Stochastic Optimization Framework Research Articles

Simultaneous stochastic optimisation of mining complexes: Integrating progressive reclamation and waste management with contextual bandits

ABSTRACT Managing environmental performance of waste dump facilities in mining complexes is an integral part of long-term production planning. Sustainable long-term production scheduling solutions are desired to mitigate risk and return the environment to a productive post-mining state. A simultaneous stochastic optimisation framework for long-term production scheduling in mining complexes is developed that integrates waste management and progressive reclamation. The waste dump placement schedule is jointly optimised with the extraction sequence, destination policy, and stockpiling decisions in a single stochastic mathematical programming framework. This includes the timing of progressive reclamation activities in parallel with production to enhance waste dump rehabilitation. Uncertainty related to the production of acid rock drainage is quantified by simulating geochemical properties of waste and managing the blending of uncertain waste properties within the optimisation framework. With respect to the framework for simultaneous stochastic optimisation, contextual bandits are explored to improve the metaheuristic solution approach and solve the corresponding large-scale optimisation model. The framework is tested in a multi-mine copper-gold mining complex leading to improved environmental performance. Risk of acid rock drainage is decreased by 52.5% in the waste dump facilities. Reclamation planning activities for meeting environmental requirements are scheduled prior to closure. The solution approach more effectively improves the objective function with contextual bandits leading to a 24% improvement in the study presented.

BM-RCWTSG: An integrated matching framework for electric vehicle ride-hailing services under stochastic guidance

Electric vehicles (EVs) are playing an increasingly vital role in sustainable ride-hailing services, primarily due to their potential to reduce carbon emissions and enhance environmental well-being. A core service of ride-hailing platforms is to match riders with nearby drivers within a short time window. In this mandate, it is crucial to ensure a high matching rate and low rider waiting time since these are key indicators of customer satisfaction and the platform’s operational effectiveness. However, existing matching mechanisms in the literature failed to consider important aspects related to EVs, including the range limit, charging detour time, and charging waiting time. These factors can significantly affect the system matching rate, rider waiting time, and vehicle utilization rate. To address the new challenges of the increased adoption of EVs in ride-hailing services, we propose a data-driven stochastic optimization framework for EV ride-hailing matching. The proposed framework integrates two stochastic optimization models, namely the stochastic guidance (SG) model and the EV matching (EVM) model. The SG model optimizes EV relocation and improves the system matching rate by proactively guiding idle EVs to the designated regions based on probabilistic rider demand forecasting. The EVM model utilizes the relocated EVs and current rider demands to provide the optimal matching solution that minimizes the overall cost associated with rider waiting time, EV charging waiting time, and charging detours. We conduct experimental validation of this approach using two real-world data sets from New York City. Comparative results suggest that by utilizing the proposed framework, the matching rate can be increased up to 22.9%, and the rider and EV waiting times can be reduced up to 14.9% and 73.6%, respectively, compared to the benchmark models.

A two-stage stochastic optimization framework for retail supply chain modeling with contemporaneous resilient strategies

A two-stage stochastic optimization framework for retail supply chain modeling with contemporaneous resilient strategies

A reinforcement learning approach for selecting infill drilling locations considering long-term production planning in mining complexes with supply uncertainty

Simultaneous stochastic optimisation frameworks provide a method for optimising long-term production schedules in mining complexes that aim to maximise net present value and manage risk related to supply uncertainty. The uncertainty and local variability related to the quality and quantity of material in the mineral deposits are modelled with a set of stochastic orebody simulations, an input into the simultaneous stochastic optimisation framework. Infill drilling provides opportunities to collect additional information associated with the mineral deposits, which can inform future production scheduling decisions. A framework is developed for optimising infill drilling locations with a criterion that seeks areas that directly affect long-term planning decisions and requires the use of geostatistical simulations. Actor-critic reinforcement learning is applied to identify infill drilling locations in a copper mining complex using this criterion. The case study demonstrates that adapting production scheduling decisions given additional information has the potential to improve the associated production and financial forecasts and identifies a stable area for infill drilling.

Stochastic optimization framework for hybridization of existing offshore wind farms with wave energy and floating photovoltaic systems

Due to the complementarity of renewable energy sources, there has been a focus on technology hybridization in recent years. In the area of hybrid offshore power plants, the current research projects mostly focus on the combinational implementation of wind, solar, and wave energy technologies. Accordingly, considering the already existing offshore wind farms, there is the potential for the implementation of hybrid power plants by adding wave energy converters and floating photovoltaics. In this work, a stochastic sizing model is developed for the hybridization of existing offshore wind farms using wave energy converters and floating photovoltaics considering the export cable capacity limitation. The problem is modeled from an investor perspective to maximize the economic profits of the hybridization, while the costs and revenues regarding the existing units and the export cable are excluded. Furthermore, to tackle the uncertainties of renewable energy generation, as well as the energy price, a scenario generation method based on copula theory is proposed to consider the dependency structure between the different random variables. Altogether, the hybridization study is modeled in a mixed integer linear programming optimization framework considering the net present value of the project as the objective function. The results showed that hybrid-sources-based energy generation provided the highest economic profit in the studied cases in the different geographical locations. Furthermore, the technical specifications of the farms have also been considerably improved providing more stable energy generation, guaranteeing a minimum level of power in a high share of the time, and with a better utilization of the capacity of the cable while the curtailment of energy is maintained within the acceptable range.

