The management of large-scale water resource systems with surface and groundwater resources requires considering stream-aquifer interactions. Optimization models applied to large-scale systems have either employed det...
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The management of large-scale water resource systems with surface and groundwater resources requires considering stream-aquifer interactions. Optimization models applied to large-scale systems have either employed deterministic optimization (with perfect foreknowledge of future inflows, which hinders their applicability to real-life operations) or stochastic programming (in which stream-aquifer interaction is often neglected due to the computational burden associated with these methods). In this paper, stream-aquifer interaction is integrated in a stochastic programming framework by combining the stochastic Dual Dynamic programming (SDDP) optimization algorithm with the Embedded Multireservoir Model (EMM). The resulting extension of the SDDP algorithm, named Combined Surface-Groundwater SDDP (CSG-SDDP), is able to properly represent the stream-aquifer interaction within stochastic optimization models of large-scale surface-groundwater resource systems. The algorithm is applied to build a hydroeconomic model for the Jucar River Basin (Spain), in which stream-aquifer interactions are essential to the characterization of water resources. Besides the uncertainties regarding the economic characterization of the demand functions, the results show that the economic efficiency of the operating policies under the current system can be improved by better management of groundwater and surface resources.
Multi-horizon stochastic programming includes short-term and long-term uncertainty in investment planning problems more efficiently than traditional multi-stage stochastic programming. In this paper, we exploit the bl...
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Multi-horizon stochastic programming includes short-term and long-term uncertainty in investment planning problems more efficiently than traditional multi-stage stochastic programming. In this paper, we exploit the block separable structure of multi-horizon stochastic linear programming, and establish that it can be decomposed by Benders decomposition and Lagrangean decomposition. In addition, we propose parallel Lagrangean decomposition with primal reduction that, (1) solves the scenario subproblems in parallel, (2) reduces the primal problem by keeping one copy for each scenario group at each stage, and (3) solves the reduced primal problem in parallel. We apply the parallel Lagrangean decomposition with primal reduction, Lagrangean decomposition and Benders decomposition to solve a stochastic energy system investment planning problem. The computational results show that: (a) the Lagrangean type decomposition algorithms have better convergence at the first iterations to Benders decomposition, and (b) parallel Lagrangean decomposition with primal reduction is very efficient for solving multi-horizon stochastic programming problems. Based on the computational results, the choice of algorithms for multi-horizon stochastic programming is discussed.
Catastrophic health events are natural or man-made incidents that create casualties in numbers that overwhelm the response capabilities of healthcare systems. Proper response planning for such events requires communit...
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Catastrophic health events are natural or man-made incidents that create casualties in numbers that overwhelm the response capabilities of healthcare systems. Proper response planning for such events requires community-based surge solutions such as the location of alternative care facilities and ways to improve coordination by considering triage and the movement of self-evacuees. In this paper, we construct a three-stage stochastic programming model to locate alternative care facilities and allocate casualties in response to catastrophic health events. Our model integrates casualty triage and the movement of self-evacuees in a systemic response framework that treats uncertainties involved in such large-scale events as probabilistically distributed scenarios. Solution times being instrumental to the practicality of the model, we propose an algorithm, based on Benders decomposition, to generate good solutions fast. We derive new valid inequalities, which we add to the Benders decomposition master problem to reduce the number of weak feasibility cuts generated. Because our algorithm can also be ineffective if the number of scenarios is large, we propose a two-stage approximation model that attempts to guess good third-stage solutions without third-stage decision variables and constraints. Our model, algorithm, and two-stage approximation are implemented in the case study of an earthquake situation in California based on the realistic ShakeOut Scenario data.
stochastic programming has been widely used in various application scenarios and theoretical research works. However, these excellent methods depend on specific explicit probability modeling with complete knowledge of...
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stochastic programming has been widely used in various application scenarios and theoretical research works. However, these excellent methods depend on specific explicit probability modeling with complete knowledge of uncertainty, which is very limited in practical problem since there is usually no way to abstract complex uncertainties into the commonly used known probability models. In this paper, a novel generative model named the Adaptive Discrete Approximation Rejection Sampling is proposed for stochastic programming with incomplete knowledge of uncertainty, which can not only simulate uncertain scenarios from a complex explicit probability model that cannot meet the constraints of existing sampling methods, but also even simulate scenarios from a sample set related to uncertainty when the specific explicit probability model of uncertainty is missing or unavailable. The method is to establish the easy-to-sample proposal distribution by approximately transforming the complex hard-to-sample target probability model, to make the proposal distribution close enough to the target distribution, so as to achieve an efficient sampling while ensuring the performance of the model. On this basis, combining the Monte Carlo method and heuristic optimization, an uncertain optimization model for stochastic programming with incomplete knowledge of uncertainty is further constructed, to solve the unavailability of the existing stochastic programming methods in the absence of explicit probability model of uncertainty. Experimental results show the advantages of the proposed method in terms of applicability, adaptability, accuracy, efficiency and model performance.
