly important in both long-haul transportation and urban distribution applications, but no optimization methodology has been proposed so far. We introduce the stochastic Variable Cost and Size Bin Packing with Capacity Loss problem and model that directly address this issue, together with a metaheuristic to efficiently address it. We perform a set of extensive numerical experiments on instances related to long-haul transportation and urban distribution contexts and derive managerial insights on how such capacity planning should be performed. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http://***/licenses/by/4.0/ )

关键词： Supply chain management Logistics capacity planning stochastic programming City logistics Long-haul freight transportation

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