Techno-economic assessment of isolated micro-grids with second-life batteries: A reliability-oriented iterative design framework

Reusing lithium-ion batteries retired from electric vehicles (EVs) has received great attention as the performance of these batteries is still adequate for many stationary energy storage applications, such as micro-grids (MGs). To date, the economic and technical performance of second-life batteries (SLBs) in isolated MG systems remains obscure. Hence, this study focuses on the economic assessment of SLBs in an isolated 100% renewable MG, in order to identify a profitable application that promotes SLBs. The MG capacity design parameters are obtained by a two-stage chance-constrained stochastic optimization framework. To enhance the robustness of the MG design, a reliability-oriented iterative design process is proposed. This process involves continuous updates to the MG design, guided by validation results, until all specified requirements are satisfied. The lifetime of SLBs is determined using a semi-empirical degradation model seamlessly integrated into the validation process. Economic comparisons between SLBs and first-life batteries (FLBs) are conducted under identical design requirements, with consideration given to estimating the “price ceiling” and the impact of market factors. The results show that SLBs prove to be a more cost-effective option, especially when there is a demand for high reliability standards and the local electricity prices are comparatively lower.

A Two-Time-Scale Stochastic Optimization Framework with Applications in Control and Reinforcement Learning

A Two-Time-Scale Stochastic Optimization Framework with Applications in Control and Reinforcement Learning

A stochastic optimization framework to planing for geographically correlated failures in coupled natural gas and electric power systems

We develop a transmission planning framework for coupled natural gas and electric power systems facing geographically correlated failures. The framework uses a stochastic optimization method incorporating uncertainty in the locations of the geographically correlated failures. We compare the proposed planning framework with the traditional N-k method which plans for geographically uncorrelated failures in terms of improving resilience effectively against geographically correlated failures. The proposed planning framework is illustrated using a small test system, but is scalable to larger system sizes and portable to other coupled-infrastructure contexts. We illustrate how planning for geographically correlated failures can enhance system-wide robustness by reinforcing the network connectivity between supply and demand locations instead of addressing local vulnerability at specific locations when planning for geographically uncorrelated failures. Planning for geographically correlated failures improves system resilience to both geographically correlated and uncorrelated failures significantly, but the converse is not true in our case study.

A high-order target phase approach for the station-keeping of periodic orbits

A novel high-order target phase approach (TPhA) for the station-keeping of periodic orbits is proposed in this work. The key elements of the TPhA method, the phase-angle Poincare map and high-order maneuver map, are constructed using differential algebra (DA) techniques to determine station-keeping epochs and calculate correction maneuvers. A stochastic optimization framework tailored for the TPhA-based station-keeping process is leveraged to search for fuel-optimal and error-robust TPhA parameters. Quasi-satellite orbits (QSOs) around Phobos are investigated to demonstrate the efficacy of TPhA in mutli-fidelity dynamical models. Monte Carlo simulations demonstrated that the baseline QSO of JAXA’s Martian Moons eXploration (MMX) mission could be maintained with a monthly maneuver budget of approximately 1 m/s.

Stochastic bandgap optimization for multiscale elastic metamaterials with manufacturing imperfections

Bandgaps are endowed to elastic metamaterials (EMMs) attributed to the rationally designed unit cells and extensive works are devoted to bandgap enlargement for improving the applicability of EMMs in multi-disciplinary applications. Nonetheless, most existing optimization frameworks neglect manufacturing imperfections, such as microscale heterogeneity and system uncertainties, which can significantly affect bandgap behaviors. Without properly accounting for these effects, the design may fail to achieve the optimal goal, exhibiting consistently ultra-wide wave attenuation bands in practical EMMs. Herein, in this paper, a stochastic bandgap optimization framework is developed for EMMs involving manufacturing imperfections, aiming at optimizing the first two statistical moments of the normalized bandwidth (NB) simultaneously. To alleviate the large computational costs in approximating statistical moments, a surrogate model is employed to reveal the constitutive relationship between system parameters and NB for the multiscale EMM. Moreover, to solve the optimization problem effectively and efficiently, a high-order mutation strategy is proposed to develop an improved particle swarm optimization (PSO) variant, namely the adaptively high-order mutation-based PSO (AHMPSO). To demonstrate the viability and efficiency of the proposed framework, a numerical investigation is implemented on a 3D EMM, which highlights enlarged bandwidths coupling with an improvement in the robustness of optimum.

