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Showing papers on "Stochastic programming published in 1991"


Journal ArticleDOI
TL;DR: This paper develops for the first time a rigorous algorithmic procedure for determining a robust decision policy in response to any weighting of the scenarios.
Abstract: A common approach in coping with multiperiod optimization problems under uncertainty where statistical information is not really enough to support a stochastic programming model, has been to set up and analyze a number of scenarios. The aim then is to identify trends and essential features on which a robust decision policy can be based. This paper develops for the first time a rigorous algorithmic procedure for determining such a policy in response to any weighting of the scenarios. The scenarios are bundled at various levels to reflect the availability of information, and iterative adjustments are made to the decision policy to adapt to this structure and remove the dependence on hindsight.

1,321 citations


Journal ArticleDOI
TL;DR: This paper presents a methodology for the solution of multistage stochastic optimization problems, based on the approximation of the expected-cost-to-go functions of Stochastic dynamic programming by piecewise linear functions.
Abstract: This paper presents a methodology for the solution of multistage stochastic optimization problems, based on the approximation of the expected-cost-to-go functions of stochastic dynamic programming by piecewise linear functions. No state discretization is necessary, and the combinatorial "explosion" with the number of states (the well known "curse of dimensionality" of dynamic programming) is avoided. The piecewise functions are obtained from the dual solutions of the optimization problem at each stage and correspond to Benders cuts in a stochastic, multistage decomposition framework. A case study of optimal stochastic scheduling for a 39-reservoir system is presented and discussed.

1,230 citations


Book
01 Aug 1991
TL;DR: This book is useful to researchers in artificial intelligence and control theory, and others concerned with the design of complex applications in robotics, automated manufacturing, and time-critical decision support.
Abstract: "Planning and Control" explores planning and control by reformulating the two areas in a common control framework, developing the corresponding techniques side-by-side, and identifying opportunities for integrating their ideas and methods. This book is organized around the central roles of prediction, observation, and computation control. The first three chapters deal with predictive models of physical systems based on temporal logic and the differential calculus. Chapter 4 and 5 present some basic concepts in planning and control, including controllability, observability, stability, feedback control, task reduction, conditional plans, and the relationship between goals and preferences. Chapters 6 and 7 consider issues of uncertainty, covering state estimation and the Kalman filter, stochastic dynamic programming, probabilistic modeling, and graph-based decision models. The remaining chapters investigate selected topics in time-critical decision making, adaptive control, and hybrid control architectures. Throughout, the reader is led to consider critical tradeoffs involving the accuracy of prediction, the availability of information from observation, and the costs and benefits of computation in dynamic environments. This book is useful to researchers in artificial intelligence and control theory, and others concerned with the design of complex applications in robotics, automated manufacturing, and time-critical decision support.

613 citations


Journal ArticleDOI
TL;DR: A cutting plane algorithm for two-stage stochastic linear programs with recourse that uses randomly generated observations of random variables to construct statistical estimates of supports of the objective function and establishes the convergence of the algorithm under relatively mild assumptions.
Abstract: We present a cutting plane algorithm for two-stage stochastic linear programs with recourse. Motivated by Benders' decomposition, our method uses randomly generated observations of random variables to construct statistical estimates of supports of the objective function. In general, the resulting piecewise linear approximations do not agree with the objective function in finite time. However, certain subsequences of the estimated supports are shown to accumulate at supports of the objective function, with probability one. From this, we establish the convergence of the algorithm under relatively mild assumptions.

457 citations


Journal ArticleDOI
TL;DR: The approach is based on an extended delta method and appears to be particularly suitable for deriving asymptotics of the optimal value of stochastic programs.
Abstract: In this paper we discuss a general approach to studying asymptotic properties of statistical estimators in stochastic programming. The approach is based on an extended delta method and appears to be particularly suitable for deriving asymptotics of the optimal value of stochastic programs. Asymptotic analysis of the optimal value will be presented in detail. Asymptotic properties of the corresponding optimal solutions are briefly discussed.

