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Industrial projects are plagued by uncertainties, often resulting in both time and cost overruns. This research introduces an innovative approach, employing Reinforcement Learning (RL), to address three distinct project management challenges within a setting of uncertain activity durations. The primary objective is to identify stable baseline schedules. The first challenge encompasses the multimode lean project management problem, wherein the goal is to maximize a project's value function while adhering to both due date and budget chance constraints. The second challenge involves the chance-constrained critical chain buffer management problem in a multimode context. Here, the aim is to minimize the project delivery date while considering resource constraints and duration-chance constraints. The third challenge revolves around striking a balance between the project value and its net present value (NPV) within a resource-constrained multimode environment. To tackle these three challenges, we devised mathematical programming models, some of which were solved optimally. Additionally, we developed competitive RL-based algorithms and verified their performance against established benchmarks. Our RL algorithms consistently generated schedules that compared favorably with the benchmarks, leading to higher project values and NPVs and shorter schedules while staying within the stakeholders' risk thresholds. The potential beneficiaries of this research are project managers and decision-makers who can use this approach to generate an efficient frontier of optimal project plans. [ABSTRACT FROM AUTHOR]

Uncertainty in classical stochastic programming models is often described solely by independent random parameters, ignoring their dependence on multidimensional features. We describe a novel contextual chance-constrained programming formulation that incorporates features, and argue that solutions that do not take them into account may not be implementable. Our formulation cannot be solved exactly in most cases, and we propose a tractable and fully data-driven approximate model that relies on weighted sums of random variables. We obtain a stochastic lower bound for the optimal value and feasibility results that include convergence to the true feasible set as the number of data points increases, as well as the minimal number of data points needed to obtain a feasible solution with high probability. We illustrate our findings in a vaccine allocation problem and compare the results with a naíve sample average approximation approach. [ABSTRACT FROM AUTHOR]

Under-Frequency Load Shedding (UFLS) schemes are the last resort to contain a frequency drop in the grid by disconnecting part of the demand. The allocation methods for selecting feeders that would contribute to the UFLS scheme have traditionally relied on the fact that electric demand followed fairly regular patterns, and could be forecast with high accuracy. However, recent integration of Distributed Generation (DG) increases the uncertainty in net consumption of feeders which, in turn, requires a reformulation of UFLS-allocation methods to account for this uncertainty. In this paper, a chance-constrained methodology for selecting feeders is proposed, with mathematical guarantees for the disconnection of the required amount of load with a certain pre-defined probability. The correlation in net-load forecasts among feeders is explicitly considered, given that uncertainty in DG power output is driven by meteorological conditions with high correlation across the network. Furthermore, this method is applicable either to systems with conventional UFLS schemes (where relays measure local frequency and trip if this magnitude falls below a certain threshold), or adaptive UFLS schemes (where relays are triggered by control signals sent in the few instants following a contingency). Relevant case studies demonstrate the applicability of the proposed method, and the need for explicit consideration of uncertainty in the UFLS-allocation process. • A chance-constrained methodology for selecting feeders contributing towards UFLS is proposed. • Uncertainty and correlation driven by Distributed Generation are explicitly considered. • A distributionally-robust option is given, requiring minimal information on uncertainty. • The method applies to several communication requirements for the operation of the power system. [ABSTRACT FROM AUTHOR]

Model predictive control (MPC) heavily relies on the accuracy of the system model. Nevertheless, process models naturally contain random parameters. To derive a reliable solution, it is necessary to design a stochastic MPC. This work studies the chance constrained MPC of systems described by parabolic partial differential equations (PDEs) with random parameters. Inequality constraints on time- and space-dependent state variables are defined in terms of chance constraints. Using a discretization scheme, the resulting high-dimensional chance constrained optimization problem is solved by our recently developed inner–outer approximation which renders the problem computationally amenable. The proposed MPC scheme automatically generates probability tubes significantly simplifying the derivation of feasible solutions. We demonstrate the viability and versatility of the approach through a case study of tumor hyperthermia cancer treatment control, where the randomness arises from the thermal conductivity coefficient characterizing heat flux in human tissue. [ABSTRACT FROM AUTHOR]

