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FiWi Network Planning for Smart Metering Based on multistage stochastic programming

IEEE LATIN AMERICA TRANSACTIONS 2015年第12期13卷 3838-3843页

作者： Peralta, A. Inga, E. Hincapie, R. Univ Politecn Salesiana Cuenca Ecuador Univ Politecn Salesiana Engn Quito Ecuador Univ Pontificia Bolivariana Telecommun Engn Medellin Colombia

This article presents a novel model of mixed integer linear programming (MILP) to conduct network planning (Fiber-Wireless-FiWi) that along a timeline space facilitates growth, expansion and scalability of resources involved in communications network, traditionally used in cellular telephony, and is possible that extends as a multiservice network to provide smart metering, as is the case in Advanced Metering Infrastructure (AMI) in Smart Grid, thus optimizing their infrastructure and minimizing investment costs. This paper proposes a hybrid architecture (fiber optic-wireless networks) with realistic approaches to planning and scalability considerations under scenarios that present uncertainty in the evolution of consumer demand, both for primary users of cell phone and smart metering as a secondary user. We propose a model for network planning based on multistage stochastic programming (MSP) with a growth in demand for stochastic users and FiWi networks scalability through expected maximum benefit for their investment. The approach of this article shows that it is possible to design real FiWi large-scale networks under a cost-effective evolution considering a scheme appropriate growth in the timeline.

关键词： smart grid advanced metering infrastructure scalability network planning fiwi network multistage stochastic programming optimization

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Minimum cardinality non-anticipativity constraint sets for multistage stochastic programming

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MATHEMATICAL programming 2016年第1期157卷 69-93页

作者： Boland, Natashia Dumitrescu, Irina Froyland, Gary Kalinowski, Thomas Univ Newcastle Univ Dr Callaghan NSW 2308 Australia IBM Res Australia Carlton Vic Australia Univ Melbourne Melbourne Vic Australia Univ New S Wales Sydney NSW Australia Univ Newcastle Callaghan NSW 2308 Australia Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA

We consider multistage stochastic programs, in which decisions can adapt over time, (i.e., at each stage), in response to observation of one or more random variables (uncertain parameters). The case that the time at which each observation occurs is decision-dependent, known as stochastic programming with endogeneous observation of uncertainty, presents particular challenges in handling non-anticipativity. Although such stochastic programs can be tackled by using binary variables to model the time at which each endogenous uncertain parameter is observed, the consequent conditional non-anticipativity constraints form a very large class, with cardinality in the order of the square of the number of scenarios. However, depending on the properties of the set of scenarios considered, only very few of these constraints may be required for validity of the model. Here we characterize minimal sufficient sets of non-anticipativity constraints, and prove that their matroid structure enables sets of minimum cardinality to be found efficiently, under general conditions on the structure of the scenario set.

关键词： stochastic programming Endogeneous uncertainty multistage stochastic programming

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Reduction of nonanticipativity constraints in multistage stochastic programming problems with endogenous and exogenous uncertainty

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2018年第1期87卷 1-18页

作者： Hooshmand, F. MirHassani, S. A. Amirkabir Univ Technol Fac Math & Comp Sci Tehran Iran

multistage stochastic programming (SP) with both endogenous and exogenous uncertainties is a novel problem in which some uncertain parameters are decision-dependent and others are independent of decisions. The main difficulty of this problem is that nonanticipativity constraints (NACs) make up a significantly large constraint set, growing very fast with the number of scenarios and leading to an intractable model. Usually, a lot of these constraints are redundant and hence, identification and elimination of redundant NACs can cause a significant reduction in the problem size. Recently, a polynomial time algorithm has been proposed in the literature which is able to identify all redundant NACs in an SP problem with only endogenous uncertainty. In this paper, however, we extend the algorithm proposed in the literature and present a new method which is able to make the upper most possible reduction in the number of NACs in any SP with both exogenous and endogenous uncertain parameters. Proving the validity of this method is another innovation of this study. Computational results confirm that the proposed approach can significantly reduce the problem size within a reasonable computation time.

