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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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Journal ArticleDOI
TL;DR: In this article, a multi-period, dynamic, portfolio optimization model is developed to address the problem of portfolio managers in the new fixed-income securities with various forms of uncertainty, in addition to the usual interest rate changes.

126 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: A general computational approach based on dynamic programming is derived that can be shown to converge to an optimal policy by computing an inner approximation to future cost functions and an outer approximation that delivers a lower bound.
Abstract: We consider a class of multistage stochastic linear programs in which at each stage a coherent risk measure of future costs is to be minimized. A general computational approach based on dynamic programming is derived that can be shown to converge to an optimal policy. By computing an inner approximation to future cost functions, we can evaluate an upper bound on the cost of an optimal policy, and an outer approximation delivers a lower bound. The approach we describe is particularly useful in sampling-based algorithms, and a numerical example is provided to show the efficacy of the methodology when used in conjunction with stochastic dual dynamic programming.

125 citations

Journal ArticleDOI
TL;DR: The goal is to provide an effective computational tool for the optimization of a large-scale transit route network to minimize transfers with reasonable route directness while maximizing service coverage.
Abstract: This paper presents a mathematical stochastic methodology for transit route network optimization. The goal is to provide an effective computational tool for the optimization of a large-scale transit route network to minimize transfers with reasonable route directness while maximizing service coverage. The methodology includes representation of transit route network solution search spaces, representation of transit route and network constraints, and a stochastic search scheme based on an integrated simulated annealing and genetic algorithm solution search method. The methodology has been implemented as a computer program, tested using previously published results, and applied to a large-scale realistic network optimization problem.

125 citations

Journal ArticleDOI
TL;DR: This paper presents a novel algorithmic approach to reformulate a joint chance constraint as a constraint on the expectation of a summation of indicator random variables, which can be incorporated into the cost function by considering a dual formulation of the optimization problem.
Abstract: Existing approaches to constrained dynamic programming are limited to formulations where the constraints share the same additive structure of the objective function (that is, they can be represented as an expectation of the summation of one-stage costs). As such, these formulations cannot handle joint probabilistic (chance) constraints, whose structure is not additive. To bridge this gap, this paper presents a novel algorithmic approach for joint chance-constrained dynamic programming problems, where the probability of failure to satisfy given state constraints is explicitly bounded. Our approach is to (conservatively) reformulate a joint chance constraint as a constraint on the expectation of a summation of indicator random variables, which can be incorporated into the cost function by considering a dual formulation of the optimization problem. As a result, the primal variables can be optimized by standard dynamic programming, while the dual variable is optimized by a root-finding algorithm that converges exponentially. Error bounds on the primal and dual objective values are rigorously derived. We demonstrate algorithm effectiveness on three optimal control problems, namely a path planning problem, a Mars entry, descent and landing problem, and a Lunar landing problem. All Mars simulations are conducted using real terrain data of Mars, with four million discrete states at each time step. The numerical experiments are used to validate our theoretical and heuristic arguments that the proposed algorithm is both (i) computationally efficient, i.e., capable of handling real-world problems, and (ii) near-optimal, i.e., its degree of conservatism is very low.

125 citations


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