scispace - formally typeset
Search or ask a question

Showing papers on "Stochastic programming published in 2010"


Journal ArticleDOI
TL;DR: In this article, the authors proposed a coordinated charging strategy to minimize the power losses and to maximize the main grid load factor of the plug-in hybrid electric vehicles (PHEVs).
Abstract: Alternative vehicles, such as plug-in hybrid electric vehicles, are becoming more popular The batteries of these plug-in hybrid electric vehicles are to be charged at home from a standard outlet or on a corporate car park These extra electrical loads have an impact on the distribution grid which is analyzed in terms of power losses and voltage deviations Without coordination of the charging, the vehicles are charged instantaneously when they are plugged in or after a fixed start delay This uncoordinated power consumption on a local scale can lead to grid problems Therefore, coordinated charging is proposed to minimize the power losses and to maximize the main grid load factor The optimal charging profile of the plug-in hybrid electric vehicles is computed by minimizing the power losses As the exact forecasting of household loads is not possible, stochastic programming is introduced Two main techniques are analyzed: quadratic and dynamic programming

2,601 citations


Journal ArticleDOI
TL;DR: This paper proposes a model that describes uncertainty in both the distribution form (discrete, Gaussian, exponential, etc.) and moments (mean and covariance matrix) and demonstrates that for a wide range of cost functions the associated distributionally robust stochastic program can be solved efficiently.
Abstract: Stochastic programming can effectively describe many decision-making problems in uncertain environments. Unfortunately, such programs are often computationally demanding to solve. In addition, their solution can be misleading when there is ambiguity in the choice of a distribution for the random parameters. In this paper, we propose a model that describes uncertainty in both the distribution form (discrete, Gaussian, exponential, etc.) and moments (mean and covariance matrix). We demonstrate that for a wide range of cost functions the associated distributionally robust (or min-max) stochastic program can be solved efficiently. Furthermore, by deriving a new confidence region for the mean and the covariance matrix of a random vector, we provide probabilistic arguments for using our model in problems that rely heavily on historical data. These arguments are confirmed in a practical example of portfolio selection, where our framework leads to better-performing policies on the “true” distribution underlying the daily returns of financial assets.

1,569 citations


Book
17 Sep 2010
TL;DR: In this paper, the authors consider stochastic programming models for decision-making under uncertainty in the context of electricity markets and provide a brief overview of modeling and solution techniques within a mathematical programming framework.
Abstract: This paper considers stochastic programming models for decision-making under uncertainty in the context of electricity markets. It provides a brief overview of modeling and solution techniques within a mathematical programming framework. Tutorial as well as recent references are provided. This paper provides the guidelines for discussion in a panel session organized by the authors on "Decision Making under Uncertainty in Electricity Markets", scheduled for the IEEE PES 2006 General Meeting.

737 citations


Journal ArticleDOI
TL;DR: A stochastic optimization approach for the storage and distribution problem of medical supplies to be used for disaster management under a wide variety of possible disaster types and magnitudes and can aid interdisciplinary agencies to both prepare and respond to disasters by considering the risk in an efficient manner.

623 citations


Journal ArticleDOI
TL;DR: A technique to derive the best offering strategy for a wind power producer in an electricity market that includes various trading floors is presented, which translates into a linear programming problem of moderate size which is readily solvable using commercially available software.
Abstract: This paper presents a technique to derive the best offering strategy for a wind power producer in an electricity market that includes various trading floors. Uncertainty pertaining to wind availability, market prices at the different trading stages, and balancing energy needs are properly taken into account. Risk on profit variability is suitably controlled at the cost of a small reduction in expected profit. The proposed technique translates into a linear programming problem of moderate size, which is readily solvable using commercially available software. A variety of numerical case studies demonstrate the interest and effectiveness of the proposed technique. Appropriate conclusions are duly drawn.