关键词： multistage stochastic programming Endogenous and exogenous uncertainties Redundant nonanticipativity constraints Constraint reduction

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Efficient constraint reduction in multistage stochastic programming problems with endogenous uncertainty

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OPTIMIZATION METHODS & SOFTWARE 2016年第2期31卷 359-376页

作者： Hooshmand, F. MirHassani, S. A. Amirkabir Univ Technol Dept Appl Math Fac Math & Comp Sci Tehran Iran

multistage stochastic programming with endogenous uncertainty is a new topic in which the timing of uncertainty realization is decision-dependent. In this case, the number of nonanticipativity constraints (NACs) increases very quickly with the number of scenarios, making the problem computationally intractable. Fortunately, a large number of NACs are typically redundant and their elimination leads to a considerable reduction in the problem size. Identifying redundant NACs has been addressed in the literature only in the special case where the scenario set is equal to the Cartesian product of all possible outcomes for endogenous parameters;however, this is a scarce condition in practice. In this paper, we consider the general case where the scenario set is an arbitrary set;and two approaches, able to identify all redundant NACs, are proposed. The first approach is by mixed integer programming formulation and the second one is an exact polynomial time algorithm. Proving the fact that the proposed algorithm is able to make the uppermost reduction in the number of NACs is another novelty of this paper. Computational results evaluate the efficiency of the proposed approaches.

关键词： multistage stochastic programming endogenous uncertainty redundant nonanticipativity constraints minimal graph exact polynomial time algorithm

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Solution strategies for multistage stochastic programming with endogenous uncertainties

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COMPUTERS & CHEMICAL ENGINEERING 2011年第11期35卷 2235-2247页

作者： Gupta, Vijay Grossmann, Ignacio E. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

In this paper, we present a generic mixed-integer linear multistage stochastic programming (MSSP) model considering endogenous uncertainty in some of the parameters. To address the issue that the number of non-anticipativity (NA) constraints increases exponentially with the number of uncertain parameters and/or its realizations, we present a new theoretical property that significantly reduces the problem size and complements two previous properties. Since one might generate reduced models that are still too large to be solved directly, we also propose three solution strategies: a k-stage constraint strategy where we only include the NA constraints up to a specified number of stages, an iterative NAC relaxation strategy, and a Lagrangean decomposition algorithm that decomposes the problem into scenarios. Numerical results for two process network examples are presented to illustrate that the proposed solution strategies yield significant computational savings. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： multistage stochastic programming Endogenous uncertainties Non-anticipativity constraints Decomposition techniques Planning under uncertainty Process networks

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multistage stochastic programming model for optimizing allocation of running time supplements

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JOURNAL OF ADVANCED MECHANICAL DESIGN SYSTEMS AND MANUFACTURING 2016年第3期10卷

作者： Shiina, Takayuki Morito, Susumu Imaizumi, Jun Waseda Univ Sch Creat Sci & Engn Shinjuku Ku 3-4-1 Okubo Tokyo 1698555 Japan Toyo Univ Fac Business Adm Bunkyo Ku 5-28-20 Hakusan Tokyo 1128606 Japan

We consider the allocation of a running time supplement to a railway timetable. Previously, Vekas et al. examined the optimal way to allocate the running time supplement. The uncertain disturbances in a railway were modeled using random variables. In their model, it was assumed that there was an upper limit to the total supplement, but its allocation was not restricted. In this paper, we suggest an improvement to the previous model and present a new stochastic programming model in which there is a constraint on the running time supplement allocated to each trip to minimize the expected delay. Then a solution algorithm to solve the problem is developed. In the previous model, allocation of the running time supplement was biased because it was not allocated to all trips. We balance the amounts of supplements for trips by adding upper and lower bounds. The fluctuations of the supplements for trips become small, and the probability of a delay decreases using our new model. Then the calculation times using the L-shaped algorithm and the former method solving a deterministic equivalent of large-scale problems are compared. It is shown that the large-scale problems can be solved effectively by using the L-shaped method.

关键词： Railway timetable Running time supplement Optimization multistage stochastic programming L-shaped method

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Optimization of the cropping pattern under seasonal fluctuations of surface water using multistage stochastic programming

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WATER SUPPLY 2022年第6期22卷 5716-5728页

作者： Mirzaei, Abbas Azarm, Hassan Naghavi, Somayeh Agr Sci & Nat Resources Univ Khuzestan Dept Agr Econ Mollasani Iran Shiraz Univ Sch Agr Dept Agr Econ Shiraz Iran Univ Jiroft Sch Agr Dept Agr Econ Kerman Iran

Regarding the rapid socio-economic development, increasing food demand and decreasing available resources, this challenge has become a major problem in the agricultural sector, causing the change consumption from surface water to groundwater resources and reduction of farmers' income. Therefore, optimal programming of the cropping pattern is necessary to handle such challenges. To accomplish the mentioned aim, a model of irrigation water allocation was developed based on the cropping pattern using multistage stochastic programming in accordance with the surface water supply fluctuations. In this model, different stochastic states are considered for all irrigation seasons in the irrigation network of Jiroft plain in Kerman province, which faces a severe shortage of surface water resources and the tendency of farmers to overuse groundwater resources. By solving multistage stochastic model, it can be observed that by utilizing an appropriate programming of the cropping pattern, more benefits for the farmers could be realized in the conditions of available surface water fluctuations. The results also indicated that if the surface water released into the canals increased in the spring, the share of profitable with high water consumption crops in pattern will increase, which will strengthen farmers' profits and pressure on groundwater resources. However, it could not expect to receive a significant reduction of groundwater resource consumption and a significant increase of cropping intensity. According to the results obtained, surface water resources cannot meet the water needs of the region, even by using optimal cropping patterns, and this has led to overuse of groundwater resources in this area. Finally, such planning can help adoption of desired policies for irrigation water management through the proper release of these resources.

