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Showing papers on "Stochastic programming published in 1990"


Journal ArticleDOI
TL;DR: The optimization problem is set up as a discrete multistage decision process and is solved by a time-delayed discrete dynamic programming algorithm, and a parallel procedure for decreasing computational costs is discussed.
Abstract: Dynamic programming is discussed as an approach to solving variational problems in vision. Dynamic programming ensures global optimality of the solution, is numerically stable, and allows for hard constraints to be enforced on the behavior of the solution within a natural and straightforward structure. As a specific example of the approach's efficacy, applying dynamic programming to the energy-minimizing active contours is described. The optimization problem is set up as a discrete multistage decision process and is solved by a time-delayed discrete dynamic programming algorithm. A parallel procedure for decreasing computational costs is discussed. >

1,014 citations


BookDOI
01 Nov 1990
TL;DR: This book discusses fuzzy logic with linguistic quantifiers in multiobjective decision making and optimization, a step towards more human-consistent models, and Stochastic Versus Fuzzy Approaches and Related Issues.
Abstract: I. The General Framework.- 1. Multiobjective programming under uncertainty : scope and goals of the book.- 2. Multiobjective programming : basic concepts and approaches.- 3. Stochastic programming : numerical solution techniques by semi-stochastic approximation methods.- 4. Fuzzy programming : a survey of recent developments.- II. The Stochastic Approach.- 1. Overview of different approaches for solving stochastic programming problems with multiple objective functions.- 2. "STRANGE" : an interactive method for multiobjective stochastic linear programming, and "STRANGE-MOMIX" : its extension to integer variables.- 3. Application of STRANGE to energy studies.- 4. Multiobjective stochastic linear programming with incomplete information : a general methodology.- 5. Computation of efficient solutions of stochastic optimization problems with applications to regression and scenario analysis.- III. The Fuzzy Approach.- 1. Interactive decision-making for multiobjective programming problems with fuzzy parameters.- 2. A possibilistic approach for multiobjective programming problems. Efficiency of solutions.- 3. "FLIP" : an interactive method for multiobjective linear programming with fuzzy coefficients.- 4. Application of "FLIP" method to farm structure optimization under uncertainty.- 5. "FULPAL" : an interactive method for solving (multiobjective) fuzzy linear programming problems.- 6. Multiple objective linear programming problems in the presence of fuzzy coefficients.- 7. Inequality constraints between fuzzy numbers and their use in mathematical programming.- 8. Using fuzzy logic with linguistic quantifiers in multiobjective decision making and optimization: A step towards more human-consistent models.- IV. Stochastic Versus Fuzzy Approaches and Related Issues.- 1. Stochastic versus possibilistic multiobjective programming.- 2. A comparison study of "STRANGE" and "FLIP".- 3. Multiobjective mathematical programming with inexact data.

291 citations


Journal ArticleDOI
TL;DR: In this article, sampling stochastic dynamic programming (SSDP) is used to capture the complex temporal and spatial structure of the streamflow process by using a large number of sample streamflow sequences.
Abstract: Most models for reservoir operation optimization have employed either deterministic optimization or stochastic dynamic programming algorithms. This paper develops sampling stochastic dynamic programming (SSDP), a technique that captures the complex temporal and spatial structure of the streamflow process by using a large number of sample streamflow sequences. The best inflow forecast can be included as a hydrologic state variable to improve the reservoir operating policy. A case study using the hydroelectric system on the North Fork of the Feather River in California illustrates the SSDP approach and its performance.

257 citations


Journal ArticleDOI
TL;DR: This paper describes an efficient implementation of a nested decomposition algorithm for the multistage stochastic linear programming problem and results compare the performance of the algorithm to MINOS 5.0.
Abstract: This paper describes an efficient implementation of a nested decomposition algorithm for the multistage stochastic linear programming problem. Many of the computational tricks developed for deterministic staircase problems are adapted to the stochastic setting and their effect on computation times is investigated. The computer code supports an arbitrary number of time periods and various types of random structures for the input data. Numerical results compare the performance of the algorithm to MINOS 5.0.

232 citations


Journal ArticleDOI
TL;DR: The paper presents computational results that were obtained by employing a Rolling Horizon Procedure to simulate the operation of the truckload carrier and indicates the superiority of the new algorithm over other approaches tested.
Abstract: The Stochastic Dynamic Vehicle Allocation problem involves managing a fleet of vehicles over time in an uncertain demand environment to maximize expected total profits. The problem is formulated as a Stochastic Programming problem. A new heuristic algorithm is developed and is contrasted to various deterministic approximations. The paper presents computational results that were obtained by employing a Rolling Horizon Procedure to simulate the operation of the truckload carrier. Results indicate the superiority of the new algorithm over other approaches tested.