A machine learning-based stochastic optimal energy management framework for a renewable energy-assisted isolated microgrid system

ABSTRACT This paper proposes a cost-based stochastic optimal energy management framework for a renewable energy-assisted isolated microgrid system. These microgrids encourage the integration of multiple distributed energy sources, including the penetration of renewable energy. For this purpose, the optimal day-ahead dispatch of the connected energy resources is obtained for an economically viable system by solving a nonlinear constrained optimization problem. The renewable energy and the load demand data forecasting are accomplished using the Gaussian process regression learning model in the MATLAB/SIMULINK® environment for obtaining the day-ahead dispatch. The optimal problem is solved through sequential quadratic programming and a hybrid function approach incorporating particle swarm optimization for a comprehensive techno-economical analysis. A comparative assessment of the results is accomplished to obtain a more feasible and economical system operation corresponding to different time horizons and other critical factors such as fast iterations, computational accuracy, solution feasibility, convergence rate, etc.

Stochastic Optimization Framework for Realizing Combined Value Streams From Customer-Side Resources–Self Service and Distribution System Operations

Customer-side resources are becoming increasingly crucial in grid modernization and transitioning to a sustainable energy future. Although most load-serving entities (LSEs) typically consider customer-side resources for single applications, these resources can be used for multiple applications simultaneously. This paper proposes a stochastic optimization framework to help LSEs capture multiple value streams from customer-side resources within their network. Specifically, we consider self-service applications – peak shaving, energy arbitrage, ramp rate reduction – and distribution system operational applications – loss reduction and voltage management. The framework is also adapted to handle the impacts of the activities of third-party aggregators on the LSE’s network. We also evaluate the performance of two algorithms – decision rule-based and optimal real-time dispatch -for dispatching the customer-side resources in the face of different sources and levels of uncertainty. Simulations were run using modified IEEE test systems within the OpenDSS simulation tool. The results show the value of customer-side resources can be maximized when multiple applications are simultaneously considered, and that value increases with increasing levels of forecast uncertainties.

Maximizing techno-economic-environmental benefits of renewable energy allocation with smart inverter in distribution system: a two-layer stochastic optimization framework

ABSTRACT The rapid proliferation of renewable energy sources (RES), such as photovoltaic (PV) generation and wind generation, poses severe challenges to distribution systems. Their intermittent nature leads to voltage profile deterioration and significant losses. Allocating RES with a smart inverter is a promising solution to address these issues. This study introduces an integrated two-layer stochastic optimization framework for RES allocation with a smart inverter in active distribution networks, aiming for techno-economic-environmental benefits. The methodology comprises a lower and upper-layer optimization model representing decisions at operational and planning levels, respectively. Additionally, the effect of volt ampere reactive (VAR) control and demand response (DR) on RES allocation with a smart inverter is investigated. A multi-level improved chimp optimization algorithm (IChOA) solver is developed to handle the nonlinear mixed-integer programming issue. The suggested methodology is validated on the IEEE 119-bus radial distribution system and the Practical System Indian 52-bus system. The assessment’s findings reveal the significance of the stochastic methodology, achieving a 48.18% and 45.95% reduction in total cost for the IEEE 119-bus radial distribution system and the Practical System Indian 52-bus system, respectively. The proposed methodology offers a promising approach to effectively and efficiently manage RES integration into distribution systems.

Two-layer multiple scenario optimization framework for integrated energy system based on optimal energy contribution ratio strategy

Rational design and advanced energy management considering multiple uncertainties are imperative for the superior integrated energy system (IES). This work proposed a novel two-layer stochastic multiple scenario optimization framework for the collaborative optimization of capacity and operation of IES. To improve the accuracy of probability density estimation, the improved kernel density estimation (KDE) was employed to obtain the probability density distributions of wind speed, sunlight and multi-demands. Then the scenario sets were generated by Latin hypercube sampling (LHS) simulation and self-organization map (SOM) clustering. To decouple the output, efficiency and part load factor of devices during operation, the following optimal contribution rate (FOCR) strategy was proposed, which could actively adjust the output ratio of energy conversion devices to realize the flexible energy supply. The developed optimization methodology was used for a case study in an office building. The results indicate that the improved KDE for probability distribution estimation of uncertainties achieves the accuracy percentage enhancement, for the average value, of 37.1% and 49.6% for root-mean-square error (RMSE), respectively, compared with the conventional KDE and parametric model. Considering energy saving, economy and environmental indicators, the performance of the FOCR strategy is superior to those of the three traditional strategies.