We study a generalized distributionally robust chance-constrained set covering problem (DRC) with a Wasserstein ambiguity set, where both decisions and uncertainty are binary-valued. We establish the NP-hardness of DRC and recast it as a two-stage stochastic program, which facilitates decomposition algorithms. Furthermore, we derive two families of valid inequalities. The first family targets the hypograph of a "shifted" submodular function, which is associated with each scenario of the two-stage reformulation. We show that the valid inequalities give a complete description of the convex hull of the hypograph. The second family mixes inequalities across multiple scenarios and gains further strength via lifting. Our numerical experiments demonstrate the out-of-sample performance of the DRC model and the effectiveness of our proposed reformulation and valid inequalities. [ABSTRACT FROM AUTHOR]

• A novel data-driven surrogate is developed for chance constraint reformulation. • Wind curtailment dispatch is explicitly modeled in chance constraints. • A correction strategy is proposed to ensure modeling accuracy. • The proposed approach is effective under arbitrary distribution assumptions. Chance-constrained optimization (CCO) has been widely used for uncertainty management in power system operation. With the prevalence of wind energy, it becomes necessary to consider wind curtailment as a dispatch variable in CCO. However, the wind curtailment will cause an impulse for the uncertainty distribution, yielding challenges for explicit modeling of chance constraint. In this paper, a novel data-driven framework is developed to handle this issue. By modeling the wind curtailment as a cap enforced on the wind power output, the proposed framework constructs a data-driven surrogate to describe the relationship between wind curtailment and the tightening boundary of chance constraints. This allows us to reformulate the CCO with wind curtailment as a mixed-integer second-order cone programming (MI-SOCP) problem. An error correction strategy is developed by solving a convex linear programming (LP) to improve the modeling accuracy. The notable characteristic of the proposed method is that the chance constraints with wind curtailment can be explicitly and accurately handled without any distribution assumptions, which provides great convenience for the power dispatch under a high percentage of renewables. Case studies performed on the PJM 5-bus and IEEE 118-bus systems demonstrate that the proposed method is capable of accurately accounting the influence of wind curtailment dispatch in CCO. It shows that the proposed method outperforms existing methods by producing more economic and secure solutions for the chance-constrained energy and reserve scheduling problem under uncertainties. [ABSTRACT FROM AUTHOR]

Chance constraints are suitable for industrial process modeling under uncertain conditions, where constraints cannot be strictly satisfied or do not need to be fully satisfied. In this paper, a single machine scheduling problem involving flexible maintenance, production, and uncertainty is modeled as a chance constrained dynamic optimization problem (CCDOP). A novel method is proposed for transforming the CCDOP into an equivalent deterministic dynamic optimization problem (DOP) with fixed state jump times. Furthermore, by using the idea of l 1 penalty function and a smooth approximation technique, the resulting deterministic DOP becomes a smoothing penalty problem, which is a non-convex nonlinear parameter optimization problem (NNPOP) with simple bounds on the variables. To solve the NNPOP, a gradient-based stochastic search algorithm (GSSA) is developed based on a gradient-based adaptive search algorithm (GASA) and a novel stochastic search algorithm (NSSA). The convergence analysis result shows that the GSSA is a globally convergent algorithm. Finally, two numerical examples are used to illustrate the effectiveness of the proposed method. Numerical results show that the GSSA has excellent convergence behavior with robust computation feature, providing better results compared with the other typical methods. • A CCDOA is developed for the single machine scheduling problem. • Propose a novel technique to transform the CCDOP into an equivalent CDPOP. • Design a GASA, which is effective for ill-conditioned problems. • Design a NSSA, in which no parameters tuning is required. • Propose a GSSA for the NNPOP and comparison results imply its superiority. [ABSTRACT FROM AUTHOR]

