Showing papers on "Stochastic programming published in 2020"
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TL;DR: The simulation results confirm that the Benders decomposing method offers extremely high levels of accuracy and power in solving the complex model of coordinated planning and operation problem in the presence of uncertainties and numerous decision variables.
116 citations
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TL;DR: To solve the proposed model, a Lagrangian relaxation-based algorithm formulated by a new adaptive strategy is employed, which considers both upper and lower bounds of the problem to reach a performance solution.
104 citations
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TL;DR: A novel real-time autonomous energy management strategy for a residential MES is proposed using a model-free deep reinforcement learning (DRL) based approach, combining state-of-the-art deep deterministic policy gradient (DDPG) method with an innovative prioritized experience replay strategy.
Abstract: Multi-energy systems (MES) are attracting increasing attention driven by its potential to offer significant flexibility in future smart grids. At the residential level, the roll-out of smart meters and rapid deployment of smart energy devices call for autonomous multi-energy management systems which can exploit real-time information to optimally schedule the usage of different devices with the aim of minimizing end-users’ energy costs. This paper proposes a novel real-time autonomous energy management strategy for a residential MES using a model-free deep reinforcement learning (DRL) based approach, combining state-of-the-art deep deterministic policy gradient (DDPG) method with an innovative prioritized experience replay strategy. This approach is tailored to align with the nature of the problem by posing it in multi-dimensional continuous state and action spaces, facilitating more cost-effective control strategies to be devised. The superior performance of the proposed approach in reducing end-user’s energy cost while coping with the MES uncertainties is demonstrated by comparing it against state-of-the-art DRL methods as well as conventional stochastic programming and robust optimization methods in numerous case studies in a real-world scenario.
99 citations
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TL;DR: To address the uncertain renewable energy in the day-ahead optimal dispatch of energy and reserve, a multi-stage stochastic programming model is established in this paper to minimize the expected total costs and to deal with the “Curse of Dimensionality” of stochastically programming.
Abstract: To address the uncertain renewable energy in the day-ahead optimal dispatch of energy and reserve, a multi-stage stochastic programming model is established in this paper to minimize the expected total costs. The uncertainties over the multiple stages are characterized by a scenario tree and the optimal dispatch scheme is cast as a decision tree which guarantees the flexibility to decide the reasonable outputs of generation and the adequate reserves accounting for different realizations of renewable energy. Most importantly, to deal with the “Curse of Dimensionality” of stochastic programming, stochastic dual dynamic programming (SDDP) is employed, which decomposes the original problem into several sub-problems according to the stages. Specifically, the SDDP algorithm performs forward pass and backward pass repeatedly until the convergence criterion is satisfied. At each iteration, the original problem is approximated by creating a linear piecewise function. Besides, an improved convergence criterion is adopted to narrow the optimization gaps. The results on the IEEE 118-bus system and real-life provincial power grid show the effectiveness of the proposed model and method.
95 citations
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TL;DR: A data-driven two-stage robust stochastic programming model for energy hub capacity planning with distributional robustness guarantee is proposed and transformed into an equivalent convex program with a nonlinear objective and linear constraints, and is solved by an outer-approximation algorithm that entails solving only linear program.
Abstract: Cascaded utilization of natural gas, electric power, and heat could leverage synergetic effects among these energy resources, precipitating the advent of integrated energy systems. In such infrastructures, energy hub is an interface among different energy systems, playing the role of energy production, conversion, and storage. The capacity of energy hub largely determines how tightly these energy systems are coupled and how flexibly the whole system would behave. This paper proposes a data-driven two-stage robust stochastic programming model for energy hub capacity planning with distributional robustness guarantee. Renewable generation and load uncertainties are modelled by a family of ambiguous probability distributions near an empirical distribution in the sense of Kullback–Leibler (KL) divergence measure. The objective is to minimize the sum of the construction cost and the expected life-cycle operating cost under the worst-case distribution restricted in the ambiguity set. Network energy flow in normal operating conditions is considered; demand supply reliability in extreme conditions is taken into account via robust chance constraints. Through duality theory and sampling average approximation, the proposed model is transformed into an equivalent convex program with a nonlinear objective and linear constraints, and is solved by an outer-approximation algorithm that entails solving only linear program. Case studies demonstrate the effectiveness of the proposed model and method.
85 citations
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TL;DR: The proposed two-stage stochastic optimization model aims at minimizing the time and cost of delivering blood to hospitals after the occurrence of a disaster, while considering possible disruptions in blood facilities and transportation routes.
