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Sample average approximation with sparsity-inducing penalty for high-dimensional stochastic programming

MATHEMATICAL programming 2019年第1-2期178卷 69-108页

作者： Liu, Hongcheng Wang, Xue Yao, Tao Li, Runze Ye, Yinyu Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA Penn State Univ Harold & Inge Marcus Dept Ind & Mfg Engn University Pk PA 16802 USA Penn State Univ Dept Stat University Pk PA 16802 USA Stanford Univ Dept Management Sci & Engn Stanford CA 94305 USA

The theory on the traditional sample average approximation (SAA) scheme for stochastic programming (SP) dictates that the number of samples should be polynomial in the number of problem dimensions in order to ensure proper optimization accuracy. In this paper, we study a modification to the SAA in the scenario where the global minimizer is either sparse or can be approximated by a sparse solution. By making use of a regularization penalty referred to as the folded concave penalty (FCP), we show that, if an FCP-regularized SAA formulation is solved locally, then the required number of samples can be significantly reduced in approximating the global solution of a convex SP: the sample size is only required to be poly-logarithmic in the number of dimensions. The efficacy of the FCP regularizer for nonconvex SPs is also discussed. As an immediate implication of our result, a flexible class of folded concave penalized sparse M-estimators in high-dimensional statistical learning may yield a sound performance even when the problem dimension cannot be upper-bounded by any polynomial function of the sample size.

关键词： Sample average approximation Folded concave penalty Second order necessary condition stochastic programming

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An enhanced L-Shaped method for optimizing periodic-review inventory control problems modeled via two-stage stochastic programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第2期275卷 677-693页

作者： Placido dos Santos, Felipe Silva Oliveira, Fabricio Pontificia Univ Catolica Rio de Janeiro Dept Engn Ind Rua Marques de Sao Vicente 225 BR-22451900 Rio De Janeiro RJ Brazil Aalto Univ Syst Anal Lab Dept Math & Syst Anal POB 11100 FI-00076 Aalto Finland

This paper presents the development of an enhanced L-Shaped method applied to an inventory management problem that considers a replenishment control system based on the periodic review (R, S) policy. We consider single-item one-echelon problems with uncertain demands and partial backorder that are modeled using two-stage stochastic programming. To enable the consideration of large-scale problems, the classical single-cut L-Shaped method and its extended multi-cut form were initially applied. Preliminary computational results indicated that the classical L-Shaped method outperformed its multi-cut counterpart, even though the former required more iterations to converge to the optimal solution. This observation inspired the development of the techniques presented for enhancing the L-Shape method, which consist of the combination of a novel acceleration technique with an efficient formulation and valid inequalities for the proposed model. Numerical experiments suggest that the proposed approach significantly reduced the computational time required to solve large-scale problems. (C) 2018 Elsevier B.V. All rights reserved.

关键词： stochastic programming Inventory control Uncertain demand Partial backordering L-Shaped method

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General Properties of Two-Stage stochastic programming Problems with Probabilistic Criteria

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AUTOMATION AND REMOTE CONTROL 2019年第6期80卷 1041-1057页

作者： Ivanov, S. V. Kibzun, A. I. Natl Res Univ Moscow Aviat Inst Moscow Russia

Two-stage stochastic programming problems with the probabilistic and quantile criteria in the general statement are considered. Sufficient conditions for the measurability of the loss function and also for the semicontinuity of the criterion functions are given. Sufficient conditions for the existence of optimal strategies are established. The equivalence of the a priori and a posteriori statements of the problems under study is proved. The application of the confidence method, which consists in the transition to a deterministic minimax problem, is described and justified. Sample approximations of the problems are constructed and also conditions under which the optimal strategies in the approximating problems converge to the optimal strategy in the original problem are presented. The results are illustrated by an example of the linear two-step problem. The two-stage problem with the probabilistic criterion is reduced to a mixed-integer problem.

关键词： stochastic programming two-stage problem probabilistic criterion quantile criterion

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GENERIC CONSISTENCY FOR APPROXIMATE stochastic programming AND STATISTICAL PROBLEMS

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SIAM JOURNAL ON OPTIMIZATION 2019年第1期29卷 290-317页

作者： Hess, Christian Seri, Raffaello PSL Res Univ Univ Paris Dauphine Dept MIDO Paris France Univ Insubria Dipartimento Econ Varese Italy

In stochastic programming, statistics, or econometrics, the aim is in general the optimization of a criterion function that depends on a decision variable theta and reads as an expectation with respect to a probability P. When this function cannot be computed in closed form, it is customary to approximate it through an empirical mean function based on a random sample. On the other hand, several other methods have been proposed, such as quasi-Monte Carlo integration and numerical integration rules. In this paper, we propose a general approach for approximating such a function, in the sense of epigraphical convergence, using a sequence of functions of simpler type which can be expressed as expectations with respect to probability measures P-n that, in some sense, approximate P. The main difference with the existing results lies in the fact that our main theorem does not impose conditions directly on the approximating probabilities but only on some integrals with respect to them. In addition, the P-n's can be transition probabilities, i.e., are allowed to depend on a further parameter, xi, whose value results from deterministic or stochastic operations, depending on the underlying model. This framework allows us to deal with a large variety of approximation procedures such as Monte Carlo, quasi-Monte Carlo, numerical integration, quantization, several variations on Monte Carlo sampling, and some density approximation algorithms. As by-products, we discuss convergence results for stochastic programming and statistical inference based on dependent data, for programming with estimated parameters, and for robust optimization;we also provide a general result about the consistency of the bootstrap for M-estimators.