464 citations


Journal ArticleDOI
TL;DR: The proposed planner computes low-cost paths that follow valleys and saddle points of the configuration-space costmap using the exploratory strength of the Rapidly exploring Random Tree (RRT) algorithm with transition tests used in stochastic optimization methods to accept or to reject new potential states.
Abstract: This paper addresses path planning to consider a cost function defined over the configuration space. The proposed planner computes low-cost paths that follow valleys and saddle points of the configuration-space costmap. It combines the exploratory strength of the Rapidly exploring Random Tree (RRT) algorithm with transition tests used in stochastic optimization methods to accept or to reject new potential states. The planner is analyzed and shown to compute low-cost solutions with respect to a path-quality criterion based on the notion of mechanical work. A large set of experimental results is provided to demonstrate the effectiveness of the method. Current limitations and possible extensions are also discussed.

342 citations


Journal ArticleDOI
TL;DR: A multi-period multi-echelon forward-reverse logistics network design under risk model is developed in a stochastic mixed integer linear programming (SMILP) decision making form as a multi-stage stochastically program to maximize the total expected profit.

328 citations


Journal ArticleDOI
TL;DR: In this paper, the authors proposed a methodology to characterize the stochastic processes pertaining to wind speed at different geographical locations via scenarios, where each one of these scenarios embodies time dependencies and is spatially dependent of the scenarios describing other wind processes.

305 citations


Journal ArticleDOI
TL;DR: The approach builds on a classical worst-case bound for order statistics problems and is applicable even if the constraints are correlated, and provides an application of the model on a network resource allocation problem with uncertain demand.
Abstract: We review and develop different tractable approximations to individual chance-constrained problems in robust optimization on a variety of uncertainty sets and show their interesting connections with bounds on the conditional-value-at-risk (CVaR) measure. We extend the idea to joint chance-constrained problems and provide a new formulation that improves upon the standard approach. Our approach builds on a classical worst-case bound for order statistics problems and is applicable even if the constraints are correlated. We provide an application of the model on a network resource allocation problem with uncertain demand.

296 citations


Journal ArticleDOI
TL;DR: A multi-layer framework that combines stochastic optimization, filtering, and local optimization is introduced and quantitative 3D pose tracking results for the complete HumanEva-II dataset are provided.
Abstract: Local optimization and filtering have been widely applied to model-based 3D human motion capture. Global stochastic optimization has recently been proposed as promising alternative solution for tracking and initialization. In order to benefit from optimization and filtering, we introduce a multi-layer framework that combines stochastic optimization, filtering, and local optimization. While the first layer relies on interacting simulated annealing and some weak prior information on physical constraints, the second layer refines the estimates by filtering and local optimization such that the accuracy is increased and ambiguities are resolved over time without imposing restrictions on the dynamics. In our experimental evaluation, we demonstrate the significant improvements of the multi-layer framework and provide quantitative 3D pose tracking results for the complete HumanEva-II dataset. The paper further comprises a comparison of global stochastic optimization with particle filtering, annealed particle filtering, and local optimization.

276 citations


Journal ArticleDOI
TL;DR: A heuristic based on tabu search, which takes into account the stochastic nature of this problem, is proposed, and some testing instances with different properties are established to investigate the algorithmic performance.

Journal ArticleDOI
TL;DR: A set of percentile criteria that are conceptually natural and representative of the trade-off between optimistic and pessimistic views of the question are presented and the use of these criteria under different forms of uncertainty for both the rewards and the transitions is studied.
Abstract: Markov decision processes are an effective tool in modeling decision making in uncertain dynamic environments. Because the parameters of these models typically are estimated from data or learned from experience, it is not surprising that the actual performance of a chosen strategy often differs significantly from the designer's initial expectations due to unavoidable modeling ambiguity. In this paper, we present a set of percentile criteria that are conceptually natural and representative of the trade-off between optimistic and pessimistic views of the question. We study the use of these criteria under different forms of uncertainty for both the rewards and the transitions. Some forms are shown to be efficiently solvable and others highly intractable. In each case, we outline solution concepts that take parametric uncertainty into account in the process of decision making.