Abstract: Emergency supply of blood in disasters is a crucial task for humanitarian aid. In this paper, we present a bi-objective robust optimization model for the design of blood supply chains that are resilient to disaster scenarios. The proposed two-stage stochastic optimization model aims at minimizing the time and cost of delivering blood to hospitals after the occurrence of a disaster, while considering possible disruptions in blood facilities and transportation routes. A Lagrangian relaxation-based algorithm is developed that is capable of solving large-scale instances of the model. We apply this framework to a real case study of blood banks in Jordan.
84 citations
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TL;DR: A multi-objective, eco-sustainability model for a supply chain including big data for an optimal sustainable procurement and transportation decision is proposed and can prevent disturbances by using a scenario-based stochastic programming approach.
80 citations
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TL;DR: The various methods and applications of scenario generation are classified and discussed and an evaluation framework for these methods is established to comprehensively understand scenario generation and optimize solutions for uncertainties.
76 citations
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TL;DR: A two-stage robust stochastic programming model for the optimal scheduling of commercial microgrids equipped with 100% RERs to handle the existing uncertainties is presented and results verify that the proposed model could provide satisfactory profits formicrogrids participated in the energy exchanging process based on the transactive energy architecture.
Abstract: At present, the power system is developing toward a fully renewable energy resources (RERs) equipped system due to significant challenges with the conventional units. This trend has led to remarkable new challenges for power system planners considering the stochastic nature of RERs, application of new emerging technologies, etc. In this article, a two-stage robust stochastic programming model for the optimal scheduling of commercial microgrids equipped with 100% RERs to handle the existing uncertainties is presented. In the day-ahead electricity market, microgrids maximize their expected profits by optimizing their bidding strategy, while minimizing the imbalance cost is targeted for microgrids by adjusting the distributed energy resources in the real-time balancing market. Transactive energy technology is effectively applied to manage the energy trading between microgrids with each other in the local energy transaction market and with the power grid. For demand-side management, the demand response program is posed considering the shiftable and interruptible features of the load. Simulation results on the IEEE 33-bus standard system integrated with microgrids verify that the proposed model could provide satisfactory profits for microgrids participated in the energy exchanging process based on the transactive energy architecture.
76 citations
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TL;DR: Results have verified the effectiveness of the proposed method, providing efficient bidding curves to the EHO through the stochastic management, and shows that the proposed strategy can balance the operational cost and service quality via the adjustment of chance constraints.
Abstract: To realize high efficient energy conversion among multiple energy carriers in market environment, the hybrid ac/dc microgrid is embedded as the electrical hub for energy hubs (EHs), and a stochastic day-ahead bidding strategy is proposed for the energy hub operators (EHOs). The electricity, heating, and cooling are managed to balance the operational cost and thermal service quality, while participating into the day-ahead market and real-time market. The uncertainties of prices, electrical loads, and ambient temperature are depicted by scenario trees, and are managed by a two-stage stochastic optimization scheme to minimize the expected and conditional value at the risk of operational cost. This stochastic optimization problem is reformulated to a linear programming (LP) problem under given conditions. In addition, a chance constraint is proposed to relax the quality of thermal services, and a two-stage chance constrained stochastic programming is formulated accordingly. It is further reformulated to a mixed integer LP problem. Simulations have been carried out on an EH with multiple types of energy generation, conversion, and storage systems. Results have verified the effectiveness of the proposed method, providing efficient bidding curves to the EHO through the stochastic management. Sensitive analysis shows that the proposed strategy can balance the operational cost and service quality via the adjustment of chance constraints.
75 citations
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TL;DR: In this paper, statistical machine learning theories are proposed to quickly solve the optimal planning for capacitors by comparing the method with the scenario reduction algorithm and the Monte Carlo method in a 33-bus distribution system.
Abstract: Distributed generation and reactive power resource allocation will affect the economy and security of distribution networks. Deterministic scenario planning cannot solve the problem of network uncertainties, which are introduced by intermittent renewable generators and a variable demand for electricity. However, stochastic programming becomes a problem of great complexity when there is a large number of scenarios to be analyzed and when the computational burden has an adverse effect on the programming solution. In this paper, statistical machine learning theories are proposed to quickly solve the optimal planning for capacitors. Various technologies are used: Markov chains and copula functions are formulated to capture the variability and correlation of weather; consumption behavior probability is involved in the weather-sensitive load model; nearest neighbor theory and nonnegative matrix decomposition are combined to reduce the dimensions and scenario scale of stochastic variables; the stochastic response surface is used to calculate the probabilistic power flow; and probabilistic inequality theory is introduced to directly estimate the objective and constraint functions of the stochastic programming model. The effectiveness and efficiency of the proposed method are verified by comparing the method with the scenario reduction algorithm and the Monte Carlo method in a 33-bus distribution system.
