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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 ChapterDOI
22 Sep 2003
TL;DR: It is shown that on rather mild conditions, including that of linear increment of the sample size, the algorithm converges with probability one to the globally optimal solution of the stochastic combinatorial optimization problem, and can usually be recommended for practical application in an unchanged form, i.e., with the ”theoretical” parameter schedule.
Abstract: The paper presents a general-purpose algorithm for solving stochastic combinatorial optimization problems with the expected value of a random variable as objective and deterministic constraints. The algorithm follows the Ant Colony Optimization (ACO) approach and uses Monte-Carlo sampling for estimating the objective. It is shown that on rather mild conditions, including that of linear increment of the sample size, the algorithm converges with probability one to the globally optimal solution of the stochastic combinatorial optimization problem. Contrary to most convergence results for metaheuristics in the deterministic case, the algorithm can usually be recommended for practical application in an unchanged form, i.e., with the ”theoretical” parameter schedule.

103 citations

Book ChapterDOI
25 Jun 2007
TL;DR: This paper develops approximation algorithms for robust two-stage robust optimization problems with an exponential number of scenarios and develops a simple buy-at-oncealgorithm that gives tight approximation factors for unweighted variants of these covering problems, but performs poorly for general weighted problems.
Abstract: Following the well-studied two-stage optimization framework for stochastic optimization [15,8], we study approximation algorithms for robust two-stage optimization problems with an exponential number of scenarios. Prior to this work, Dhamdhere et al. [8] introduced approximation algorithms for two-stage robust optimization problems with explicitly given scenarios. In this paper, we assume the set of possible scenarios is given implicitly, for example by an upper bound on the number of active clients. In two-stage robust optimization, we need to pre-purchase some resources in the first stage before the adversary's action. In the second stage, after the adversary chooses the clients that need to be covered, we need to complement our solution by purchasing additional resources at an inflated price. The goal is to minimize the cost in the worst-case scenario. We give a general approach for solving such problems using LP rounding. Our approach uncovers an interesting connection between robust optimization and online competitive algorithms. We use this approach, together with known online algorithms, to develop approximation algorithms for several robust covering problems, such as set cover, vertex cover, and edge cover. We also study a simple buy-at-oncealgorithm that either covers all items in the first stage or does nothing in the first stage and waits to build the complete solution in the second stage. We show that this algorithm gives tight approximation factors for unweighted variants of these covering problems, but performs poorly for general weighted problems.

103 citations

Journal ArticleDOI
TL;DR: One of the most common motivations for public transport investments is to reduce congestion and increase capacity as mentioned in this paper. But public transport congestion leads to crowding discomfort, denied boardings and low capacity.
Abstract: One of the most common motivations for public transport investments is to reduce congestion and increase capacity. Public transport congestion leads to crowding discomfort, denied boardings and low ...

102 citations

Journal ArticleDOI
TL;DR: The model clearly demonstrates that, use of fuzzy linear programming in multireservoir system optimization presents a potential alternative to get the steady state solution with a lot lesseffort than classical stochastic dynamic programming.
Abstract: For a multireservoir system, where the number of reservoirs is large, the conventional modelling by classical stochastic dynamic programming (SDP) presents difficulty, due to the curse of dimensionality inherent in the model solution. It takes a long time to obtain a steady state policy and also it requires large amount of computer storage space, which form drawbacks in application. An attempt is made to explore the concept of fuzzy sets to provide a viable alternative in this context. The application of fuzzy set theory to water resources systems is illustrated through the formulation of a fuzzy mathematical programming model to a multireservoir system with a number of upstream parallel reservoirs, and one downstream reservoir. The study is aimed to minimize the sum of deviations of the irrigation withdrawals from their target demands, on a monthly basis, over a year. Uncertainty in reservoir inflows is considered by treating them as fuzzy sets. The model considers deterministic irrigation demands. The model is applied to a three reservoir system in the Upper Cauvery River basin, South India. The model clearly demonstrates that, use of fuzzy linear programming in multireservoir system optimization presents a potential alternative to get the steady state solution with a lot less effort than classical stochastic dynamic programming.

102 citations


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