260 citations


Proceedings ArticleDOI
04 Nov 1991
TL;DR: The authors address incorporating a meta-level evolutionary programming that can simultaneously evolve optimal settings for these parameters while a search for the appropriate extrema is being conducted, and indicate the suitability of such a procedure.
Abstract: A brief review of efforts is simulated evolution is given. Evolutionary programming is a stochastic optimization technique that is useful for discovering the extrema of a nonlinear function. To implement such a search, several high-level parameters must be chosen, such as the amount of mutational noise, the severity of the mutation noise, and so forth. The authors address incorporating a meta-level evolutionary programming that can simultaneously evolve optimal settings for these parameters while a search for the appropriate extrema is being conducted. The preliminary experiments reported indicate the suitability of such a procedure. Meta-evolutionary programming was able to converge to points on each of two response surfaces that were close to the global optimum. >

175 citations


Journal ArticleDOI
TL;DR: This paper presents consistency results for sequences of optimal solutions to convex stochastic optimization problems constructed from empirical data, by applying the strong law of large numbers to these problems.
Abstract: This paper presents consistency results for sequences of optimal solutions to convex stochastic optimization problems constructed from empirical data, by applying the strong law of large numbers fo...

149 citations


Journal ArticleDOI
TL;DR: This paper examines the progressive hedging algorithm for solving multi-scenario generalized networks and presents computational results demonstrating the effect of various internal tactics on the algorithm's performance.
Abstract: The introduction of uncertainty to mathematical programs greatly increases the size of the resulting optimization problems. Specialized methods that exploit program structures and advances in computer technology promise to overcome the computational complexity of certain classes of stochastic programs. In this paper we examine the progressive hedging algorithm for solving multi-scenario generalized networks. We present computational results demonstrating the effect of various internal tactics on the algorithm's performance. Comparisons with alternative solution methods are provided.

134 citations


Journal ArticleDOI
TL;DR: In this paper, a method based on stochastic dynamic programming is proposed to handle uncertainties in important variables such as energy demand and prices of energy carriers together with the dynamics of the system.
Abstract: Most generation expansion planning tools do not model uncertainties in important variables such as energy demand and prices of energy carriers together with the dynamics of the system. A method for handling these uncertainties in generation expansion problems is described. The method is based on stochastic dynamic programming. As the uncertain variables are modeled by Markov chains they give a natural year-to-year dependence of the variables. This modeling makes it possible to describe the connection between investment decisions, time, construction periods, and uncertainty. The importance of modeling these connections is demonstrated by a realistic example. >

118 citations


Journal ArticleDOI
TL;DR: An approach for modeling two-stage stochastic programs that yields a form suitable for interior point algorithms by replacing first stage variables with sparse "split variables" in conjunction with side-constraints is described.
Abstract: This paper describes an approach for modeling two-stage stochastic programs that yields a form suitable for interior point algorithms. A staircase constraint structure is created by replacing first stage variables with sparse "split variables" in conjunction with side-constraints. Dense columns are thereby eliminated. The resulting model is larger than traditional stochastic programs, but computational savings are substantial-over a tenfold improvement for the problems tested. A series of experiments with stochastic networks drawn from financial planning demonstrates the attained efficiencies. Comparisons with MINOS and the dual block angular stochastic programming model are provided as benchmarks. The split variable approach is applicable to general two-stage stochastic programs and other dual block angular models.

113 citations


Journal ArticleDOI
TL;DR: Stability and sensitivity studies for stochastic programs have been motivated by the problem of incomplete information about the true probability measure through which the Stochastic program is formulated and in connection with the development and evaluation of algorithms as mentioned in this paper.
Abstract: Stability and sensitivity studies for stochastic programs have been motivated by the problem of incomplete information about the true probability measure through which the stochastic program is formulated and in connection with the development and evaluation of algorithms. The first part of this survey paper briefly introduces and compares different approaches and points out the contemporary efforts to remove and weaken assumptions that are not realistic (e.g., strict complementarity conditions). The second part surveys recent results on qualitative and quantitative stability with respect to the underlying probability measure and describes the ways and means of statistical sensitivity analysis based on Gâteaux derivatives. The last section comments on parallel statistical sensitivity results obtained in the parametric case, i.e., for probability measures belonging to a parametric family indexed by a finite dimensional vector parameter.

Journal ArticleDOI
TL;DR: The possibility of using alternative models for stochastic programming is studied on a small-size but meaningful example connected with water management of a real-life water resource system in Eastern Czechoslovakia.