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TL;DR: This study suggests an optimal bidding strategy considering uncertainty of renewable energy resources and DRP based on their outage probabilities and investigates the efficiency of the stochastic programming in uncertainty integration into the bidding problem.
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TL;DR: A game theoretic approach based incentive mechanism to encourage the “best” neighbor mobile devices to share their own resource for sensing and a auction based task migration algorithm, which can guarantee the truthfulness of announced price of auctioneer, individual rationality, profitability, and computational efficiency.
Abstract: With the exponentially increasing number of mobile devices, crowdsensing has been a hot topic to use the available resource of neighbor mobile devices to perform sensing tasks cooperatively. However, there still remain three main obstacles to be solved in the practical system. First, since mobile devices are selfish and rational, it is natural to provide cooperation for sensing with a reasonable payment. Meanwhile, due to the arrival and departure of sensing tasks, resource should be allocated and released dynamically when sensing task comes or leaves. To this end, this paper designs a game theoretic approach based incentive mechanism to encourage the “best” neighbor mobile devices to share their own resource for sensing. Next, in order to adjust resource among mobile devices for the better crowdsensing response, an auction based task migration algorithm is proposed, which can guarantee the truthfulness of announced price of auctioneer, individual rationality, profitability, and computational efficiency. Moreover, taking into account the random movement of mobile devices resulting in the stochastic connection, we also use multi-stage stochastic decision to take posterior resource allocation to compensate for inaccurate prediction. The numerical results show the effectiveness and improvement of the proposed multi-stage stochastic programming based distributed game theoretic methodology ( SPG ) for crowdsensing.
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TL;DR: This model determines the optimum location-allocation and inventory management decisions and aims to minimize the total cost of the supply chain includes fixed costs, operating costs, inventory holding costs, wastage costs, and transportation costs along with minimizing the substitution levels to provide safer blood transfusion services.
Abstract: Based on the uncertain conditions such as uncertainty in blood demand and facility disruptions, and also, due to the uncertain nature of blood products such as perishable lifetime, distinct blood groups, and ABO-Rh(D) compatibility and priority rules among these groups, this paper aims to contribute blood supply chains under uncertainty. In this respect, this paper develops a bi-objective two-stage stochastic programming model for managing a red blood cells supply chain that observes above-mentioned issues. This model determines the optimum location-allocation and inventory management decisions and aims to minimize the total cost of the supply chain includes fixed costs, operating costs, inventory holding costs, wastage costs, and transportation costs along with minimizing the substitution levels to provide safer blood transfusion services. To handle the uncertainty of the blood supply chain environment, a robust optimization approach is devised to tackle the uncertainty of parameters, and the TH method is utilized to make the bi-objective model solvable. Then, a real case study of Mashhad city, in Iran, is implemented to demonstrate the model practicality as well as its solution approaches, and finally, the computational results are presented and discussed. Further, the impacts of the different parameters on the results are analyzed which help the decision makers to select the value of the parameters more accurately.
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23 Sep 2020
TL;DR: In this paper, the Lipschitzian stability of nonlinear programs in infinite-dimensional function spaces has been analyzed for certain trust region methods with approximate data on the role of the Mangasarian-Fromovitz constraint.
Abstract: Discretization and mesh-independent of Newton's method for generalized differentiability of optimal solutions in non-linear parametric optimization characterisations of Lipschitzian stability in nonlinear programming on second order sufficient conditions for structured nonlinear programs in infinite-dimensional function spaces algorithmic stability analysis for certain trust region methods a note on using linear knowledge to solve efficiency linear programs specified with approximate data on the role of the Mangasarian-Fromovitz constraint qualification for penalty-, exact penalty-, and Lagrange multiplier methods Hoffman's error bound for systems of convex functions and applications to nonlinear optimization on well-posedness and stability analysis optimization convergence of approximations to nonlinear optimal control problems a perturbation-based duality classification for max-flow min-cut problems of Strang and Iri central and peripheral results in the study of marginal and performance functions topological stability of feasible sets in semi-infinite optimization - a tutorial solution existence for infinite quadratic programming sensitivity analysis of nonlinear programming problems via minimax functions parametric linear complementary problems sufficient conditions for weak sharp minima of order two and directional derivatives of the value function.