关键词： groundwater consumption multistage stochastic programming optimal cropping pattern surface water fluctuations

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Value function gradient learning for large-scale multistage stochastic programming problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第1期308卷 321-335页

作者： Lee, Jinkyu Bae, Sanghyeon Kim, Woo Chang Lee, Yongjae Korea Adv Inst Sci & Technol KAIST Dept Ind & Syst Engn Daejeon South Korea Ulsan Natl Inst Sci & Technol UNIST Dept Ind Engn Ulsan South Korea

A stagewise decomposition algorithm called "value function gradient learning" (VFGL) is proposed for large-scale multistage stochastic convex programs. VFGL finds the parameter values that best fit the gra-dient of the value function within a given parametric family. Widely used decomposition algorithms for multistage stochastic programming, such as stochastic dual dynamic programming (SDDP), approximate the value function by adding linear subgradient cuts at each iteration. Although this approach has been successful for linear problems, nonlinear problems may suffer from the increasing size of each subprob-lem as the iteration proceeds. On the other hand, VFGL has a fixed number of parameters;thus, the size of the subproblems remains constant throughout the iteration. Furthermore, VFGL can learn the param-eters by means of stochastic gradient descent, which means that it can be easil0y parallelized and does not require a scenario tree approximation of the underlying uncertainties. VFGL was compared with a deterministic equivalent formulation of the multistage stochastic programming problem and SDDP ap-proaches for three illustrative examples: production planning, hydrothermal generation, and the lifetime financial planning problem. Numerical examples show that VFGL generates high-quality solutions and is computationally efficient.(c) 2022 Elsevier B.V. All rights reserved.

关键词： Decision processes Large-scale optimization multistage stochastic programming Stagewise decomposition Value function approximation

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A multistage stochastic programming model for a multi-period strategic expansion of biofuel supply chain under evolving uncertainties

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TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW 2018年 111卷 130-148页

作者： Xie, Fei Huang, Yongxi Oak Ridge Natl Lab Natl Transportat Res Ctr 2360 Cherahala Blvd Knoxville TN 37932 USA Clemson Univ Glenn Dept Civil Engn Clemson SC 29634 USA

We develop a multistage, stochastic mixed-integer model to support biofuel supply chain expansion under evolving uncertainties. By utilizing the block-separable recourse property, we reformulate the multistage program in an equivalent two-stage program and solve it using an enhanced nested decomposition method with maximal non-dominated cuts. We conduct extensive numerical experiments and demonstrate the application of the model and algorithm in a case study based on the South Carolina settings. The value of multistage stochastic programming method is also explored by comparing the model solution with the counterparts of an expected value based deterministic model and a two-stage stochastic model.

关键词： Biofuel supply chain multistage stochastic programming Uncertainty Enhanced nested decomposition

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Models and computational strategies for multistage stochastic programming under endogenous and exogenous uncertainties

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COMPUTERS & CHEMICAL ENGINEERING 2017年 103卷 233-274页

作者： Apap, Robert M. Grossmann, Ignacio E. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

In this work, we address the modeling and solution of mixed-integer linear multistage stochastic programming problems involving both endogenous and exogenous uncertain parameters. We first propose a composite scenario tree that captures both types of uncertainty, and we exploit its unique structure to derive new theoretical properties that can drastically reduce the number of non-anticipativity constraints (NACs). Since the reduced model is often still intractable, we discuss two special solution approaches. The first is a sequential scenario decomposition heuristic in which we sequentially solve endogenous MILP subproblems to determine the binary investment decisions, fix these decisions to satisfy the first-period and exogenous NACs, and then solve the resulting model to obtain a feasible solution. The second is Lagrangean decomposition. We present numerical results for a process network and an oilfield development planning problem. The results clearly demonstrate the efficiency of the special solution methods over solving the reduced model directly. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： multistage stochastic programming Endogenous uncertainty Exogenous uncertainty Non-anticipativity constraints Lagrangean decomposition Oilfield planning

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