For optimal power flow problems with chance constraints, a particularly effective method is based on a fixed point iteration applied to a sequence of deterministic power flow problems. However, a priori, the convergence of such an approach is not necessarily guaranteed. This article analyses the convergence conditions for this fixed point approach, and reports numerical experiments including for large IEEE networks. [ABSTRACT FROM AUTHOR]

We propose a chance-constrained formulation for the problem of dimensioning frequency restoration reserves on a power transmission network. We cast our problem as a two-stage stochastic mixed integer linear program, and propose a heuristic algorithm for solving the problem. Our model accounts for the simultaneous sizing of both upward and downward reserves, and uncertainty driven by imbalances, contingencies and available transmission capacity. Our core methodology is further adapted in order to minimize inter-zonal flows and in order to split reserve requirements between automatic and manual frequency restoration reserves. We apply our methodology to the problem of sizing reserves in the four load frequency control areas of the Swedish power system. We demonstrate the benefits of our method in terms of decreasing reserve requirements in the absence of reserve sharing, we analyze the spatial allocation of reserves, and we perform various sensitivity analyses. [ABSTRACT FROM AUTHOR]

This paper designs a model predictive control (MPC) law for constrained linear systems with stochastic additive disturbances and noisy measurements, minimising a discounted cost subject to a discounted expectation constraint. It is assumed that sensor data is lost with a known probability. Taking into account the data losses modelled by a Bernoulli process, we parameterise the predicted control policy as an affine function of future observations and obtain a convex linear-quadratic optimal control problem. Constraint satisfaction and a discounted cost bound are ensured without imposing bounds on the distributions of the disturbance and noise inputs. In addition, the average long-run undiscounted closed loop cost is shown to be finite if the discount factor takes appropriate values. We analyse robustness of the proposed control law with respect to possible uncertainties in the arrival probability of sensor data and we bound the impact of these uncertainties on constraint satisfaction and the discounted cost. Numerical simulations are provided to illustrate these results. [ABSTRACT FROM AUTHOR]

We present an adaptive grid refinement algorithm to solve probabilistic optimization problems with infinitely many random constraints. Using a bilevel approach, we iteratively aggregate inequalities that provide most information not in a geometric but in a probabilistic sense. This conceptual idea, for which a convergence proof is provided, is then adapted to an implementable algorithm. The efficiency of our approach when compared to naive methods based on uniform grid refinement is illustrated for a numerical test example as well as for a water reservoir problem with joint probabilistic filling level constraints. [ABSTRACT FROM AUTHOR]

Intelligent home energy management system (IHEMS) manages various home appliances depending on user preferences in order to save energy cost and assure user satisfaction. To realize cooperation between the distribution system operator (DSO) and end-user, a two-stage scheduling optimization model is developed based on the flexibility quantification, with the user privacy in demand-side management in a specific cluster taken into account. It also aids to reduce the network operation cost, and the distribution system's uncertainty caused by wind power is represented using chance constraints. The user uploads the IHEMS-calculated offered flexibility to DSO via cluster; DSO optimizes the optimal flexibility to minimize the operation cost; then, clusters distribute the flexibility requirement based on the flexibility index; finally, the user updates the optimal schedule. The numerical results using MATLAB are provided to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Most state-of-the-art algorithms for the Vehicle Routing Problem, such as Branch-and-Price algorithms or meta heuristics, rely on a fast feasibility test for a given route. We devise the first approach to approximately check feasibility in the Stochastic Vehicle Routing Problem with time windows, where travel times are correlated and depend on the time of the day. Assuming jointly normally distributed travel times, we use a chance constraint approach to model feasibility, where two different application scenarios are considered, depending on whether missing a customer makes the rest of the route infeasible or not. The former case may arise, e.g., in drayage applications or in the pickup-and-delivery VRP. In addition, we present an adaptive sampling algorithm that is tailored for our setting and is much faster than standard sampling techniques. We use a case study for both scenarios, based on instances with realistic travel times, to illustrate that taking correlations and time dependencies into account significantly improves the quality of the solutions, i.e., the precision of the feasibility decision. In particular, the nonconsideration of correlations often leads to solutions containing infeasible routes. [ABSTRACT FROM AUTHOR]