Journal ArticleDOI
TL;DR: This approach relaxes the nonanticipativity constraints that require decisions to depend only on the information available at the time a decision is made and imposes a “penalty” that punishes violations of nonant anticipativity.
Abstract: We describe a general technique for determining upper bounds on maximal values (or lower bounds on minimal costs) in stochastic dynamic programs. In this approach, we relax the nonanticipativity constraints that require decisions to depend only on the information available at the time a decision is made and impose a “penalty” that punishes violations of nonanticipativity. In applications, the hope is that this relaxed version of the problem will be simpler to solve than the original dynamic program. The upper bounds provided by this dual approach complement lower bounds on values that may be found by simulating with heuristic policies. We describe the theory underlying this dual approach and establish weak duality, strong duality, and complementary slackness results that are analogous to the duality results of linear programming. We also study properties of good penalties. Finally, we demonstrate the use of this dual approach in an adaptive inventory control problem with an unknown and changing demand distribution and in valuing options with stochastic volatilities and interest rates. These are complex problems of significant practical interest that are quite difficult to solve to optimality. In these examples, our dual approach requires relatively little additional computation and leads to tight bounds on the optimal values.

Journal ArticleDOI
TL;DR: A pre-disaster planning problem that seeks to strengthen a highway network whose links are subject to random failures due to a disaster is addressed and it is shown that using the first order terms of this function leads to a knapsack problem whose solution is a local optimum to the original problem.

Book ChapterDOI
01 Jan 2010
TL;DR: In this article, a two-stage hybrid search method, called Eagle Strategy, was proposed for stochastic optimization problems, which combines the random search using Levy walk with the firefly algorithm in an iterative manner.
Abstract: Most global optimization problems are nonlinear and thus difficult to solve, and they become even more challenging when uncertainties are present in objective functions and constraints. This paper provides a new two-stage hybrid search method, called Eagle Strategy, for stochastic optimization. This strategy intends to combine the random search using Levy walk with the firefly algorithm in an iterative manner. Numerical studies and results suggest that the proposed Eagle Strategy is very efficient for stochastic optimization. Finally practical implications and potential topics for further research will be discussed.

Journal ArticleDOI
TL;DR: This paper provides an overview of the key contributions within the planning and scheduling communities with specific emphasis on uncertainty analysis, and is the first work which attempts to provide a comprehensive description of two-stage stochastic programming and parametric programming.
Abstract: This paper provides an overview of the key contributions within the planning and scheduling communities with specific emphasis on uncertainty analysis. As opposed to focusing in one particular industry, several independent sectors have been reviewed in order to find commonalities and potential avenues for future interdisciplinary collaborations. The objectives and physical constraints present within the planning and scheduling problems may vary greatly from one sector to another; however, all problems share the common attribute of needing to model parameter uncertainty in an explicit manner. It will be demonstrated through the literature review that two-stage stochastic programming, parametric programming, fuzzy programming, chance constraint programming, robust optimization techniques, conditional value-at-risk, and other risk mitigation procedures have found widespread application within all of the analyzed sectors. This review is the first work which attempts to provide a comprehensive description of t...

