Browsing by Subject "Risk-averse optimization"

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Open Access
Risk-averse multi-stage mixed-integer stochastic programming problems
(2019-01) Mahmutoğulları, Ali İrfan
Risk-averse multi-stage mixed-integer stochastic programming problems form a class of extremely challenging problems since the problem size grows exponentially with the number of stages, they are non-convex due to integrality restrictions, and their objective functions are nonlinear in general. In this thesis, we first focus on such problems with an objective of dynamic mean conditional value-at-risk. We propose a scenario tree decomposition approach to obtain lower and upper bounds for their optimal values and then use these bounds in an evaluate-and-cut procedure which serves as an exact solution algorithm for such problems with integer first-stage decisions. Later, we consider a risk-averse day-ahead scheduling of electricity generation or unit commitment problem where the objective is a dynamic coherent risk measure. We consider two different versions of the problem: adaptive and non-adaptive. In the adaptive model, the commitment decisions are updated in each stage, whereas in the non-adaptive model, the commitment decisions are fixed in the first-stage. We provide theoretical and empirical analyses on the benefit of using an adaptive multi-stage stochastic model. Finally, we investigate the trade off between the adaptivity of the model and the computational effort to solve it for risk-averse multi-stage production planning problems with an objective of dynamic coherent risk measure. We also conduct computational experiments in order to verify the theoretical findings and discuss the results of these experiments.
Open Access
Risk-averse stochastic orienteering problems
(Eskişehir Teknik Üniversitesi, 2019) Çavuş, Özlem
In this study, we consider risk-averse orienteering problems with stochastic travel times or stochastic rewards. In risk-neutral orienteering problems, the objective is generally to maximize the expected total reward of visited nodes. However, due to uncertain travel times or uncertain rewards, the dispersion in total reward collected may be large, which necessitates an approach that minimizes the dispersion (risk) in addition to maximizing the expected total reward. To handle this, for the orienteering problems with stochastic travel times or stochastic rewards, we suggest two different formulations with an objective of coherent measures of risk. For both problems, we conduct an experimental study using two different coherent measures of risk, which have been extensively used in the literature, and compare the results. The computational results show that, in both models suggested and under both risk measures used, the decision maker is able to obtain a tour with expected total reward being close to the expected total reward of risk-neutral solution, however with a significant decrease in the standard deviation of total reward.
Open Access
The value of multi-stage stochastic programming in risk-averse unit commitment under uncertainty
(IEEE, 2019) Mahmutoğulları, Ali İrfan; Ahmed, S.; Çavuş, Özlem; Aktürk, M. Selim
Day-ahead scheduling of electricity generation or unit commitment is an important and challenging optimization problem in power systems. Variability in net load arising from the increasing penetration of renewable technologies has motivated study of various classes of stochastic unit commitment models. In two-stage models, the generation schedule for the entire day is fixed while the dispatch is adapted to the uncertainty, whereas in multi-stage models the generation schedule is also allowed to dynamically adapt to the uncertainty realization. Multi-stage models provide more flexibility in the generation schedule; however, they require significantly higher computational effort than two-stage models. To justify this additional computational effort, we provide theoretical and empirical analyses of the value of multi-stage solution for risk-averse multi-stage stochastic unit commitment models. The value of multi-stage solution measures the relative advantage of multi-stage solutions over their two-stage counterparts. Our results indicate that, for unit commitment models, the value of multi-stage solution increases with the level of uncertainty and number of periods, and decreases with the degree of risk aversion of the decision maker.