Posted ContentDOI
TL;DR: The paper concludes with a discussion of the importance of correctly understanding the way risk impacts upon the target farming system, and then of formulating a programming model appropriate to the case.
Abstract: The complexity of modelling risk in farming systems is explained and the artistic nature of the task noted. A brief outline is presented of an appropriate conceptual framework, drawing attention to the merits of stochastic efficiency criteria for analysis of systems when risk preferences of individual farmers are unavailable. A distinction is drawn between planning problems with and without embedded risk. The merits of 'utility efficient' (UE) programming are explained. Extensions of programming models, including UE formulations, to embedded risk using discrete stochastic programming are reviewed. The paper concludes with a discussion of the importance of correctly understanding the way risk impacts upon the target farming system, and then of formulating a programming model appropriate to the case.

Journal ArticleDOI
TL;DR: In this paper, stochastic programming problems are viewed as parametric programs with respect to the probability distributions of the random coefficients and quantitative continuity results for optimal values and optimal solution sets are proved.
Abstract: In this paper, stochastic programming problems are viewed as parametric programs with respect to the probability distributions of the random coefficients. General results on quantitative stability in parametric optimization are used to study distribution sensitivity of stochastic programs. For recourse and chance constrained models quantitative continuity results for optimal values and optimal solution sets are proved (with respect to suitable metrics on the space of probability distributions). The results are useful to study the effect of approximations and of incomplete information in stochastic programming.

Journal ArticleDOI
TL;DR: This paper describes how the scenario aggregation principle can be combined with approximate solutions of the individual scenario problems, resulting in a computationally efficient algorithm where two individual Lagrangian-based procedures are merged into one.
Abstract: This paper describes how the scenario aggregation principle can be combined with approximate solutions of the individual scenario problems, resulting in a computationally efficient algorithm where two individual Lagrangian-based procedures are merged into one. Computational results are given for an example from fisheries management. Numerical experiments indicate that only crude scenario solutions are needed.

Journal ArticleDOI
01 Oct 1991-Networks
TL;DR: The scenario aggregation algorithm is specialized for stochastic networks and determines a solution that does not depend on hindsight and accounts for the uncertain environment depicted by a number of appropriately weighted scenarios, thus preserving the network structure.
Abstract: The scenario aggregation algorithm is specialized for stochastic networks. The algorithm determines a solution that does not depend on hindsight and accounts for the uncertain environment depicted by a number of appropriately weighted scenarios. The solution procedure decomposes the stochastic program to its constituent scenario subproblems, thus preserving the network structure. Computational results are reported demonstrating the algorithm's convergence behavior. Acceleration schemes are discussed along with termination criteria. The algorithm's potential for execution on parallel multiprocessors is discussed.

Journal ArticleDOI
TL;DR: Methods for verification of optimality conditions within the framework of Stochastic Decomposition (SD) algorithms for two stage linear programs with recourse are developed and the use of “bootstrap methods” to confirm the satisfaction of generalized Kuhn-Tucker conditions and conditions based on Lagrange duality is proposed.
Abstract: Statistically motivated algorithms for the solution of stochastic programming problems typically suffer from their inability to recognize optimality of a given solution algorithmically. Thus, the quality of solutions provided by such methods is difficult to ascertain. In this paper, we develop methods for verification of optimality conditions within the framework of Stochastic Decomposition (SD) algorithms for two stage linear programs with recourse. Consistent with the stochastic nature of an SD algorithm, we provide termination criteria that are based on statistical verification of traditional (deterministic) optimality conditions. We propose the use of “bootstrap methods” to confirm the satisfaction of generalized Kuhn-Tucker conditions and conditions based on Lagrange duality. These methods are illustrated in the context of a power generation planning model, and the results are encouraging.

Journal ArticleDOI
TL;DR: In this paper, a three-step modeling approach is presented for comprehensive analysis of the planning problem involving integrated use of surface and ground water in irrigation in the Bagmati River Basin in Nepal.
Abstract: A three‐step modeling approach is presented for comprehensive analysis of the planning problem involving integrated use of surface and ground water in irrigation. Applicability of the approach is illustrated by a case study of the Bagmati River Basin in Nepal. In the first step, a stochastic dynamic programming model, which considers most of the interacting processes of the conjunctive‐use system, is used to derive the long‐term operation policy guidelines for alternative plans. Then, a lumped simulation model is used to evaluate the alternative plans and policies, considering a number of mutually related synthetic sequences of streamflow and rainfall. Various economic (cost and benefit) as well as risk‐related (reliability, vulnerability, and resiliency) performance measures and their tradeoffs are evaluated. Finally, a multiple‐criteria decision‐making method (compromise programming) is used to select the most satisfactory alternative plan for indicating the system design (pumping and diversion canal) c...

