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Stochastic programming

About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.


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Book
01 Jun 1971
TL;DR: The Classics Edition contains applications of Static Optimization and Dynamic Optimization for Economizing and the Economy, and theory of the Household Theory of the Firm and General Equilibrium Welfare Economics.
Abstract: Preface to the Classics Edition Preface Part I. Introduction. Economizing and the Economy Part II. Static Optimization. The Mathematical Programming Problem Classical Programming Nonlinear Programming Linear Programming Game Theory Part III. Applications of Static Optimization. Theory of the Household Theory of the Firm General Equilibrium Welfare Economics Part IV. Dynamic Optimization. The Control Problem Calculus of Variations Dynamic Programming Maximum Principle Differential Games Part V. Applications of Dynamic Optimization. Optimal Economic Growth Appendix A: Analysis Appendix B: Matrices Index.

857 citations

Journal ArticleDOI
TL;DR: Two new versions of forward and backward type algorithms are presented for computing such optimally reduced probability measures approximately for convex stochastic programs with an (approximate) initial probability distribution P having finite support supp P.
Abstract: We consider convex stochastic programs with an (approximate) initial probability distribution P having finite support supp P, i.e., finitely many scenarios. The behaviour of such stochastic programs is stable with respect to perturbations of P measured in terms of a Fortet-Mourier probability metric. The problem of optimal scenario reduction consists in determining a probability measure that is supported by a subset of supp P of prescribed cardinality and is closest to P in terms of such a probability metric. Two new versions of forward and backward type algorithms are presented for computing such optimally reduced probability measures approximately. Compared to earlier versions, the computational performance (accuracy, running time) of the new algorithms has been improved considerably. Numerical experience is reported for different instances of scenario trees with computable optimal lower bounds. The test examples also include a ternary scenario tree representing the weekly electrical load process in a power management model.

851 citations

Journal ArticleDOI
TL;DR: Arguments from stability analysis indicate that Fortet-Mourier type probability metrics may serve as such canonical metrics in a convex stochastic programming problem with a discrete initial probability distribution.
Abstract: Given a convex stochastic programming problem with a discrete initial probability distribution, the problem of optimal scenario reduction is stated as follows: Determine a scenario subset of prescribed cardinality and a probability measure based on this set that is the closest to the initial distribution in terms of a natural (or canonical) probability metric. Arguments from stability analysis indicate that Fortet-Mourier type probability metrics may serve as such canonical metrics. Efficient algorithms are developed that determine optimal reduced measures approximately. Numerical experience is reported for reductions of electrical load scenario trees for power management under uncertainty. For instance, it turns out that after 50% reduction of the scenario tree the optimal reduced tree still has about 90% relative accuracy.

838 citations

Book
01 Jan 1988
TL;DR: In this paper, the authors describe a powerful and flexible technique for the modeling of behavior, based on evolutionary principles, which employs stochastic dynamic programming and permits the analysis of behavioral adaptations wherein organisms respond to changes in their environment and in their own current physiological state.
Abstract: This book describes a powerful and flexible technique for the modeling of behavior, based on evolutionary principles. The technique employs stochastic dynamic programming and permits the analysis of behavioral adaptations wherein organisms respond to changes in their environment and in their own current physiological state. Models can be constructed to reflect sequential decisions concerned simultaneously with foraging, reproduction, predator avoidance, and other activities. The authors show how to construct and use dynamic behavioral models. Part I covers the mathematical background and computer programming, and then uses a paradigm of foraging under risk of predation to exemplify the general modeling technique. Part II consists of five "applied" chapters illustrating the scope of the dynamic modeling approach. They treat hunting behavior in lions, reproduction in insects, migrations of aquatic organisms, clutch size and parental care in birds, and movement of spiders and raptors. Advanced topics, including the study of dynamic evolutionarily stable strategies, are discussed in Part III.

817 citations

Journal ArticleDOI
TL;DR: A new theory of pedestrian behavior under uncertainty based on the concept of utility maximization is put forward, which proposes a trade-off between the utility gained from performing activities at a specific location and the predicted cost of walking subject to the physical limitations of the pedestrians and the kinematics of the pedestrian.
Abstract: Among the most interesting and challenging theoretical and practical problems in describing pedestrians behavior are route choice and activity scheduling. Compared to other modes of transport, a characteristic feature of pedestrian route choice is that routes are continuous trajectories in time and space: since a pedestrian chooses a route from an infinite set of alternatives, dedicated theories and models describing pedestrian route choice are required. This article puts forward a new theory of pedestrian behavior under uncertainty based on the concept of utility maximization. The main behavioral assumption is that pedestrians optimize some predicted pedestrian-specific utility function, representing a trade-off between the utility gained from performing activities at a specific location, and the predicted cost of walking subject to the physical limitations of the pedestrians and the kinematics of the pedestrian. The uncertainty reflects the randomness of the experienced traffic conditions. Based on this normative theory, route choice, activity area choice, and activity scheduling are simultaneously optimized using dynamic programming for different traffic conditions and uncertainty levels. Throughout the article, the concepts are illustrated by examples.

757 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023175
2022423
2021526
2020598
2019578
2018532