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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 paper, a branch-and-bound algorithm is proposed to solve a portfolio optimization problem with a probabilistic constraint, where the expected return of the constructed portfolio must exceed a prescribed return threshold with a high confidence level.
Abstract: In this paper, we study extensions of the classical Markowitz mean-variance portfolio optimization model. First, we consider that the expected asset returns are stochastic by introducing a probabilistic constraint, which imposes that the expected return of the constructed portfolio must exceed a prescribed return threshold with a high confidence level. We study the deterministic equivalents of these models. In particular, we define under which types of probability distributions the deterministic equivalents are second-order cone programs and give closed-form formulations. Second, we account for real-world trading constraints (such as the need to diversify the investments in a number of industrial sectors, the nonprofitability of holding small positions, and the constraint of buying stocks by lots) modeled with integer variables. To solve the resulting problems, we propose an exact solution approach in which the uncertainty in the estimate of the expected returns and the integer trading restrictions are simultaneously considered. The proposed algorithmic approach rests on a nonlinear branch-and-bound algorithm that features two new branching rules. The first one is a static rule, called idiosyncratic risk branching, while the second one is dynamic and is called portfolio risk branching. The two branching rules are implemented and tested using the open-source Bonmin framework. The comparison of the computational results obtained with state-of-the-art MINLP solvers ( MINLP_BB and CPLEX ) and with our approach shows the effectiveness of the latter, which permits to solve to optimality problems with up to 200 assets in a reasonable amount of time. The practicality of the approach is illustrated through its use for the construction of four fund-of-funds now available on the major trading markets.

148 citations

Journal ArticleDOI
TL;DR: The framework is based on a two-state stochastic MINLP formulation for the maximization of a function comprising the expected value of the profit, operating and fixed costs of the plant to address process synthesis problems under uncertainty.

148 citations

Journal ArticleDOI
Lu Zhen1
TL;DR: This study finds that the robust method can derive a near optimal solution to the stochastic model in a fast way, and also has the benefit of limiting the worst-case outcome of the tactical BAP decisions.

147 citations

Proceedings ArticleDOI
TL;DR: In this article, a unified framework for optimizing energy and reserve bidding strategies under a deregulated market is presented, where the hourly MCPs and reserve prices are modeled as discrete random variables, whose probability mass functions are predicted with a classification based neural network approach.
Abstract: In the deregulated power industry, a generation company (GenCo) sells energy and ancillary services primarily through bidding at a daily market. Developing effective strategies to optimize hourly bid curves for a hydrothermal power system to maximize profits becomes one of the most important tasks of a GenCo. This paper presents a unified framework for optimizing energy and reserve bidding strategies under a deregulated market. In view of high volatilities of market clearing prices (MCP), the hourly MCPs and reserve prices are modeled as discrete random variables, whose probability mass functions are predicted with a classification based neural network approach. The mean-variance method is applied to manage bidding risks, where a risk penalty term related to MCP and reserve price variances is added to the objective function. To avoid buying too much power from the market at high prices, a GenCo may also require covering at least a certain percentage of its own customer load. This self-scheduling requirement is modeled similar to the system demand in traditional unit commitment problems. The formulation is a stochastic mixed-integer optimization with a separable structure. An optimization based algorithm combining Lagrangian relaxation and stochastic dynamic programming is presented to optimize bids for both energy and reserve markets. Numerical testing based on an 11-unit system in New England market shows that the method can significantly reduce profit variances and thus reduce bidding risks. Near-optimal energy and reserve bid curves are obtained in 4-5 minutes on a 600 Hz Pentium III PC, efficient for daily use.

147 citations

Journal ArticleDOI
TL;DR: In this article, a new approach is proposed to solve a kind of nonlinear optimization problem under uncertainty, in which some dependent variables are to be constrained with a predefined probability.
Abstract: Optimization under uncertainty is considered necessary for robust process design and operation. In this work, a new approach is proposed to solve a kind of nonlinear optimization problem under uncertainty, in which some dependent variables are to be constrained with a predefined probability. Such problems are called optimization under chance constraints. By employment of the monotony of these variables to one of the uncertain variables, the output feasible region will be mapped to a region of the uncertain input variables. Thus, the probability of holding the output constraints can be simply achieved by integration of the probability density function of the multivariate uncertain variables. Collocation on finite elements is used for the numerical integration, through which sensitivities of the chance constraints can be computed as well. The proposed approach is applied to the optimization of two process engineering problems under various uncertainties.

147 citations


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