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Critical chain buffer management (CCBM) has been extensively studied in recent years. This paper investigates a new formulation of CCBM, the multimode chance-constrained CCBM problem. A flow-based mixed-integer linear programming model is described and the chance constraints are tackled using a scenario approach. A reinforcement learning (RL)-based algorithm is proposed to solve the problem. A factorial experiment is conducted and the results of this study indicate that solving the chance-constrained problem produces shorter project durations than the traditional approach that inserts time buffers into a baseline schedule generated by solving the deterministic problem. This paper also demonstrates that our RL method produces competitive schedules compared to established benchmarks. The importance of solving the chance-constrained problem and obtaining a project buffer tailored to the desired probability of completing the project on schedule directly from the solution is highlighted. Because of its potential for generating shorter schedules with the same on-time probabilities as the traditional approach, this research can be a useful aid for decision makers. [ABSTRACT FROM AUTHOR]

In this paper we investigate optimal control problems perturbed by random events. We assume that the control has to be decided prior to observing the outcome of the perturbed state equations. We investigate the use of probability functions in the objective function or constraints to define optimal or feasible controls. We provide an extension of differentiability results for probability functions in infinite dimensions usable in this context. These results are subsequently combined with the optimal control setting to derive a novel Pontryagin’s optimality principle. [ABSTRACT FROM AUTHOR]

We investigate an empirical quantile estimation approach to solve chance-constrained nonlinear optimization problems. Our approach is based on the reformulation of the chance constraint as an equivalent quantile constraint to provide stronger signals on the gradient. In this approach, the value of the quantile function is estimated empirically from samples drawn from the random parameters, and the gradient of the quantile function is estimated via a finite-difference approximation on top of the quantile-function-value estimation. We establish a convergence theory of this approach within the framework of an augmented Lagrangian method for solving general nonlinear constrained optimization problems. The foundation of the convergence analysis is a concentration property of the empirical quantile process, and the analysis is divided based on whether or not the quantile function is differentiable. In contrast to the sampling-and-smoothing approach used in the literature, the method developed in this paper does not involve any smoothing function and hence the quantile-function gradient approximation is easier to implement and there are less accuracy-control parameters to tune. We demonstrate the effectiveness of this approach and compare it with a smoothing method for the quantile-gradient estimation. Numerical investigation shows that the two approaches are competitive for certain problem instances. [ABSTRACT FROM AUTHOR]

The flight environment of aerodynamically controlled missiles is full of complexity and uncertainty. To cope with the uncertainty more effectively and enhance the convergence performance in trajectory optimization problems for aerodynamically controlled missiles simultaneously, the chance-constrained sequential convex programming (CC-SCP) algorithm is proposed in this paper. The uncertainty is regarded as the chance constraint, and a smooth and differential approximation function is designed to transform this chance constraint into the constraint that the convex optimization method can handle. Subsequently, the originally non-convex trajectory optimization problem is reformulated into a series of convex optimization subproblems, in which an initial reference trajectory guess generation strategy is proposed, and a theoretical proof of the exact convex relaxation is given to enhance the algorithm's convergence performance and theoretical value, respectively. Numerical simulations are provided to verify the convergence and effectiveness of the CC-SCP algorithm, and the advantages of using the CC-SCP algorithm to cope with the uncertainty are illustrated. Furthermore, comparative simulation examples show that the proposed algorithm possesses a low conservatism, which means the proposed algorithm can obtain a bigger convergence region and a better solution than other current methods when handling the same chance constraints. Finally, the robustness of the algorithm is discussed. • The algorithm can handle the trajectory optimization problem with uncertainties. • The algorithm outperforms other current methods when handling the chance constraints. • A theoretical proof is given for the exact convex relaxation. [ABSTRACT FROM AUTHOR]

Forecast uncertainties pose a considerable challenge to the success of model predictive control (MPC) in buildings. Numerous possibilities for considering forecast uncertainties in MPCs are available, but an in-depth comparison is lacking. This paper compares two main approaches to consider uncertainties: robust and stochastic MPC. They are benchmarked against a deterministic MPC and an MPC with perfect forecast. The MPCs utilize a holistic building model to reflect modern smart homes that include photovoltaic power generation and storage, thermally controlled loads, and smart appliances. Real-world data are used to identify the thermal building model. The performance of the various controllers is investigated under three levels of uncertainty for two building models with different envelope performance. For the highly insulated building, the deterministic MPC achieves satisfactory thermal comfort when the forecast error is medium or low, but the thermal comfort is compromised for high forecast errors. In the poorly insulated building, thermal comfort is compromised at medium and high forecast errors. Compared to the deterministic MPC, the robust MPC increases the electricity cost by up to 4.5% and provides complete temperature constraint satisfaction while the stochastic MPC increases the electricity cost by less than 1% and fulfills the thermal comfort requirements. [ABSTRACT FROM AUTHOR]

The rapid development of microgrids (MGs) with various prosumers promotes the accommodation of renewable distributed generation (RDG) and provides platforms for local energy sharing among prosumers. However, the operational uncertainties pose enormous challenges to the day-ahead bidding of MGs in the wholesale electricity market and there is an urgent need for a local market to facilitate the local energy sharing. Thus, this paper proposes a risk-averse day-ahead bidding strategy for MGs with full consideration of the multiple uncertainties originating from the wholesale electricity market, RDG and loads. Based on the transactive energy (TE) sharing concept, the local market is formulated as a Stackelberg game (SG) to effectively capture the strategic interaction among the MG and prosumers, where a distributed iterative algorithm with a bisection approach that only requires exchanging TE-related information is adopted to achieve the SG equilibrium without compromising privacy concerns. To handle the uncertainties of RDG and loads, the power balances are formulated as chance constraints and a data-driven quantile forecasting method is developed for achieving the computational tractability of chance constraints without any prior knowledge or probability distribution assumptions. Furthermore, a risk criterion of the conditional value-at-risk is incorporated in the day-ahead bidding model of MGs for risk aversion towards uncertainties of the wholesale electricity market. The effectiveness of the proposed solution is extensively demonstrated through numerical simulation. • A risk-averse day-ahead bidding strategy of TE sharing MGs is presented. • A SG-based local TE market with privacy protection is developed. • The wholesale market uncertainties are addressed in a risk-averse manner via CVaR. • The power balance chance constraints are built to handle RDG and load uncertainties. • A data-driven quantile forecasting method is proposed to solve chance constraints. [ABSTRACT FROM AUTHOR]