151 citations


Journal ArticleDOI
TL;DR: In this paper, theoretical results are presented for several classes of mathematical programming problems that include: the general quadratic programming problem, and unconstrained and constrained optimization problems with polynomial terms in the objective function and/or constraints.

132 citations


Journal ArticleDOI
01 Nov 1990
TL;DR: This paper presents a method for the solution of a one stage stochastic programming problem, where the underlying problem is an LP and some of the right hand side values are random variables, by a dual type algorithm.
Abstract: In this paper we present a method for the solution of a one stage stochastic programming problem, where the underlying problem is an LP and some of the right hand side values are random variables. The stochastic programming problem that we formulate contains probabilistic constraint and penalty, incorporated into the objective function, used to penalize violation of the stochastic constraints. We solve this problem by a dual type algorithm. The special case where only penalty is used while the probabilistic constraint is disregarded, the simple recourse problem, was solved earlier by Wets, using a primal simplex algorithm with individual upper bounds. Our method appears to be simpler. The method has applications to nonstochastic programming problems too, e.g., it solves the constrained minimum absolute deviation problem.

126 citations


Journal ArticleDOI
TL;DR: Two fundamental classes of problems in large-scale linear and quadratic programming are described and strong properties of duality are revealed which support the development of iterative approximate techniques of solution in terms of saddlepoints.
Abstract: Two fundamental classes of problems in large-scale linear and quadratic programming are described. Multistage problems covering a wide variety of models in dynamic programming and stochastic programming are represented in a new way. Strong properties of duality are revealed which support the development of iterative approximate techniques of solution in terms of saddlepoints. Optimality conditions are derived in a form that emphasizes the possibilities of decomposition.

100 citations


Journal ArticleDOI
TL;DR: The application of mathematical programming techniques to optimization in simulation, response surface methodology and designs, perturbation analysis, and frequency domain simulation experiments are discussed.
Abstract: Simulation is commonly used to find the best values of decision variables for problems which defy analytical solutions. This objective is similar to that of optimization problems and thus, mathematical programming techniques may be applied to simulation. However, the application of mathematical programming techniques, e.g., the gradient methods, to simulation is compounded by the random nature of simulation responses and by the complexity of the statistical issues involved. The literature relevant to optimization in simulation is scattered, and no comprehensive and up-to-date treatment of the subject is presently available. To that end, this article brings together numerous concepts related to t he problem of optimization in simulation. Specifically, it discusses the application of mathematical programming techniques to optimization in simulation, response surface methodology and designs, perturbation analysis, and frequency domain simulation experiments. The article provides a user with an overview of the available optimization techniues and identifies future research possibilities.

91 citations


Book ChapterDOI
01 Jan 1990
TL;DR: A new interdisciplinary science is about to be born-stochastic programming with several objective functions, which aims to treat uncertainty within decision oriented models in a coherent and systematic way.
Abstract: Stochastic programming is one of the most exciting and challenging developments of mathematical programming. It aims to treat uncertainty within decision oriented models in a coherent and systematic way. Lack of such an approach is one of the objections raised to deterministic mathematical programming modelling. The requirement for a single objective or payoff functions is another objection; it can be argued that most decision makers usually have several decision criteria, and multi-objective programming aims to reflect this. Also simple examples show (similar to the Endorsed paradox and Arrow impossibility theorems) that there are, in general, no good ways of aggregating several criteria into one objective function. But maybe sometimes there are. Worse, even when there is a natural objective function, but stochastic elements come into play maximizing the expectation will often involve unacceptable large variances. In this way, a new interdisciplinary science is about to be born-stochastic programming with several objective functions.

87 citations


Journal ArticleDOI
TL;DR: A unified survey of mathematical programming models and their experimental results where applicable, to put the degree of usefulness of these models in doubt.
Abstract: The mathematical programming approach to linear disciminant analysis was first introduced in the early 1980's. Since then, numerous mathematical programming models have appeared in the literature. Some of these models were merely formulated while others were subjected to experimentation, in some cases rather extensively. The purpose of this paper is to present a unified survey of these models and their experimental results where applicable. Some mathematical programming (MP) models, unfortunately, have certain pathologies inherent in their structure which puts the degree of usefulness of these models in doubt. When known, such pathologies are also identified for the specific model in question.