• Novel constrained grey-box optimization framework using Gaussian process models. • New almost everywhere differentiable acquisition function for composite functions. • Efficient moment-based approximation of chance constraints. • Tailored algorithm for enrichment sub-problem that exploits model structure. • Performance comparison with Bayesian optimization on diverse set of test problems. [Display omitted] Many engineering problems involve the optimization of computationally expensive models for which derivative information is not readily available. The Bayesian optimization (BO) framework is a particularly promising approach for solving these problems, which uses Gaussian process (GP) models and an expected utility function to systematically tradeoff between exploitation and exploration of the design space. BO, however, is fundamentally limited by the black-box model assumption that does not take into account any underlying problem structure. In this paper, we propose a new algorithm, COBALT, for constrained grey-box optimization problems that combines multivariate GP models with a novel constrained expected utility function whose structure can be exploited by state-of-the-art nonlinear programming solvers. COBALT is compared to traditional BO on seven test problems including the calibration of a genome-scale bioreactor model to experimental data. Overall, COBALT shows very promising performance on both unconstrained and constrained test problems. [ABSTRACT FROM AUTHOR]

Motion primitive planning under parametric uncertainty may be modeled as a chance-constrained Markov Decision Process (CCMDP). Single-query solutions to CCMDPs can be obtained by searching the And/Or graph representing the state–action space of the system. The Risk-bounded AO* (RAO*) algorithm has been proposed as a solution method for this problem, but it scales poorly to MDPs resulting from a motion primitive discretization because it has no mechanism to prioritize expansion of AND nodes. This paper describes an induced heuristic for state–action pairs that can be rapidly computed by leveraging the properties of motion primitives; its value can be used to prioritize AND nodes for more efficient search. Search is further accelerated by leveraging shared symmetry in constraints and dynamics to move almost all computation necessary to enforce convex polytope constraints offline. The performance improvements are demonstrated with path planning problems involving a Dubins Car and a nonlinear aircraft model. • Motion primitives discretize vehicle action set while retaining high performance. • Koopman operator based expected value calculations combine with primitives. • And/Or graph search techniques produce optimal chance constrained primitive plans. • A novel admissible heuristic accelerates the presented algorithm by a factor of 15. [ABSTRACT FROM AUTHOR]

The increasing complexity of modern technical systems can exacerbate model uncertainty in model-based control, posing a great challenge to safe and effective system operation under closed loop. Online learning of model uncertainty can enhance control performance by reducing plant–model mismatch. This article presents a learning-based stochastic model predictive control (LB-SMPC) strategy for reference tracking of stochastic linear systems with additive state-dependent uncertainty. The LB-SMPC strategy adapts the state-dependent uncertainty model online to reduce plant–model mismatch for control performance optimization. Standard reachability and statistical tools are leveraged along with the state-dependent uncertainty model to develop a chance constraint-tightening approach, which ensures state constraint satisfaction in probability. The stability and recursive feasibility of the LB-SMPC strategy are established for tracking time-varying targets, without the need to redesign the controller every time the target is changed. The performance of the LB-SMPC strategy is experimentally demonstrated on an atmospheric pressure plasma jet (APPJ) testbed with prototypical applications in plasma medicine and materials processing. Real-time control comparisons with learning-based MPC with no uncertainty handling and offset-free MPC showcase the usefulness of LB-SMPC for predictive control of safety-critical systems with hard-to-model and/or time-varying dynamics. [ABSTRACT FROM AUTHOR]