Journal ArticleDOI
TL;DR: A novel and tractable approximate dynamic programming method is developed that, coupled with Monte Carlo simulation, computes lower and upper bounds on the value of storage and finds that these heuristics are extremely fast to execute but significantly suboptimal compared to the upper bound.
Abstract: The valuation of the real option to store natural gas is a practically important problem that entails dynamic optimization of inventory trading decisions with capacity constraints in the face of uncertain natural gas price dynamics. Stochastic dynamic programming is a natural approach to this valuation problem, but it does not seem to be widely used in practice because it is at odds with the high-dimensional natural gas price evolution models that are widespread among traders. According to the practice-based literature, practitioners typically value natural gas storage heuristically. The effectiveness of the heuristics discussed in this literature is currently unknown because good upper bounds on the value of storage are not available. We develop a novel and tractable approximate dynamic programming method that, coupled with Monte Carlo simulation, computes lower and upper bounds on the value of storage, which we use to benchmark these heuristics on a set of realistic instances. We find that these heuristics are extremely fast to execute but significantly suboptimal compared to our upper bound, which appears to be fairly tight and much tighter than a simpler perfect information upper bound; computing our lower bound takes more time than using these heuristics, but our lower bound substantially outperforms them in terms of valuation. Moreover, with periodic reoptimizations embedded in Monte Carlo simulation, the practice-based heuristics become nearly optimal, with one exception, at the expense of higher computational effort. Our lower bound with reoptimization is also nearly optimal, but exhibits a higher computational requirement than these heuristics. Besides natural gas storage, our results are potentially relevant for the valuation of the real option to store other commodities, such as metals, oil, and petroleum products.

Book
08 Dec 2010
TL;DR: Optimal Quadratic Programming Algorithms presents recently developed algorithms for solving large QP problems that are, in a sense optimal, i.e., they can solve important classes of problems at a cost proportional to the number of unknowns.
Abstract: Solving optimization problems in complex systems often requires the implementation of advanced mathematical techniques. Quadratic programming (QP) is one technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. QP problems arise in fields as diverse as electrical engineering, agricultural planning, and optics. Given its broad applicability, a comprehensive understanding of quadratic programming is a valuable resource in nearly every scientific field. Optimal Quadratic Programming Algorithms presents recently developed algorithms for solving large QP problems. The presentation focuses on algorithms which are, in a sense optimal, i.e., they can solve important classes of problems at a cost proportional to the number of unknowns. For each algorithm presented, the book details its classical predecessor, describes its drawbacks, introduces modifications that improve its performance, and demonstrates these improvements through numerical experiments. This self-contained monograph can serve as an introductory text on quadratic programming for graduate students and researchers. Additionally, since the solution of many nonlinear problems can be reduced to the solution of a sequence of QP problems, it can also be used as a convenient introduction to nonlinear programming. The reader is required to have a basic knowledge of calculus in several variables and linear algebra.

Book
29 Apr 2010
TL;DR: In this paper, the Riccati equations of stochastic control are defined by positive operators and robust stability and robust stabilization of discrete-time linear systems are investigated for linear quadratic optimization problems.
Abstract: Elements of probability theory.- Discrete-time linear equations defined by positive operators.- Mean square exponential stability.- Structural properties of linear stochastic systems.- Discrete-time Riccati equations of stochastic control.- Linear quadratic optimization problems.- Discrete-time stochastic optimal control.- Robust stability and robust stabilization of discrete-time linear stochastic systems.

Journal ArticleDOI
TL;DR: It is shown that, under certain conditions, the presented model has a set of closed-form solutions, and the effects of random wind speed on the generated power can be readily assessed.
Abstract: In this paper a load dispatch model for the system consisting of both thermal generators and wind turbines is developed. The stochastic wind power is included in the model as a constraint. It is shown that, under certain conditions, the presented model has a set of closed-form solutions. The availability of closed-form solutions is helpful to gain more fundamental insights, such as the impact of a particular parameter on the optimal solution. Moreover, the feasible ranges of optimal solutions are given in the case that the output power of thermal turbines is restricted. Furthermore, the probability distribution and the average of solutions are derived. This is called the wait-and-see approach in the discipline of stochastic programming. The present work shows that the effects of random wind speed on the generated power can be readily assessed.