Journal ArticleDOI
TL;DR: In this paper, the concept of stochastic equilibrium programming (SEP) has been used for the modeling of imperfect competition on uncertain dynamic markets and it has been shown that the equilibria computed via SEP correspond to an information structure, called S-adapted open-loop, which is not common in the dynamic game literature.
Abstract: This paper deals with the concept of stochastic equilibrium programming (SEP), which has recently been proposed for the modeling of imperfect competition on uncertain dynamic markets. We show that the equilibria computed via SEP correspond to an information structure, called S-adapted open-loop, which is not common in the dynamic game literature. We compare the single-player case with the many-player case using a simple two-stage dynamical system. An illustration of the use of the approach for the modeling of imperfect dynamic markets is also provided.

Journal ArticleDOI
TL;DR: This paper shows how an optimization problem involving the expected performance of a stochastic system can be estimated using a single simulation experiment using a probability measure transformation and generation of a Stochastic counterpart to the deterministic optimization program.

Journal ArticleDOI
TL;DR: In this article, a combination of finite element simulation of groundwater contaminant transport with nonlinear optimization is one approach to determine the best well selection and optimal fluid withdrawal and injection rates to contain and remove the contaminated water.
Abstract: Once subsurface water supplies become contaminated, designing cost-effective and reliable remediation schemes becomes a difficult task. The combination of finite element simulation of groundwater contaminant transport with nonlinear optimization is one approach to determine the best well selection and optimal fluid withdrawal and injection rates to contain and remove the contaminated water. Both deterministic and stochastic programming problems have been formulated and solved. These tend to be large scale problems, owing to the simulation component which serves as a portion of the constraint set. The overall problem of combined groundwater process simulation and nonlinear optimization is discussed along with example problems. Because the contaminant transport simulation models give highly uncertain results, quantifying their uncertainty and incorporating reliability into the remediation design results in a class of large stochastic nonlinear problems. The reliability problem is beginning to be addressed, and some strategies and formulations involving chance constraints and Monte Carlo methods are presented.

Journal ArticleDOI
TL;DR: A new class of algorithms, called finite-envelope methods, is described that reduce the solution of a high-dimensional extended linear-quadratic program to that of a sequence of low-dimensional ordinary quadratic programs.
Abstract: Numerical approaches are developed for solving large-scale problems of extended linear-quadratic programming that exhibit Lagrangian separability in both primal and dual variables simultaneously. Such problems are kin to large-scale linear complementarity models as derived from applications of variational inequalities, and they arise from general models in multistage stochastic programming and discrete-time optimal control. Because their objective functions are merely piecewise linear-quadratic, due to the presence of penalty terms, they do not fit a conventional quadratic programming framework. They have potentially advantageous features, however, which so far have not been exploited in solution procedures. These features are laid out and analyzed for their computational potential. In particular, a new class of algorithms, called finite-envelope methods, is described that does take advantage of the structure. Such methods reduce the solution of a high-dimensional extended linear-quadratic program to that of a sequence of low-dimensional ordinary quadratic programs.

Journal ArticleDOI
TL;DR: This work first construct the distribution of the optimal valve of the objective function to show a major difference between stochastic and possibilistic programming, and introduces a new solution concept where both programming problems are modeled as multiobjective games against Nature.

Journal ArticleDOI
TL;DR: This paper considers an extension to the situation of stochastic programming of the Auxiliary Problem Principle formerly introduced in a deterministic setting to serve as a general framework for decomposition/coordination optimization algorithms.
Abstract: This paper considers an extension to the situation of stochastic programming of the Auxiliary Problem Principle formerly introduced in a deterministic setting to serve as a general framework for decomposition/coordination optimization algorithms The idea is based upon that of the stochastic gradient, that is, independent noise realizations are considered successively along the iterations As a consequence, deterministic subproblems are solved at each iteration whereas iterations fulfill the two tasks of coordination and stochastic approximation at the same time Coupling cost function (expectation of some performance index) and deterministic coupling constraints are considered Price (dual) decomposition (encompassing extensions of the Uzawa and Arrow–Hurwicz algorithms to this stochastic case) are studied as well as resource allocation (primal decomposition)

Journal ArticleDOI
TL;DR: In this paper, an error correction model is derived from a stochastic dynamic programming problem incorporating rational expectations, and a parametric restriction is derived that allows a test for the theoretical proposition that the optimal strategy behind the error correction from entails the failure to asymptotically close the gap between the choice variable and the growing target.
Abstract: An error correction model is derived from a stochastic dynamic programming problem incorporating rational expectations. A parametric restriction is derived that allows a test for the theoretical proposition that the optimal strategy behind the error correction from entails the failure to asymptotically close the gap between the choice variable and the growing target. This is accomplished by nesting a partial adjustment model with forward-looking expectations within the error correction paradigm. The counterintuitive behaviour embodied in the error correction model is not supported by the data in the context of a cross-country comparison of cash balances relationships.