Journal ArticleDOI
TL;DR: In this paper, a computational approach is taken to solve the optimal partially observed nonlinear stochastic control problem, where the amount of computation depends on the uncertainty in the problem and the length of the horizon, and the cost degrades monotonically as the complexity of the algorithm is reduced.
Abstract: A computational approach is taken to solve the optimal partially observed nonlinear stochastic control problem. The approach is to systematically solve the stochastic dynamic programming equations forward in time, using a nested stochastic approximation technique. Although computationally intensive, this provides a straightforward numerical solution for this class of problems and provides an alternative to the usual 'curse of dimensionality' associated with solving the dynamic programming equation backwards in time. In particular, the 'curse' is seen to take a new form, where the amount of computation depends on the amount of uncertainty in the problem and the length of the horizon. As a matter of more practical interest, it is shown that the cost degrades monotonically as the complexity of the algorithm is reduced. This provides a strategy for suboptimal control with clear performance/computation trade-offs. A numerical study focusing on a generic optimal stochastic adaptive control example is included to demonstrate the feasibility of the method. >

Journal ArticleDOI
TL;DR: In this paper, a tutorial survey of finite dimensional optimization problems which depend on parameters is presented, focusing on unfolding and singularity theory, structural analysis of families of constraint sets, constrained optimization problems and semi-infinite optimization.
Abstract: In this tutorial survey we study finite dimensional optimization problems which depend on parameters. It is our aim to work out several basic connections with different mathematical areas. In particular, attention will be paid to unfolding and singularity theory, structural analysis of families of constraint sets, constrained optimization problems and semi-infinite optimization.

Journal ArticleDOI
TL;DR: In this paper, a stochastic dynamic programming model for the optimization of hydropower prroduction of a multiple storage reservoir system with correlated inflows was developed, and application was made to a sub-substation.
Abstract: A stochastic dynamic programming model for the optimization of hydropower prroduction of a multiple storagereservoir system with correlated inflows has been developed. Application was made to a sub...

Journal ArticleDOI
TL;DR: The reformulation of the standard dynamic programming algorithm in a form able to exploit new machine architectures enable faster and less costly solution of optimization problems involving a system model having two state variables and a number of states such as to guarantee a high numerical accuracy.
Abstract: The solution via dynamic programming (DP) of a reservoir optimal control problem is often computationally prohibitive when the proper description of the inflow process leads to a system model having several state variables and/or when a sufficiently dense state discretization is required to achieve numerical accuracy. Thus, to simplify, the inflow correlation is usually neglected and/or a coarse state discretization is adopted. However, these simplifications may significantly affect the reliability of the solution of the optimization problem. Nowadays, the availability of very powerful computers based on innovative architectures (vector and parallel machines), even in the domain of personal computers (transputer architectures), stimulates the reformulation of the standard dynamic programming algorithm in a form able to exploit these new machine architectures. The reformulated DP algorithm and new machines enable faster and less costly solution of optimization problems involving a system model having two state variables (storage and previous period inflow, then taking into account the inflow correlation) and a number of states (of the order of 104) such as to guarantee a high numerical accuracy.

Journal ArticleDOI
TL;DR: In this paper, a stochastic multi-period decision model was developed to analyse a continuous wheat cropping system infested by wild oats ( Avena fatua L.), in southern Australia.

Journal ArticleDOI
TL;DR: In this article, the authors compared four types of stochastic dynamic programming (SDP) for on-line reservoir operation, relying on observed or forecasted inflows, and found that the SDP model that relies on the observed inflows of the preceeding time step provides the best performance.
Abstract: This paper presents and compares four types of stochastic dynamic programming (SDP) for on‐line reservoir operation, relying on observed or forecasted inflows. The models are different because of the assumptions regarding the inflow in the next time period. If this inflow is known (or a forecast is possible with 100% reliability) models with expected value of the future returns are possible (present returns are deterministic). Otherwise, a simple forecast based on conditional probabilities is necessary, and present and future returns are random. The objective is to maximize expected annual hydropower generation. In a case study of the Feitsui Reservoir in Taiwan, SDP models appear to provide efficient long‐term operating policies. The simulation of on‐line operation of the reservoir reveals that the SDP model that relies on the observed inflows of the preceeding time step provides the best performance. Nevertheless, under different hydrological regimes this finding might be not universal, but dependent up...