Journal ArticleDOI
TL;DR: The study indicates a clear niche of evolutionary algorithms in solving such difficult problems of practical importance compared to their usual solution by a computationally expensive nested procedure.
Abstract: Bilevel optimization problems involve two optimization tasks (upper and lower level), in which every feasible upper level solution must correspond to an optimal solution to a lower level optimization problem. These problems commonly appear in many practical problem solving tasks including optimal control, process optimization, game-playing strategy developments, transportation problems, and others. However, they are commonly converted into a single level optimization problem by using an approximate solution procedure to replace the lower level optimization task. Although there exist a number of theoretical, numerical, and evolutionary optimization studies involving single-objective bilevel programming problems, not many studies look at the context of multiple conflicting objectives in each level of a bilevel programming problem. In this paper, we address certain intricate issues related to solving multi-objective bilevel programming problems, present challenging test problems, and propose a viable and hybrid evolutionary-cum-local-search based algorithm as a solution methodology. The hybrid approach performs better than a number of existing methodologies and scales well up to 40-variable difficult test problems used in this study. The population sizing and termination criteria are made self-adaptive, so that no additional parameters need to be supplied by the user. The study indicates a clear niche of evolutionary algorithms in solving such difficult problems of practical importance compared to their usual solution by a computationally expensive nested procedure. The study opens up many issues related to multi-objective bilevel programming and hopefully this study will motivate EMO and other researchers to pay more attention to this important and difficult problem solving activity.

Journal ArticleDOI
TL;DR: This paper considers production planning when inputs have different and uncertain quality levels, and there are capacity constraints, and formulate the problem as a stochastic program that can be solved easily using Cplex.
Abstract: In this paper, we consider production planning when inputs have different and uncertain quality levels, and there are capacity constraints. This situation is typical of most remanufacturing environments, where inputs are product returns (also called cores). Production (remanufacturing) cost increases as the quality level decreases, and any unused cores may be salvaged at a value that increases with their quality level. Decision variables include, for each period and under a certain probabilistic scenario, the amount of cores to grade, the amount to remanufacture for each quality level, and the amount of inventory to carry over for future periods for ungraded cores, graded cores, and finished remanufactured products. Our model is grounded with data collected at a major original equipment manufacturer that also remanufactures. We formulate the problem as a stochastic program; although it is a large linear program, it can be solved easily using Cplex. We provide a numeric study to generate insights into the nature of the solution.

Journal ArticleDOI
TL;DR: In this paper, a reinforcement learning approach, called fitted Q-iteration, is presented: it combines the principle of continuous approximation of the value functions with a process of learning off-line from experience to design daily, cyclostationary operating policies.
Abstract: [1] Although being one of the most popular and extensively studied approaches to design water reservoir operations, Stochastic Dynamic Programming is plagued by a dual curse that makes it unsuitable to cope with large water systems: the computational requirement grows exponentially with the number of state variables considered (curse of dimensionality) and an explicit model must be available to describe every system transition and the associated rewards/costs (curse of modeling). A variety of simplifications and approximations have been devised in the past, which, in many cases, make the resulting operating policies inefficient and of scarce relevance in practical contexts. In this paper, a reinforcement-learning approach, called fitted Q-iteration, is presented: it combines the principle of continuous approximation of the value functions with a process of learning off-line from experience to design daily, cyclostationary operating policies. The continuous approximation, performed via tree-based regression, makes it possible to mitigate the curse of dimensionality by adopting a very coarse discretization grid with respect to the dense grid required to design an equally performing policy via Stochastic Dynamic Programming. The learning experience, in the form of a data set generated combining historical observations and model simulations, allows us to overcome the curse of modeling. Lake Como water system (Italy) is used as study site to infer general guidelines on the appropriate setting for the algorithm parameters and to demonstrate the advantages of the approach in terms of accuracy and computational effectiveness compared to traditional Stochastic Dynamic Programming.

