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Stochastic Optimization Applications for Robotics and Human Modeling
Published in Vincent G. Duffy, Advances in Applied Human Modeling and Simulation, 2012
Qiuling Zou, Jingzhou (James) Yang*, Daan Liang
In RBDO approaches, objective functions are minimized with a reliability level for various sources of uncertainties. Two types of algorithms are included in this approach: MPP-based methods and sampling-based methods. The general MPPbased methods include nested RBDO (Hohenbichler and Rackwitz, 1986; Nikolaidis and Burdisso, 1988), single-loop RBDO (Liang et al., 2008) and sequential RBDO (Du and Chen, 2004). Based on the general algorithms, many customized approaches have been developed. The research on stochastic programming often focuses on decision-making processes, in which, the uncertainty can be gradually reduced as more information is available. The goal is to find values of the initial decision variables and functions to update these variables when additional information about the problem evolves. Stochastic programming includes programming with recourse (Sahinidis, 2004), chance-constrained programming (Prékopa, 1995), and stochastic dynamic programming (Bellman, 1957).
Classical Optimization Methods
Published in A Vasuki, Nature-Inspired Optimization Algorithms, 2020
Stochastic programming is an optimization method where some of the variables associated with the objective function are random variables with a defined probability distribution. In engineering design problems there could be a minimum and maximum bound for the associated design variables and the actual value might be randomly placed within these bounds. Whenever there are random variables involved in the problem it becomes a stochastic programming problem. Even though the variables associated with the problem are random in nature, the mathematical equations related to the problem make it linear or non-linear, geometric or dynamic, and these problems can be solved using the existing standard techniques.
Hydrothermal Producer Self-Scheduling
Published in João P. S. Catalão, Electric Power Systems, 2017
Christos K. Simoglou, Pandelis N. Biskas, Anastasios G. Bakirtzis
Each stochastic programming problem is defined in a number of stages. Each stage denotes a point in time where related decisions are made or uncertainty is revealed. In general, stochastic programming problems are grouped in two categories depending on the number of stages considered, namely two-stage and multistage stochastic programming problems. As the hydrothermal Producer self-scheduling problem is later formulated as a two-stage stochastic problem, in this section the two-stage stochastic programming problems are only described. The multistage stochastic programming problems are formulated similarly [28,49].
Avoiding momentum crashes using stochastic mean-CVaR optimization with time-varying risk aversion
Published in The Engineering Economist, 2023
Having selected CVaR as the risk measure, a mean-CVaR stochastic program with time-varying risk aversion is developed to balance the tradeoff between investment risk and reward. Stochastic programming provides a modeling framework for decision making under uncertainty. It is well suited for portfolio management as investment decisions have to be made before the return information is revealed. Numerous applications of stochastic programming to portfolio management have been studied in the past decades (Bergk et al., 2021; Cui et al., 2020; Guo & Ryan, 2021 2021a; Lim et al., 2011; Moazeni et al., 2016; Topaloglou et al., 2011). Motivated by the regime-switching model (Bae et al., 2014; Li et al., 2022), in this paper, we incorporate time-varying risk aversion to select portfolio weights that dynamically balance the tradeoff between expectation and CVaR of the return of the constructed portfolio according to various stock market conditions. As momentum crashes happen when the market is volatile, we explore three volatility-related measures, namely (1) estimated market volatility, (2) the ratio of estimated market return to estimated market volatility, and (3) the Chicago Board Options Exchange (CBOE) Volatility Index (VIX), to determine the tail probability in CVaR and the risk-aversion parameter in the mean-CVaR model.
A literature review on robust and real-time models for cross-docking
Published in International Journal of Production Research, 2023
In Table 6, we also observe two other techniques to handle uncertainty cited by Herroelen and Leus (2005), namely stochastic and fuzzy approaches. The articles employing these techniques appear in their respective categories. These techniques are directly interested in the representation of the uncertain input data. Stochastic programming is a mathematical programming approach where some of the data incorporated into the objective function and/or the set of constraints is uncertain. This data is usually modelled as a probability distribution on the model parameters. Unlike the stochastic programming approach where uncertainty is represented through a statistical data modelling process, the fuzzy approaches deal with imprecise and non-numerical information. The fuzzy models provide mathematical means to represent vagueness and imprecise information. Proactive (robust) and reactive (real-time) approaches are different in the essence compared to fuzzy and stochastic models; they are mostly focused on the solution than the data itself. Therefore, it is not surprising to see different modelling and solution techniques for each one of these approaches used against uncertainty. Since each approach has a different philosophy against uncertainty, they are not comparable. Nevertheless, proactive and reactive approaches seem quite attractive for application purposes since they are solution-oriented and complementary approaches.
Analytics and machine learning in vehicle routing research
Published in International Journal of Production Research, 2023
Ruibin Bai, Xinan Chen, Zhi-Long Chen, Tianxiang Cui, Shuhui Gong, Wentao He, Xiaoping Jiang, Huan Jin, Jiahuan Jin, Graham Kendall, Jiawei Li, Zheng Lu, Jianfeng Ren, Paul Weng, Ning Xue, Huayan Zhang
This subsection reviews several ML assisted VRP modelling techniques, primarily for better handling of uncertainties. In the OR community, the most popular uncertainty handling approaches are robust optimisation and stochastic programming. The robust optimisation seeks the guaranteed protections against the worst-case scenarios and the approach can be over-conservative for many applications because the probability of these extreme cases can be very small. Stochastic programming aims to optimise the expectations over uncertainties and hence requires the knowledge of the distributions of the random variables, which is often subject to criticisms because the distribution may not be known, preventing it being solved analytically. Additionally, in stochastic programming, although the expected objective value is optimised but for risk-critical applications, solution failures in worst-case scenarios could be catastrophic. In such situations, robust optimisation is more attractive. The chance-constrained programming can be considered as a soft version of the stochastic programming in the sense that the constraints may be violated with a small pre-defined probability. Finally, the ML-based predictive models are popular in practice because they are often used in conjunction with well-studied deterministic models. The main challenge of the predictive models lies in the large number of parameter estimation calls required during problem resolving in the event of big changes in forecasts. The computational time is often a bottle neck.