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TL;DR: A stochastic programming framework for the optimal scheduling of an MG equipped with RESs and plug-in electric vehicles (PEVs) using an effective and efficient optimization algorithm named “modified harmony search (MHS) algorithm” is provided.
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TL;DR: The proposed DRO approach can overcome the limitations of stochastic programming in its inherent dependence of exact probability distributions along with a huge computational burden, but also becomes less conservative than classical robust optimization.
Abstract: Coordinated operations of electricity and district heating networks offer a potential for mitigating inherent variability of renewable energy sources (RES) in the ongoing transition to smart grids. This paper proposes a two-stage distributionally robust optimization (DRO) approach to determine the optimal day-ahead unit commitment in coordinated electricity and district heating networks with variable RES power output. The proposed formulation is to minimize the worst-case expected total cost over an ambiguity set comprising a family of probability distributions with given support and moments of RES power output. As such, the proposed DRO approach can overcome the limitations of stochastic programming in its inherent dependence of exact probability distributions along with a huge computational burden, but also becomes less conservative than classical robust optimization. The pertinent DRO model is eventually reformulated as a tractable mixed-integer second-order cone (SOC) programming after employing linear decision rules and the SOC duality. Simplified affine policies are utilized to further improve computational tractability and performance. Finally, case studies are conducted based on Barry Island electricity and district heating networks. The numerical results demonstrate the decision-making superiority of the proposed method as compared with deterministic, stochastic programming, and robust optimization approaches. They also validate the computational improvement of the proposed approach by employing simplified affine policies.
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TL;DR: Numerical simulation results verify that the proposed method achieves superior fuel economy that is close to that by stochastic dynamic programming method, and the effective state of charge tracking in terms of different reference trajectories highlight that the propose method is effective for online application requiring a fast calculation speed.
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TL;DR: The results highlight that higher emissions price does not always contribute to the efficiency of the cold supply chain system and indicate that using heterogeneous fleet including light duty and medium duty vehicles can lead to further cost saving and emissions reduction.
Abstract: Increasing awareness of sustainability in supply chain management has prompted organizations and individuals to consider environmental impacts when managing supply chains. The issues concerning environmental impacts are significant in cold supply chains due to substantial carbon emissions from storage and distribution of temperature-sensitive product. This paper investigates the impact of carbon emissions arising from storage and transportation in the cold supply chain in the presence of carbon tax regulation, and under uncertain demand. A two-stage stochastic programming model is developed to determine optimal replenishment policies and transportation schedules to minimize both operational and emissions costs. A matheuristic algorithm based on the Iterated Local Search (ILS) algorithm and a mixed integer programming is developed to solve the problem in realistic sizes. The performance and robustness of the matheuristic algorithm are analyzed using test instances in various sizes. A real-world case study in Queensland, Australia is used to demonstrate the application of the model. The results highlight that higher emissions price does not always contribute to the efficiency of the cold supply chain system. Furthermore, the analyses indicate that using heterogeneous fleet including light duty and medium duty vehicles can lead to further cost saving and emissions reduction.
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TL;DR: A new paradigm digital twin network is proposed to build network topology and the stochastic task arrival model in IIoT systems to minimize the long-term energy efficiency and an asynchronous actor-critic algorithm is presented to find the optimal stoChastic computation offloading policy.
Abstract: The rapid development of Industrial Internet of Things (IIoT) requires industrial production towards digitalization to improve network efficiency. Digital Twin is a promising technology to empower the digital transformation of IIoT by creating virtual models of physical objects. However, the provision of network efficiency in IIoT is very challenging due to resource-constrained devices, stochastic tasks, and resources heterogeneity. Distributed resources in IIoT networks can be efficiently exploited through computation offloading to reduce energy consumption while enhancing data processing efficiency. In this paper, we first propose a new paradigm Digital Twin Networks (DTN) to build network topology and the stochastic task arrival model in IIoT systems. Then, we formulate the stochastic computation offloading and resource allocation problem to minimize the long-term energy efficiency. As the formulated problem is a stochastic programming problem, we leverage Lyapunov optimization technique to transform the original problem into a deterministic per-time slot problem. Finally, we present Asynchronous Actor-Critic (AAC) algorithm to find the optimal stochastic computation offloading policy. Illustrative results demonstrate that our proposed scheme is able to significantly outperforms the benchmarks.