关键词： stochastic programming approximation methods statistical inference epigraphical convergence transition probabilities robust optimization

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A stochastic programming model for the optimal allocation of distributed generation in electrical distribution systems considering load variations and generation uncertainty

A stochastic programming model for the optimal allocation of...

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作者： Kheirkhah, Ali Reza Universidade Estadual Paulista

Atualmente, a penetração de unidades de geração distribuída (DG) em sistemas de energia está aumentando devido aos seus importantes impactos nas principais características dos sistemas de energia. O local, o tipo e o tamanho da DG desempenham um papel importante na redução de perda de energia, melhoria da qualidade de energia, aprimoramento da segurança e redução de custos. Portanto, a localização e o dimensionamento ideais das DGs em sistemas de energia elétrica são um dos problemas mais importantes que devem ser avaliados cuidadosamente. A alocação de DG é um problema de otimização restrito com objetivos diferentes, como minimização de perda de energia, melhoria do perfil de tensão, aprimoramento da confiabilidade, investimento e redução de custos operacionais. Nesta dissertação, o problema de alocação de DG fotovoltaica é resolvido para unidades fotovoltaicas, visando minimizar os custos de energia e investimento, considerando a incerteza de geração e a variação de carga. Devido às altas incertezas dos recursos de energia solar, o problema é avaliado em diferentes cenários de radiação solar sob uma abordagem de programação estocástica. No presente trabalho, a alocação de DG fotovoltaica é formulada como um problema de programação cônica de segunda ordem com número inteiro misto. Os testes foram realizados usando os sistemas de distribuição de 33 e 136 nós e os resultados obtidos demonstram a vantagem da alocação ótima de DG, bem como a eficiência da matemática adotada para encontrar a solução ***, the penetration of distributed generation (DG) units in power systems is increasing because of their important impacts on the main features of power systems. Place, type, and size of DG play an important role in power loss reduction, power quality improvement, security enhancement, and cost reduction. Therefore, optimal placement and sizing of DGs in electric power systems are one of the most important problems that should be evaluated carefully. DG allocatio

关键词： Distributed generation Mathematical modeling Optimal allocation Solar uncertainty stochastic programming Geração distribuída Modelagem matemática Alocação ideal Incerteza solar Programação estocástica Dissertação de mestrado

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Robust optimization vs. stochastic programming incorporating risk measures for unit commitment with uncertain variable renewable generation

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ENERGY SYSTEMS-OPTIMIZATION MODELING SIMULATION AND ECONOMIC ASPECTS 2019年第3期10卷 517-541页

作者： Kazemzadeh, Narges Ryan, Sarah M. Hamzeei, Mahdi Iowa State Univ Dept Ind & Mfg Syst Engn Ames IA 50011 USA Univ Maryland Baltimore MD 21201 USA

Unit commitment seeks the most cost effective generator commitment schedule for an electric power system to meet net load, defined as the difference between the load and the output of renewable generation, while satisfying the operational constraints on transmission system and generation resources. stochastic programming and robust optimization are the most widely studied approaches for unit commitment under net load uncertainty. We incorporate risk considerations in these approaches and investigate their comparative performance for a multi-bus power system in terms of economic efficiency as well as the risk associated with the commitment decisions. We explicitly account for risk, via Conditional Value at Risk (CVaR) in the stochastic programming objective function, and by employing a CVaR-based uncertainty set in the robust optimization formulation. The numerical results indicate that the stochastic program with CVaR evaluated in a low-probability tail is able to achieve better cost-risk trade-offs than the robust formulation with less conservative preferences. The CVaR-based uncertainty set with the most conservative parameter settings outperforms an uncertainty set based only on ranges.

