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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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TL;DR: This paper synergistically integrate methods that had previously and independently been developed by the authors, thereby leading to optimal-robust-designs, and establishes the general superiority of physical programming over other conventional methods in solving multiobjective optimization problems.
Abstract: Computational optimization for design is effective only to the extent that the aggregate objective function adequately captures designer's preference. Physical programming is an optimization method that captures the designer's physical understanding of the desired design outcome in forming the aggregate objective function. Furthermore, to be useful, a resulting optimal design must be sufficiently robust/insensitive to known and unknown variations that to different degrees affect the design's performance. This paper explores the effectiveness of the physical programming approach in explicitly addressing the issue of design robustness. Specifically, we synergistically integrate methods that had previously and independently been developed by the authors, thereby leading to optimal-robust-designs. We show how the physical programming method can be used to effectively exploit designer preference in making tradeoffs between the mean and variation of performance, by solving a bi-objective robust design problem. The work documented in this paper establishes the general superiority of physical programming over other conventional methods (e.g., weighted sum) in solving multiobjective optimization problems. It also illustrates that the physical programming method is among the most effective multicriteria mathematical programming techniques for the generation of Pareto solutions that belong to both convex and non-convex efficient frontiers.

140 citations

Journal ArticleDOI
TL;DR: This work proposes an approach for ToU tariff design based in quadratically constrained quadratic programming and stochastic optimization techniques, addressing uncertainties and dealing with various aspects of tariff design from the point of view of the regulator/regulated utility.
Abstract: Time-of-use (ToU) electricity tariffs are currently employed or considered for implementation in many jurisdictions around the world. In ToU modalities, a set of different tariffs for different hours of the day and/or seasons of the year is defined at the beginning of a given horizon, and then kept constant until its end. While designing ToU tariffs, one of the most significant sources of uncertainty to be considered relates to price-elasticities of demand. We propose an approach for ToU tariff design based in quadratically constrained quadratic programming and stochastic optimization techniques, addressing these uncertainties and dealing with various aspects of tariff design from the point of view of the regulator/regulated utility.

140 citations

Journal ArticleDOI
TL;DR: A class of discrete optimization problems, where the objective function for a given configuration can be expressed as the expectation of a random variable, and an iterative algorithm called the stochastic comparison (SC) algorithm is developed.
Abstract: In this paper we study a class of discrete optimization problems, where the objective function for a given configuration can be expressed as the expectation of a random variable. In such problems, only samples of the random variables are available for the optimization process. An iterative algorithm called the stochastic comparison (SC) algorithm is developed. The convergence of the SC algorithm is established based on an examination of the quasi-stationary probabilities of a time-inhomogeneous Markov chain. We also present some numerical experiments.

140 citations

Journal ArticleDOI
TL;DR: This work defines the class of polyhedral risk measures such that stochastic programs with risk measures taken from this class have favorable properties and proposes multiperiod extensions of the Conditional-Value-at-Risk.
Abstract: We consider stochastic programs with risk measures in the objective and study stability properties as well as decomposition structures. Thereby we place emphasis on dynamic models, i.e., multistage stochastic programs with multiperiod risk measures. In this context, we define the class of polyhedral risk measures such that stochastic programs with risk measures taken from this class have favorable properties. Polyhedral risk measures are defined as optimal values of certain linear stochastic programs where the arguments of the risk measure appear on the right-hand side of the dynamic constraints. Dual representations for polyhedral risk measures are derived and used to deduce criteria for convexity and coherence. As examples of polyhedral risk measures we propose multiperiod extensions of the Conditional-Value-at-Risk.

140 citations

Journal ArticleDOI
TL;DR: In this paper, a lifting technique was proposed to map a given stochastic program to an equivalent problem on a higher-dimensional probability space, and it was shown that solving the lifted problem in primal and dual linear decision rules provides tighter bounds than those obtained from applying linear decision rule to the original problem.
Abstract: Stochastic programming provides a versatile framework for decision-making under uncertainty, but the resulting optimization problems can be computationally demanding. It has recently been shown that primal and dual linear decision rule approximations can yield tractable upper and lower bounds on the optimal value of a stochastic program. Unfortunately, linear decision rules often provide crude approximations that result in loose bounds. To address this problem, we propose a lifting technique that maps a given stochastic program to an equivalent problem on a higher-dimensional probability space. We prove that solving the lifted problem in primal and dual linear decision rules provides tighter bounds than those obtained from applying linear decision rules to the original problem. We also show that there is a one-to-one correspondence between linear decision rules in the lifted problem and families of nonlinear decision rules in the original problem. Finally, we identify structured liftings that give rise to highly flexible piecewise linear and nonlinear decision rules, and we assess their performance in the context of a dynamic production planning problem.

139 citations


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