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TL;DR: An extensive out-of-sample comparison demonstrates that the optimal policy obtained by the stochastic program clearly outperforms deterministic planning, a pure day-ahead strategy, a benchmark that only uses the day- Ahead market and the first intraday market, as well as a proprietary stochastically programming approach developed in the industry.
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TL;DR: The maximum potential of clean energy production units is used in comparison with fossil fuel-based units through the optimal scheduling of the wind-thermal-hydropower-pumped storage system through the two-stage stochastic programming model.
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TL;DR: It is found that the proposed two-stage stochastic mixed-integer programming method can effectively determine the optimal DER sizes to meet a required resilience goal at the maximum net-benefit.
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TL;DR: A hybrid robust-stochastic optimization model for smart home energy management in day-ahead (DA) and real-time (RT) energy markets which the uncertainties of energy prices and PV generation are investigated in the proposed model.
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TL;DR: A stochastic optimization model for the optimal design and operation strategy of regional electric power system is proposed to achieve conventional resource-consumption reduction and CO2 emission mitigation under cost-risk control and can not only deal with the complex uncertainties expressed as discrete intervals and probability distribution, but also help decision-makers make cost- risk tradeoff under predetermined budget.
Abstract: Restricted by conventional energy resources and environmental space, the sustainable development of urban power sector faces enormous challenges. Renewable energy generation and carbon capture and storage (CCS) are attractive technologies for reducing conventional energy resource consumption and improving CO2 emission mitigation. Considering the limitation of expensive investment cost on their wide application, a stochastic optimization model for the optimal design and operation strategy of regional electric power system is proposed to achieve conventional resource-consumption reduction and CO2 emission mitigation under cost-risk control. The hybrid method integrates interval two-stage stochastic programming with downside risk theory. It can not only effectively deal with the complex uncertainties expressed as discrete intervals and probability distribution, but also help decision-makers make cost-risk tradeoff under predetermined budget. The proposed model is applied in the electric power system planning of Zhejiang Province, an economically developed area with limited fossil energy resources. The influences of different resource and environmental policies on the investment portfolio and power system operation are analyzed and discussed under various scenarios. The results indicated that different policies would lead to different generation technology portfolios. The aggressive CO2 emission reduction policy could stimulate the development of CCS technology, and the electric power system would still heavily rely on coal resource, while the tough coal-consumption control policy could directly promote regional renewable energy development and electric power structure adjustment.
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TL;DR: A hybrid two-stage bi-level optimization model is proposed to manage such uncertainties so that wind power, load demand, and day-ahead market prices are handled through scenario-based stochastic programming and an information gap decision theory is applied to model the uncertainty of real-time market prices.
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TL;DR: A two-stage stochastic programming problem is proposed for the optimal sizing of a hybrid renewable energy system consisted of wind turbine, concentrated solar plant, and electric heater and the superiority of JADE is validated by algorithm comparisons with several popular intelligent optimization algorithms.
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TL;DR: In this paper, a novel risk management approach called downside risk constraints (DRC) is applied to get the optimal offering and bidding strategies of the pumped hydro storages (PHS) in the energy market.
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TL;DR: This study provides a new metric to quantify the SC resilience by using the stochastic programming, which measures the expected value of the SC's cost increase due to a possible disruption event during its recovery period.
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TL;DR: Decision dependent distributionally robust optimization models, where the ambiguity sets of probability distributions can depend on the decision variables, are studied, to allow solutions of such problems using global optimization techniques within the framework of a cutting surface algorithm.
Abstract: We study decision dependent distributionally robust optimization models, where the ambiguity sets of probability distributions can depend on the decision variables. These models arise in situations with endogenous uncertainty. The developed framework includes two-stage decision dependent distributionally robust stochastic programming as a special case. Decision dependent generalizations of five types of ambiguity sets are considered. These sets are based on bounds on moments, covariance matrix, Wasserstein metric, Phi-divergence and Kolmogorov–Smirnov test. For the finite support case, we use linear, conic or Lagrangian duality to give reformulations of these models with a finite number of constraints. Reformulations are also given for the continuous support case for moment, covariance, Wasserstein and Kolmogorov–Smirnov based models. These reformulations allow solutions of such problems using global optimization techniques within the framework of a cutting surface algorithm. The importance of decision dependence in the ambiguity set is demonstrated with the help of a numerical example modeling simultaneous determination of order quantity and selling price for a newsvendor problem.