We show that a Riccati-based Multistage stochastic programming solver for problems with separable convex linear/nonlinear objective developed in previous papers can be extended to solve more general stochastic Program...
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We show that a Riccati-based Multistage stochastic programming solver for problems with separable convex linear/nonlinear objective developed in previous papers can be extended to solve more general stochastic programming problems. With a Lagrangean relaxation approach, also local and global equality constraints can be handled by the Riccati-based primal interior point solver. The efficiency of the approach is demonstrated on a 10 staged stochastic programming problem containing both local and global equality constraints. The problem has 1.9 million scenarios, 67 million variables and 119 million constraints, and was solved in 97 min on a 32 node PC cluster.
In this work, we consider the allocation problem in stratified surveys as a problem of non-linear stochastic programming of integers. An example is solved by the following techniques: Lagrange multipliers, modified E-...
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In this work, we consider the allocation problem in stratified surveys as a problem of non-linear stochastic programming of integers. An example is solved by the following techniques: Lagrange multipliers, modified E-model, E-model, V-model and chance constraints. (c) 2006 Elsevier B.V. All rights reserved.
In this paper, we propose a two-stage stochastic linear programming model considering some of the right hand side parameters of the first stage constraints as multi-choice parameters and rest of the right hand side pa...
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In this paper, we propose a two-stage stochastic linear programming model considering some of the right hand side parameters of the first stage constraints as multi-choice parameters and rest of the right hand side parameters of the constraints as exponential random variables with known means. Both the randomness and multi-choiceness are simultaneously considered for the model parameters. Randomness is characterized by some random variables with its distribution and multi-choiceness is handled by using interpolating polynomials. To solve the proposed problem, first we remove the fuzziness and then for multi-choice parameters interpolating polynomials are established. After establishing the deterministic equivalent of the model, standard mathematical programming technique is applied to solve the problem. A numerical example is presented to demonstrate the usefulness of the proposed methodology. (C) 2014 Elsevier Inc. All rights reserved.
Probabilistic realizations of outages and their effects on the operational costs are highly overlooked aspects in power system expansion planning. Since the effect of randomness in contingencies can be more prominent ...
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Probabilistic realizations of outages and their effects on the operational costs are highly overlooked aspects in power system expansion planning. Since the effect of randomness in contingencies can be more prominent especially when transmission switching is considered, in this paper we introduce contingency-dependent transmission switching concept to ensure N-1 criterion. To include randomness of outages and the outputs (i.e. flow on the lines/generation amounts) during the outages, we represent each contingency by a single scenario. Status of transmission lines, generation amounts and power flow decisions are defined as recourse actions of our two-stage stochastic model, therefore, expected operational cost during the contingencies are taken into account in a more accurate manner. A solution methodology with a filtering technique is also proposed to overcome the computational burden. The model and the solution methodology are tested on the IEEE Reliability Test System and IEEE 118-bus power system and the results show that the solution method finds the solutions for these power systems in significantly shorter solution times. The solution method is also tested on a new data set for the 380-kV Turkish transmission network. Suggestions for possible extensions of the problem and the modifications of the solution approach to handle these extensions are also discussed.
This paper presents a novel multi-objective model of active distribution network planning based on stochastic programming and uncertain random network (URN) theory. The planning model is proposed to find the final sch...
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This paper presents a novel multi-objective model of active distribution network planning based on stochastic programming and uncertain random network (URN) theory. The planning model is proposed to find the final scheme with optimal alternative, location, size and operational strategy for the candidate distribution lines, transformer substations (TSs), distribution generations (DGs), static var compensators (SVCs) and on-load tap changers (OLTCs). Firstly, a scenario-based approach is developed to analyse the uncertainties in network system, such as the demand and intermittency of renewable sources. Since the impact of multiple uncertain factors on network cannot be ignored, a network frame is then modelled by uncertain and random weights of spanning tree (ST) instead of fixed value. In order to achieve the minimization of total cost, and further the selection of a minimum spanning tree (MST) with the uncertain and random weight, a 3-dimensional uncertain space is constructed based on the combination of the previous two targets. In addition, a second-order cone programming (SOCP) is applied to cope with the multi-objective, mixed-integer nonlinear nature of the proposed planning model. Simulation is performed on a modified Pacific Gas and Electric Company (PG&E) 69-bus distribution system, and the results demonstrate the effectiveness of the proposed model.
Integration of scheduling and dynamic optimization significantly improves the overall performance of a production process compared to the traditional sequential method. However, most integrated methods focus on solvin...