Journal ArticleDOI
TL;DR: In this article, a hybrid model for failure detection using chance constrained programming and stochastic linear programming features is proposed, and a purely chance constrained model is then described for nonconvex programming problems.

Journal ArticleDOI
TL;DR: A stochastic dynamic programming model is designed on the personal computer to determine the economic optimal replacement policy in swine breeding herds, which maximizes the present value of expected annual net returns over a specified planning horizon, from sows present in the herd and subsequent replacement gilts.

Journal ArticleDOI
01 May 1991-Oikos
TL;DR: A stochastic dynamic programming model of the situation envisioned by the marginal value theorem is developed, however the forager's objective function is to avoid death, not to maximize its long term rate of energy gain.
Abstract: I have developed a stochastic dynamic programming model of the situation envisioned by the marginal value theorem, however I have treated prey encounter as a stochastic event, included a consideration of predation hazard and incorporated the use of a refuge. Unlike the marginal value theorem, in my model the forager's objective function is to avoid death, not to maximize its long term rate of energy gain. The model is solved numerically and the resulting optimal policy (strategy for utilizing patches) is then used in computer simulations to generate distributions of predicted patch-residence times. I solve the model to predict differences caused by changes in the parameter values

Journal ArticleDOI
TL;DR: In this paper, a model for optimal multi-period operation of a multi-reservoir system with uncertain inflows and water demands is formulated and solved by the Finite Generation Algorithm.
Abstract: A model for optimal multi-period operation of a multi-reservoir system with uncertain inflows and water demands is formulated and solved by the Finite Generation Algorithm. Uncertainties are considered in chance constraints and in penalties due to deviations from meeting demand and reservoir level targets. The penalty functions are linear-quadratic, can be imposed on deviations in one or both directions from the target, and are easily fitted to data by selection of parameters. The stochastic variables are assigned discrete probability distributions. The primal (optimal operation) problem is solved by formulating the dual and then finding its optimum (which is proven to be global for the conditions specified) via a sequence of linear-quadratic deterministic optimization problems of controlled size. The method is demonstrated for a three-reservoir two-period problem. Sensitivity analysis with respect to parameter values is presented. Stochastic simulation is used, to augment the information given by the opt...

Journal ArticleDOI
TL;DR: This paper describes a specific adaptive model of behavior in discrete choice problems, one that is closely related to adaptive algorithms for optimization, and shows that this model can be fruitfully applied in studying several economic issues.
Abstract: Economists have found a need to model agents who behave in ways that are not consistent with the traditional notions of rational behavior under uncertainty but that are oriented in some looser manner toward achieving “good” outcomes Adaptation over time in a myopic manner, rather that forward-looking optimization, has been proposed as one such model of behavior that displays bounded rationality This paper investigates the relationship between adaptation as a model of behavior and as an algorithmic approach that has been used in computing solutions to optimization problems It describes a specific adaptive model of behavior in discrete choice problems, one that is closely related to adaptive algorithms for optimization, and shows that this model can be fruitfully applied in studying several economic issues

Journal ArticleDOI
TL;DR: In this paper, a stochastic dynamic programming model was used for determining optimal economic strategies for density management in loblolly pine (Pinustaeda L.) stands in the southern United States.
Abstract: A method is described for determining optimal economic strategies for density management in loblolly pine (Pinustaeda L.) stands in the southern United States. A stochastic dynamic programming model employs a price state transition matrix constructed using a first-order conditional cumulative density function for price based on time-series data for national forest pine stumpage in the South. The model also incorporates WTHIN, a pine growth and yield simulator widely used in the South to support analyses of alternative stand management strategies. Results indicate that at current average prices for pulpwood, on average sites, optimal planting density decisions recommended by the stochastic model are very similar to those obtained with a deterministic price equivalent. However, there are many instances where the thinning decisions recommended by the two models are different, especially when they are used to evaluate better sites or when the price of pulpwood is substantially increased above current region-w...