Journal ArticleDOI
TL;DR: In this paper, the optimal calf retention and marketing activities for cow-calf producers were examined using a expected utility-maximizing discrete stochastic programming model, where steer, heifer, and corn prices were modeled as stochastically variable.
Abstract: Optimal calf retention and marketing activities for cow-calf producers are examined using a expected utility-maximizing discrete stochastic programming model. Steer, heifer, and corn prices are modeled as stochastic variables. The mathematical model is used to consider retention at weaning and yearling stages and marketing alternatives of cash, hedging, and options. Results show how calf retention decisions depend upon current profit, expected future profit distributions, pricing alternatives available, and the cow-calf producer's aversion to risk.

Journal ArticleDOI
TL;DR: This paper proposes an efficient and specific algorithm for solving large-scale 0-1 GP problems in particular structures, which are termed GUB structures, and introduces two numerical examples from among the problems of system reliability.
Abstract: Upon to now, system optimal allocation problems such as system reliability and system availability problems have been formulated as single-objective problems and solved through the use of various well-developed optimization techniques. However, in this field, there are many problems that cannot be solved without applying MODM (multiple-objective decision making) methods. These methods deal with multiple objectives that conflict with each other instead of formulating the problem as a single objective programming problem which optimizes only the reliability of the cost function, as is done in previous methods. GP (goal programming) is one of the most powerful MODM tools in this field. In practical MODM problems, many GP problems involve a large number of 0-1 decision variables and a special type of 0-1 variable, which arises during the transformation of non-linear integer programming into 0-1 linear programming. In this paper, we propose an efficient and specific algorithm for solving large-scale 0-1 GP problems in particular structures, which are termed GUB structures. Furthermore, to illustrate the effectiveness of the algorithm proposed here, we introduce two numerical examples from among the problems of system reliability, and compare the algorithm proposed with previous methods.

Journal ArticleDOI
Duan Li1
TL;DR: In this paper, a general separable class of stochastic multiobjective optimization problems with perfect state information is considered and a generating approach using a Stochastic Multiobjective Dynamic Programming method is developed to find the set of non-inferior solutions.
Abstract: A general separable class of stochastic multiobjective optimization problems with perfect state information is considered. A generating approach using a stochastic multiobjective dynamic programming method is developed to find the set of non-inferior solutions. The results reveal the variation of the optimal weighting coefficient vector along a non-inferior trajectory. Non-separability is not an inherent property of dynamic programming. A general class of non-separable dynamic problems can be transformed into corresponding separable multiobjective dynamic programming problems. Multiobjective dynamic programming is shown to be a separation strategy to solve non-separable dynamic programming.

Journal ArticleDOI
TL;DR: In this paper, optimal solutions of a stochastic programming problem are considered as functions of the underlying probability distribution, and their directional derivatives, in the sense of Gâteaux, are calculated by applying some recent results from the sensitivity analysis of nonlinear programs.
Abstract: In this paper optimal solutions of a stochastic programming problem are considered as functions of the underlying probability distribution. Their directional derivatives, in the sense of Gâteaux, are calculated by applying some recent results from the sensitivity analysis of nonlinear programs. These derivatives are employed as a heuristic device in order to derive the asymptotic distribution of statistical estimators of the optimal solutions.

Journal ArticleDOI
TL;DR: In this article, the same structural features used in the development of circuit analysis are employed here with the addition that a formal probabilistic interpretation is given to the unit partition coefficients.

Journal ArticleDOI
TL;DR: This paper presents parallel bundle-based decomposition algorithms to solve a class of structured large-scale convex optimization problems, and presents computational experience with block-angular linear programming problems.
Abstract: In this paper, we present parallel bundle-based decomposition algorithms to solve a class of structured large-scale convex optimization problems. An example in this class of problems is the block-angular linear programming problem. By dualizing, we transform the original problem to an unconstrained nonsmooth concave optimization problem which is in turn solved by using a modified bundle method. Further, this dual problem consists of a collection of smaller independent subproblems which give rise to the parallel algorithms. We discuss the implementation on the CRYSTAL multi-computer. Finally, we present computational experience with block-angular linear programming problems and observe that more than 70% efficiency can be obtained using up to eleven processors for one group of test problems, and more than 60% efficiency can be obtained for relatively smaller problems using up to five processors for another group of problems.