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Integration of scheduling and dynamic optimization significantly improves the overall performance of a production process compared to the traditional sequential method. However, most integrated methods focus on solving deterministic problems without explicitly taking process uncertainty into account. We propose a novel integrated method for sequential batch processes under uncertainty. The integrated problem is formulated into a two-stage stochastic program. The first-stage decisions are modeled with binary variables for assignment and sequencing while the second-stage decisions are the remaining ones. To solve the resulting complicated integrated problem, we develop two efficient algorithms based on the framework of generalized Benders decomposition. The first algorithm decomposes the integrated problem according to the scenarios so that the subproblems can be optimized independently over each scenario. Besides the scenario decomposition, the second algorithm further decomposes dynamic models from the scheduling model, resulting in a nested decomposition structure. For a complicated case study with more than 3 million variables/equations under 100 scenarios, the direct solution approach does not find a feasible solution while the two decomposition algorithms return the optimal solution. The computational time for the first algorithm is 23.9 h, and that for the second algorithm is only 3.3 h. Furthermore, the integrated method returns a higher average profit than the sequential method by 17.6%.
Traditional methods for hedging interest rate risk do not take transaction costs into account as they aim to eliminate all risk. We propose a two-stage stochastic programming model for hedging interest rate risk where...
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Traditional methods for hedging interest rate risk do not take transaction costs into account as they aim to eliminate all risk. We propose a two-stage stochastic programming model for hedging interest rate risk where transaction costs are weighed against portfolio variance. High-quality measurements of term structures enable us to extract the systematic risk factors and make precise estimates of the perceived transaction costs. The hedging cost is weighed against the reduction in portfolio variance by using an adjustable hedging parameter. The hedging procedure is simulated on a daily basis in a realistic setting over an out-of-sample period from 2002 to 2018, and the results are compared to traditional hedging methods through detailed performance attribution. Using second-order stochastic dominance, we show that the proposed method is preferred by all risk-averse investors. (C) 2022 The Author(s). Published by Elsevier B.V.
Variable message signs (VMS) are electronic signage systems that display real-time traffic information to drivers to mitigate congestion and reduce travel time. We propose a heterogeneous VMS location problem based on...
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Variable message signs (VMS) are electronic signage systems that display real-time traffic information to drivers to mitigate congestion and reduce travel time. We propose a heterogeneous VMS location problem based on a stochastic model of accidents on a freeway network. We consider both gantry and cantilever mounted VMS that displays both passive and active real-time messages. The problem is formulated as a two-stage stochastic programming model. The first-stage model determines the location and type of VMS installation. The second stage evaluates the performance of VMS location solutions by minimizing travelers' travel time and the penalty for misleading guidance. The model is formulated as a mixed-integer linear programming (MILP) problem that can be solved using the Benders decomposition (BD) algorithm. The Nguyen-Dupuis and Sioux-Fall networks are used to verify the effectiveness of the proposed models. We believe this study will provide practical guidance to freeway administrators.
One of the important issues in range query (RQ) retrieval problems is to determine the key's resolution for multiattribute records. Conventional models need to be improved because of potential degeneracy, less des...
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One of the important issues in range query (RQ) retrieval problems is to determine the key's resolution for multiattribute records. Conventional models need to be improved because of potential degeneracy, less desired computability, and possible inconsistency with the partial match query (PMQ) models. This paper presents a new RQ model to overcome these drawbacks and introduces a new methodology, stochastic programming (SP), to conduct the optimization process. The model is established by using a monotone increasing function to. characterize range sizes. Three SP approaches, wait-and-see (WS), here-and-now (HN), and scenario tracking (ST) methods are integrated into this RQ model. Analytical expressions of the optimal solution are derived. It seems that HN has advantage over WS because the latter usually involves complicated multiple summations or integrals. For the ST method, a nonlinear programming software package is designed. Results of numerical experiments are presented that optimized a 10-dimensional RQ model and tracked a middle size (100) and a large size (1,000) scenarios.
Resource portfolio planning optimization is crucial to high-tech manufacturing industries. One of the most important characteristics of such a problem is intensive investment and risk in demands. In this study, a nonl...
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Resource portfolio planning optimization is crucial to high-tech manufacturing industries. One of the most important characteristics of such a problem is intensive investment and risk in demands. In this study, a nonlinear stochastic optimization model is developed to maximize the expected profit under demand uncertainty. For solution efficiency, a stochastic programming-based genetic algorithm (SPGA) is proposed to determine a profitable capacity planning and task allocation plan. The algorithm improves a conventional two-stage stochastic programming by integrating a genetic algorithm into a stochastic sampling procedure to solve this large-scale nonlinear stochastic optimization on a real-time basis. Finally, the tradeoff between profits and risks is evaluated under different settings of algorithmic and hedging parameters. Experimental results have shown that the proposed algorithm can solve the problem efficiently. (C) 2006 Elsevier B.V. All rights reserved.
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