关键词： Unit commitment Renewable energy stochastic programming Robust optimization CVaR

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A strategic and global manufacturing capacity management optimisation model: A Scenario-based multi-stage stochastic programming approach

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2020年第0期93卷 102026-000页

作者： Sabet, Ehsan Yazdani, Baback Kian, Ramez Galanakis, Kostas Loughborough Univ Wolfson Sch Mech Elect & Mfg Engn Loughborough LE11 3TU Leics England Nottingham Trent Univ Nottingham Business Sch Nottingham NG1 4FQ England

Large-scale multinational manufacturing firms often require a significant investment in production capacity and extensive management efforts in strategic planning in an uncertain business environment. In this research we first discuss what decision terms and boundary conditions a holistic capacity management model for the manufacturing industry must contain. To better understand how these decision terms and constraints have been employed by the recent model developers in the area of capacity and resource management modelling for manufacturing, 69 optimisation-based (deterministic and stochastic) models have been carefully selected from 2000 to 2018 for a brief comparative analysis. The results of this comparison shows although applying uncertainty into capacity modelling (in stochastic form) has received a greater deal of attention most recently (since 2010), the existing stochastic models are yet very simplistic, and not all the strategic terms have been employed in the current model developments in the field. This lack of a holistic approach although is evident in deterministic models too, the existing stochastic counterparts proved to include much less decision terms and inclusive constraints, which limits them to a limited applications and may cause sub-optimal solutions. Employing this set of holistic decision terms and boundary conditions, this work develops a scenario-based multi-stage stochastic capacity management model, which is capable of modelling different strategic terms such as capacity level management (slight, medium and large capacity volume adjustment to increase/decrease capacity), location/relocation decisions, merge decomposition options, and product management (R&D, new product launch, productto-plant and product-to-market allocation, and product phase-out management). Possibility matrix, production rates, different financial terms and international taxes, inflation rates, machinery depreciation, investment lead-time and product cycle-time are

关键词： stochastic programming Optimisation modelling Capacity management Manufacturing

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A hybrid robust stochastic programming for a bi-objective blood collection facilities problem (Case study: Iranian blood transfusion network)

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JOURNAL OF INDUSTRIAL AND PRODUCTION ENGINEERING 2019年第3期36卷 154-167页

作者： Attari, Mandi Yousefi Nejad Pasandideh, Seyed Hamid Reza Niaki, Seyed Taghi Akhavan Islamic Azad Univ Dept Ind Engn Bonab Branch Bonab Iran Kharazmi Univ Fac Engn Dept Ind Engn Tehran Iran Sharif Univ Technol Dept Ind Engn Tehran Iran

In this paper, a generalized network optimization model is developed for a complex blood supply chain including a regionalized blood bank system. This system consist of collection sites, testing and processing facilities, storage facilities, distribution centers, as well as points of demand (hospitals). To keep the network in contradiction of the uncertainty, a consolidated approach based on a recently developed stochastic robust approach is extended. An accelerated stochastic Benders decomposition algorithm is proposed to solve the problem modeled in this paper. To speed up the convergence of the solution algorithm, valid inequalities are introduced to get better quality lower bounds. Numerical illustrations are given to verify the mathematical formulation and also to show the benefits of using the stochastic robust approach. At the end, the performance improvements attained by the valid inequalities and the Pareto-optimal cuts are demonstrated in a real-world application.

关键词： Blood supply chain stochastic programming epsilon-constraint robust optimization accelerating benders decomposition

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stochastic programming technique for portfolio optimization with minimax risk and bounded parameters

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SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES 2018年第9期43卷 1-16页

作者： Kumar, P. Panda, G. Gupta, U. C. SRM Inst Sci & Technol Dept Math Madras Tamil Nadu India Indian Inst Technol Dept Math Kharagpur W Bengal India

In this paper a portfolio optimization problem with bounded parameters is proposed taking into consideration the minimax risk measure, in which liquidity of the stocks is allied with selection of the portfolio. Interval uncertainty of the model is dealt with through a fusion between interval and random variable. As a result of this, the interval inequalities are converted to chance constraints. A solution methodology is developed using this concept to obtain an efficient portfolio. The theoretical developments are illustrated on a large data set taken from National Stock Exchange, India.

关键词： stochastic programming minimax risk portfolio optimization interval analysis

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A multi-stage stochastic programming model for sustainable closed-loop supply chain network design with financial decisions: A case study of plastic production and recycling supply chain

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SCIENTIA IRANICA 2020年第1期27卷 377-395页

作者： Mohammadi, A. S. Alemtabriz, A. Pishvaee, M. S. Zandieh, M. Shahid Beheshti Univ Fac Management & Accounting Dept Ind Management Tehran Iran Iran Univ Sci & Technol Sch Ind Engn Tehran Iran

This paper proposes a multi-objective, multi-stage programming model to design a sustainable closed-loop supply chain network considering financial decisions. A multi-product, sustainable closed-loop plastic Supply Chain Network Design (SCND) problem, which encompasses economic, environmental, and social objectives, is modeled in a mathematical manner. The decisions to be made were concerned with the location of facilities, flow of products, loans to take, and investments to make. Uncertainty issue was about the demand of customers and the rate of return on investment. The decision making model was formulated as a multi-objective, multi-stage mixed-integer linear programming problem and solved by implementing path formulation and augmented epsilon-constraint methods. Computational analysis was carried out based on the subject company to determine the significance of the proposed model and the efficiency of integrating financial decisions with SCND decisions. (C) 2020 Sharif University of Technology. All rights reserved.

关键词： Supply chain management Sustainability stochastic programming Supply chain network design Multi-objective optimization

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