Journal ArticleDOI
TL;DR: In this article, a multi-product, multi-period production planning problem with uncertainty in the quality of raw materials and consequently in processes yields, as well as uncertainty in products demands is studied.
Abstract: Motivated by the challenges encountered in sawmill production planning, we study a multi-product, multi-period production planning problem with uncertainty in the quality of raw materials and consequently in processes yields, as well as uncertainty in products demands. As the demand and yield own different uncertain natures, they are modelled separately and then integrated. Demand uncertainty is considered as a dynamic stochastic data process during the planning horizon, which is modelled as a scenario tree. Each stage in the demand scenario tree corresponds to a cluster of time periods, for which the demand has a stationary behaviour. The uncertain yield is modelled as scenarios with stationary probability distributions during the planning horizon. Yield scenarios are then integrated in each node of the demand scenario tree, constituting a hybrid scenario tree. Based on the hybrid scenario tree for the uncertain yield and demand, a multi-stage stochastic programming (MSP) model is proposed which is full ...

Journal ArticleDOI
TL;DR: This work develops a detailed formal description of project portfolio management as a multistage stochastic integer program with endogenous uncertainty, and proposes an efficient solution approach, which involves the development of a formulation technique that is amenable to scenario decomposition.

Journal ArticleDOI
TL;DR: A solution approach is developed that explicitly optimizes all objectives under demand uncertainty by simultaneously generating a family of optimal solutions known as the Pareto optimal solution set.
Abstract: Transportation network design problem (NDP) is inherently multi-objective in nature, because it involves a number of stakeholders with different needs. In addition, the decision-making process sometimes has to be made under uncertainty where certain inputs are not known exactly. In this paper, we develop three stochastic multi-objective models for designing transportation network under demand uncertainty. These three stochastic multi-objective NDP models are formulated as the expected value multi-objective programming (EVMOP) model, chance constrained multi-objective programming (CCMOP) model, and dependent chance multi-objective programming (DCMOP) model in a bi-level programming framework using different criteria to hedge against demand uncertainty. To solve these stochastic multi-objective NDP models, we develop a solution approach that explicitly optimizes all objectives under demand uncertainty by simultaneously generating a family of optimal solutions known as the Pareto optimal solution set. Numerical examples are also presented to illustrate the concept of the three stochastic multi-objective NDP models as well as the effectiveness of the solution approach.

Journal ArticleDOI
TL;DR: A general framework for carrying out perturbation analysis in Stochastic Hybrid Systems (SHS) of arbitrary structure is presented and Infinitesimal Perturbation Analysis (IPA) is used to provide unbiased gradient estimates of performance metrics with respect to various controllable parameters.

Journal ArticleDOI
TL;DR: In this article, a stochastic programming based approach to account for the design of sustainable logistics network under uncertainty is proposed, where a solution approach integrating the sample average approximation scheme with an importance sampling strategy is developed.

Journal ArticleDOI
TL;DR: The method the advocate first convexifies the problem and then solves a sequence of subproblems, whose solutions form a trajectory that leads to the solution, to illustrate how well the algorithm performs.
Abstract: One of the challenging optimization problems is determining the minimizer of a nonlinear programming problem that has binary variables. A vexing difficulty is the rate the work to solve such problems increases as the number of discrete variables increases. Any such problem with bounded discrete variables, especially binary variables, may be transformed to that of finding a global optimum of a problem in continuous variables. However, the transformed problems usually have astronomically large numbers of local minimizers, making them harder to solve than typical global optimization problems. Despite this apparent disadvantage, we show that the approach is not futile if we use smoothing techniques. The method we advocate first convexifies the problem and then solves a sequence of subproblems, whose solutions form a trajectory that leads to the solution. To illustrate how well the algorithm performs we show the computational results of applying it to problems taken from the literature and new test problems with known optimal solutions.

Journal ArticleDOI
TL;DR: This work examines and compares simulation-based algorithms for solving the agent scheduling problem in a multiskill call center and proposes a solution approach that combines simulation with integer or linear programming, with cut generation.