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 di...
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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.
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 wirel...
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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.
Under the trend of global carbon neutrality, the integrated energy system with the characteristics of multi-energy scheduling and gradient utilizing will be widely constructed and applied in the future energy market. ...
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Under the trend of global carbon neutrality, the integrated energy system with the characteristics of multi-energy scheduling and gradient utilizing will be widely constructed and applied in the future energy market. For the construction of energy systems in emerging building complex, this paper analyzes the load probability characteristics of regional building complex at the planning stage, and conducts an aggregation analysis of its multiple uncertainties, and obtains the conclusion that the load factor at time t obeys the normal distribution. In order to formulate this uncertainty, this paper combines the case study with the scenario analysis method containing scenario generation and reduction to transform the stochastic programming model into several deterministic models and analyses the discrepancies of the optimization results under different objectives and different load variances. The results show that after considering load-side uncertainty, the total system capacity increases by 7 %, the total investment under the minimum investment objective by 4 %, and the carbon emission under the minimum carbon emission objective by 3 %. In addition, the system needs to pay 32.8 % of the total investment increment to obtain 80 % carbon reduction when adopting carbon emissions as the objective.
PurposeThis study addresses resilient mixed supply chain network design (SCND) and aims to minimize the expected total cost of the supply chain (SC) considering disruptions. The capacity of facilities is considered un...
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PurposeThis study addresses resilient mixed supply chain network design (SCND) and aims to minimize the expected total cost of the supply chain (SC) considering disruptions. The capacity of facilities is considered uncertain. In order to get closer to real-world situations, competition between SCs is ***/methodology/approachA two-stage stochastic programming model is developed for designing the SC network. The location of facilities and selection of suppliers are considered first-stage decisions, and the determination of materials and products flows are second-stage decisions. Some resilience strategies are applied to mitigate the negative impacts of *** results indicate that considering resilience and applying the related strategies are vitally important, and resilience strategies can significantly improve the SC objective and maintain market share. Also, it is confirmed that unrealistic decisions will be made without considering the ***/valueThis study contributes to the literature by proposing a novel mathematical model for the resilient mixed SCND problem. The other contribution is considering the chain-to-chain competition in collecting returned products and selling recycled products to other SCs in a mixed SC under disruptions. Also, a novel hybrid metaheuristic is developed to cope with the complexity of the model.
Rolling forecasts have been almost overlooked in the renewable energy storage literature. In this paper, we provide a new approach for handling uncertainty not just in the accuracy of a forecast, but in the evolution ...
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Rolling forecasts have been almost overlooked in the renewable energy storage literature. In this paper, we provide a new approach for handling uncertainty not just in the accuracy of a forecast, but in the evolution of forecasts over time. Our approach shifts the focus from modeling the uncertainty in a looka-head model to accurate simulations in a stochastic base model. We develop a robust policy for making energy storage decisions by creating a parametrically modified lookahead model, where the parameters are tuned in the stochastic base model. Since computing unbiased stochastic gradients with respect to the parameters require restrictive assumptions, we propose a simulation-based stochastic approximation algorithm based on numerical derivatives to optimize these parameters. While numerical derivatives, cal-culated based on the noisy function evaluations, provide biased gradient estimates, an online variance reduction technique built in the framework of our proposed algorithm, will enable us to control the ac-cumulated bias errors and establish the finite-time rate of convergence of the algorithm. Our numerical experiments show the performance of this algorithm in finding policies outperforming the deterministic benchmark policy. & COPY;2023 Elsevier B.V. All rights reserved.
In the field of logistics and transportation, drones and trucks effectively enhance each other's capabilities by offering complementary benefits in terms of speed, cargo capacity, and charging frequency. Thus, eff...
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In the field of logistics and transportation, drones and trucks effectively enhance each other's capabilities by offering complementary benefits in terms of speed, cargo capacity, and charging frequency. Thus, efficient management of their collaboration is an important task. Although there is a vast literature addressing different aspects of drone-truck combined operations (DTCO), only a few studies incorporate the energy consumption of drones into the optimization model, and the existing ones have made simplified assumptions. This paper proposes an optimization model for DTCO by incorporating a comprehensive energy function affected by the drone speed, cargo weight, wind speed, and wind direction, paying attention to environmental viewpoints. Due to this energy function, the problem is formulated as a mixed-integer nonlinear programming (MINLP) model. To enhance tractability and efficiency, we provide a linear approximation for the MINLP model. Given the stochastic nature of wind conditions throughout the day, we extend the deterministic model as a scenario-based stochastic one. Incorporating uncertainty makes the model more complex and hence, we adopt a modified progressive hedging algorithm (PHA) to efficiently solve the model. Computational results over a variety of instances confirm the effectiveness of the proposed approach.