This paper is concerned with power system expansion planning under uncertainty. In our approach, integer programming and stochastic programming provide a basic framework. We develop a multistage stochastic programming...
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This paper is concerned with power system expansion planning under uncertainty. In our approach, integer programming and stochastic programming provide a basic framework. We develop a multistage stochastic programming model in which some of the variables are restricted to integer values. By utilizing the special property of the problem, called block separable recourse, the problem is transformed into a two-stage stochastic program with recourse. The electric power capacity expansion problem is reformulated as the problem with first stage integer variables and continuous second stage variables. We propose an L-shaped algorithm to solve the problem.
Wind imposes costs on power systems due to uncertainty and variability of real-time resource availability. stochastic programming and demand response are offered as two possible solutions to mitigate these so-called w...
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Wind imposes costs on power systems due to uncertainty and variability of real-time resource availability. stochastic programming and demand response are offered as two possible solutions to mitigate these so-called wind-uncertainty costs. We examine the benefits of these two solutions, and show that although both will reduce wind-uncertainty costs, demand response is significantly more effective. We also examine the impacts of using demand response and stochastic optimization together. We show that most of the value of demand response in reducing wind-uncertainty costs remain if a stochastic optimization is used and that there are subadditive benefits from using the two together.
Due to the new carbon neutral policies, many district heating operators start operating their combined heat and power plants using different types of biomass instead of fossil fuel. The contracts with the biomass supp...
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Due to the new carbon neutral policies, many district heating operators start operating their combined heat and power plants using different types of biomass instead of fossil fuel. The contracts with the biomass suppliers are negotiated months in advance and involve many uncertainties from the energy producer's side. The demand for biomass is uncertain at that time, and heat demand and electricity prices vary drastically during the planning period. Furthermore, the optimal operation of combined heat and power plants has to consider the existing synergies between the power and heating systems. We propose a solution method using stochastic optimization to support the biomass supply planning for combined heat and power plants. Our two-phase approach determines mid-term decisions about biomass supply contracts as well as short-term decisions regarding the optimal production of the producer to ensure profitability and feasibility. We present results based on ten realistic test cases placed in two municipalities.
The paper suggests a possible cooperation between stochastic programming and optimal control for the solution of multistage stochastic optimization problems. We propose a decomposition approach for a class of multista...
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The paper suggests a possible cooperation between stochastic programming and optimal control for the solution of multistage stochastic optimization problems. We propose a decomposition approach for a class of multistage stochastic programming problems in arborescent form (i.e. formulated with implicit non-anticipativity constraints on a scenario tree). The objective function of the problem can be either linear or nonlinear, while we require that the constraints are linear and involve only variables from two adjacent periods (current and lag 1). The approach is built on the following steps. First, reformulate the stochastic programming problem into an optimal control one. Second, apply a discrete version of Pontryagin maximum principle to obtain optimality conditions. Third, discuss and rearrange these conditions to obtain a decomposition that acts both at a time stage level and at a nodal level. To obtain the solution of the original problem we aggregate the solutions of subproblems through an enhanced mean valued fixed point iterative scheme.
This paper investigates some common interest rate models for scenario generation in financial applications of stochastic optimization. We discuss conditions for the underlying distributions of state variables which pr...
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This paper investigates some common interest rate models for scenario generation in financial applications of stochastic optimization. We discuss conditions for the underlying distributions of state variables which preserve convexity of value functions in a multistage stochastic program. One- and multi-factor term structure models are estimated based on historical data Fur the Swiss Franc. An analysis of the dynamic behavior of interest rates generated with these models reveals several deficiencies which have an impact on the performance of investment policies derived from the stochastic program. While barycentric approximation is used here for the generation of scenario trees, these insights may be generalized to other discretization techniques as well.
In this paper we shall deal with statistical estimates in stochastic programming problems. The estimate problem is a very important one. Namely, from a mathematical point of view many practical optimization problems w...
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In this paper we shall deal with statistical estimates in stochastic programming problems. The estimate problem is a very important one. Namely, from a mathematical point of view many practical optimization problems with a random element lead to deterministic optimization problems depending on the random element through probability measure only. Moreover, this probability measure is hardly ever known in real-life situations. We consider the case when the theoretical distribution function is completely unknown. Then the empirical distribution function usually replaces the theoretical one in order to obtain some estimates of the optimal value and the optimal solution, at least. These estimates will just be the subject of our investigation. In detail, we shall mostly deal with the case of dependent samples. Evidently, the dependent samples appear more often in real-life situations than the independent ones. First, we shall briefly mention the consistence results. Further, we shall study the convergence rate with respect to various types of random samples dependence. We compare these results with those achieved earlier, including some results on asymptotic distribution. We shall recognize that the convergence rate is ''the best one'' for the independent case, of course. However: we shall introduce the dependent types with the same convergence rate.
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