Book ChapterDOI
01 Jan 1990
TL;DR: This paper is not concerned with uncertainties (probabilities) of the Kolmogroroff type but rather with uncertainties as they are considered in the theory of fuzzy sets, possibility theory and the like, and it will be shown that for this type of uncertainty (vagueness) which is assumed to be more relevant for MCDM, models and methods exist, which are also adequate for M CDM and which are computationally still feasable.
Abstract: In Multi Criteria Decision Making one is generally concerned with decisions under certainty, i. e. decisions for which the “state” is assumed to be known with certainty. Multi Criteria Decision Making under risk or uncertainty would imply the super-imposition of the problem structures of classical MCDM and that of single criteria decision making under risk, i. e., for instance, the combinations of goal programming with stochastic programming. This would, obviously, become very involved mathematically! In this paper we are not concerned with uncertainties (probabilities) of the Kolmogroroff type but rather with uncertainties as they are considered in the theory of fuzzy sets, possibility theory and the like. It will be shown that for this type of uncertainty (vagueness) which is assumed to be more relevant for MCDM, models and methods exist, which are also adequate for MCDM and which are computationally still feasable.

Proceedings ArticleDOI
01 Dec 1990
TL;DR: The author has developed a stochastic optimization algorithm that is more robust than the older algorithms in that it is guaranteed to converge on a larger class of problems.
Abstract: Classical stochastic optimization algorithms have severe problems associated with them: they converge extremely slowly on problems where the objective function is very flat, and they often diverge when the objective function is steep. The author has developed a stochastic optimization algorithm that is more robust than the older algorithms in that it is guaranteed to converge on a larger class of problems. This algorithm is guaranteed to converge even when the iterates are not assumed a priori to be bounded. This algorithm is also observed to converge faster on a significant class of problems. As the parameters can be chosen so that the new algorithm behaves very much like the older algorithms (except that it converges on a larger class of problems), this algorithm should always be used in preference to the older algorithms. >

Journal ArticleDOI
TL;DR: The present model can approximate the theoretical global optimum with a dramatic reduction in computer processing time and eliminates the rigidity of the policy derived by the explicit approach, since it provides irrigation planners with alternative decision policies which incorporate intangibles and other nonengineering factors.
Abstract: A two-step (deterministic and stochastic) dynamic programming approach has been introduced in this study to solve the complex problem of optimal water allocation in a run-of-the-river-type irrigation project. The complexity of a real-world situation is represented by incorporating in the optimization model the stochasticity of water supply and the nonlinearity of crop production functions. A nonlinear, dated, and multiplicative production function is transformed into a sequentially additive type to replace the usual method of creating an additional ‘state of the plant variable’ which only increases the dimension of the problem. As compared to the explicit stochastic dynamic programming which necessitates, along with its use, an enormous computational complexity due to the so-called ‘curse of dimensionality’, the present model can approximate the theoretical global optimum, at least for the present case study, with a dramatic reduction in computer processing time. It also eliminates the rigidity of the policy derived by the explicit approach, since it provides irrigation planners with alternative decision policies which incorporate intangibles and other nonengineering factors. The traditional method of fixing the cropping pattern based on deterministic estimates of a dependable water supply can likewise be evaluated by the use of the present model. The results of the model's application appear to be practically acceptable.

Journal ArticleDOI
TL;DR: An approach for solving optimization problems of chemical processes in which some search variables must take only some standard discrete values is described, based on joint application of branch and bound procedure and nonlinear programming algorithms.

Journal ArticleDOI
TL;DR: This paper implies the transformation of the stochastic objective functions and constraints in order to obtain an equivalent deterministic MOLP problem and the solving of this last problem by an interactive approach derived from the STEM method.
Abstract: Numerous multiobjective linear programming (MOLP) methods have been proposed in the last two decades, but almost all for contexts where the parameters of problems are deterministic. However, in many real situations, parameters of a stochastic nature arise. In this paper, we suppose that the decision-maker is confronted with a situation of partial uncertainty where he possesses incomplete information about the stochastic parameters of the problem, this information allowing him to specify only the limits of variation of these parameters and eventually their central values. For such situations, we propose a multiobjective stochastic linear programming methodology; it implies the transformation of the stochastic objective functions and constraints in order to obtain an equivalent deterministic MOLP problem and the solving of this last problem by an interactive approach derived from the STEM method. Our methodology is illustrated by a didactical example.