Wind is distinguished by its eco-friendliness and sustainability, making it one of the most rapidly expanding forms of renewable energy sources (RESs). Hence, it is necessary to determine the most profitable plan for ...
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Wind is distinguished by its eco-friendliness and sustainability, making it one of the most rapidly expanding forms of renewable energy sources (RESs). Hence, it is necessary to determine the most profitable plan for wind farm installation. This paper constructs a novel scheme for market-based wind power investment (WPI) problems using adaptive robust optimization (ARO). A tri-level robust WPI (RWPI) model is established, the first level of which is to minimize the investment cost plus the worst-case loss. In the second level, the worst-case loss (also known as the maximum regret) is identified by maximizing the minimum value of minus profit over the uncertainty sets. The third level maximizes the wind farm profit. Since the profit calculation requires the determination of the locational marginal price (LMP), the third level constitutes bi-level programming, with the upper level being the profit maximization and the lower level being the market clearing process. First, Karush-KuhnTucker (KKT) conditions are applied to convert the bi-level model to a single-level model, resulting in an ARO with binary variables at the third level. Afterward, the nested column-and-constraint generation (NCCG) strategy is employed to solve the ARO with mixed-integer recourse. A case study is used to verify the scalability and practical applicability of the proposed model.
We address the problem of determining the start times of activities in order to maximize the expected net present value of a project given precedence constraints. We assume that each activity has a random duration and...
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We address the problem of determining the start times of activities in order to maximize the expected net present value of a project given precedence constraints. We assume that each activity has a random duration and profit with a known probability distribution. Most approaches generate either: a baseline schedule that is robust to uncertainty (using proactive approaches), or a policy that reacts to the revelation of uncertainty (using reactive approaches). We propose an integrated proactive-reactive technique that generates both a baseline time window for each activity's start time, and a policy that indicates how the schedule should be adapted for each realization of uncertainty. The time window explicitly constrains the extent to which the realized start times vary. An important feature of our approach is that, once computed, it can easily be communicated and implemented in practice. Numerical experiments show that the objective value of the solutions generated by our technique can be within 4%, on average, of the optimal value obtained with perfect information, and up to 50% better when compared to an earliest-start policy. Moreover, the variability of activities' start times can be 10 times smaller when compared to those generated by other policies. We solve an instance with 300 scenarios and 357 activities in 30 min, illustrating the scalability of our technique on a real-world problem that produces out-of-sample feasible solutions with a desired probability.
Recently, stochastic variational inequality (SVI) has been extended from single stage to multistage by Rockafellar and Wets (Math. Program., 165:331-360, 2017) and progressive hedging algorithm (PHA) has also been ext...
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Recently, stochastic variational inequality (SVI) has been extended from single stage to multistage by Rockafellar and Wets (Math. Program., 165:331-360, 2017) and progressive hedging algorithm (PHA) has also been extended from stochastic programming to multistage stochastic linear comple-mentarity and SVI by Rockafellar and Sun (Math. Program., 174:453-471, 2019). However, the per-iteration cost of PHA can be prohibitively high when the scenario set is large, despite the decomposition and parallelizable nature of the algorithm. To address this issue, we propose a randomized PHA that allows us to control the per-iteration cost by randomly selecting a small subset of scenarios and updating only the corresponding variable components while freezing the variables corresponding to the unselected scenarios at the current iteration. By measuring the quality of an approximate solution using a re-stricted merit function, we demonstrate that despite the significant reduction in per-iteration cost, the randomized PHA converges in expectation and in an ergodic sense at the same sublinear rate as the original PHA.
Rapid integration of distributed energy resources (DERs) in active distribution networks (ADNs) necessitates advanced planning methods to optimally determine the size, site, and installation time of DERs. However, exi...
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Rapid integration of distributed energy resources (DERs) in active distribution networks (ADNs) necessitates advanced planning methods to optimally determine the size, site, and installation time of DERs. However, existing approaches often assume balanced networks and neglect health degradation of DER assets, limiting the accuracy and practicality of the planning results. This paper proposes a new planning method for utility-owned distributed generators (DGs) and energy storage systems (ESSs) in an unbalanced ADN considering asset health degradation. First, the three-phase branch flow is modeled for unbalanced characteristics of ADNs, and host DERs separately in different phases. Then, based on the Wiener degradation process, the aging path of each DG unit is modeled to estimate its available capacity along with service time;the ESS aging is modeled to reflect the degradation cost during charging and discharging. Finally, a copula-based stochastic programming method is presented considering the correlations between renewables and power demands. The inclusion of market volatility in electricity price uncertainty further enhances planning realism. Numerical case studies on an IEEE-34 bus three-phase ADN demonstrate the effectiveness and advantages of the proposed method.
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