Potential Welfare Gains from Optimal Macro Hedging for Oil Exporters

This paper computes the welfare gains from optimal hedging with futures contracts for an oil-exporting country. Unlike previous studies, this paper derives the welfare gains under a more realistic futures hedging model. This is accomplished by considering basis risk and by relaxing the full-hedging assumption. Furthermore, this is the first paper to derive the welfare gains under optimal hedging strategies. We also incorporate the empirical relationship between spot and futures prices within our models, rather than the theoretical relationship which most studies employ. The models were developed under a dynamic stochastic optimization framework and the optimal consumption and value functions were found using the method of Endogenous Gridpoints. The results showed that the choice of the optimal hedging strategy employed led to a slight improvement in the country’s welfare gains relative to full hedging. We also found that the strategies with the highest welfare gains were the most effective at volatility reduction. Finally, this paper provides compelling evidence for the use of optimal macro futures hedging as an effective risk management tool for oil-exporting developing countries.

Learning When to Use Adaptive Adversarial Image Perturbations Against Autonomous Vehicles

Deep neural network (DNN) models are widely used in autonomous vehicles for object detection using camera images. However, these models are vulnerable to adversarial image perturbations. Existing methods for generating these perturbations use the image frame as the decision variable, resulting in a computationally expensive optimization process that starts over for each new image. Few approaches have been developed for attacking online image streams while considering the physical dynamics of autonomous vehicles, their mission, and the environment. To address these challenges, we propose a multi-level stochastic optimization framework that monitors the attacker's capability to generate adversarial perturbations. Our framework introduces a binary decision attack/not attack based on the attacker's capability level to enhance its effectiveness. We evaluate our proposed framework using simulations for vision-guided autonomous vehicles and actual tests with a small indoor drone in an office environment. Our results demonstrate that our method is capable of generating real-time image attacks while monitoring the attacker's proficiency given state estimates.

Optimization of isocenter position for multiple brain metastases single-isocenter stereotactic radiosurgery to minimize dosimetric variations due to rotational uncertainty

PurposeThis paper studied a novel calculation framework that can determine the optimal value isocenter position of single isocenter SRS treatment plan for multiple brain metastases, in order to minimize the dosimetric variations caused by rotational uncertainty. Materials and methods21 patients with 2–4 GTVswho received SRS treatment for multiple brain metastases in our institution were selected for the retrospective study. The PTVwas obtained by expanding GTV 1 mm isotropic margin. We studied a stochastic optimization framework, which determined the optimal value isocenter location by maximizing the average target dose coverageCtarget,meanwith a rotation error of no more than 1°. We evaluated the performance of the optimal isocenter by comparing theCtarget,meanand average dice similarity coefficient (DSC)with the optimal value and the center of mass (CM) respectively as the treatment isocenter. The extra PTV margin to achieve 100% target dose coverage was calculated by our framework. ResultsCompared to the CM method, the optimal value isocenter method increased the averageCtarget,meanof all targets from 97.0% to 97.7%and the average DSC from 0.794to 0.799. Throughout all the cases, the average extra PTV margin to obtain full target dose coverage was 0.7 mmwhen using the optimal value isocenter as the treatment isocenter. ConclusionWe studied a novel computational framework using stochastic optimization to determine the optimal isocenter position of SRS treatment plan for multiple brain metastases. At the same time, our framework gave the extra PTV margin to obtain full target dose coverage.

A two-stage stochastic optimization framework to allocate operating room capacity in publicly-funded hospitals under uncertainty.

Surgery demand is an uncertain parameter in addressing the problem of surgery block allocations, and its typical variability should be considered to ensure the feasibility of surgical planning. We develop two models, a stochastic recourse programming model and a two-stage stochastic optimization (SO) model with incorporated risk measure terms in the objective functions to determine a planning decision that is made to allocate surgical specialties to operating rooms (ORs). Our aim is to minimize the costs associated with postponements and unscheduled demands as well as the inefficient use of OR capacity. The results of these models are compared using a case of a real-life hospital to determine which model better copes with uncertainty. We propose a novel framework to transform the SO model based on its deterministic counterpart. Three SO models are proposed with respect to the variability and infeasibility of the measures of the objective function to encode the construction of the SO framework. The analysis of the experimental results demonstrates that the SO model offers better performance under a highly volatile demand environment than the recourse model. The originality of this work lies in its use of SO transformation framework and its development of stochastic models to address the problem of surgery capacity allocation based on a real case.

Concurrent multi-peak Bragg coherent x-ray diffraction imaging of 3D nanocrystal lattice displacement via global optimization

In this paper we demonstrated a method to reconstruct vector-valued lattice distortion fields within nanoscale crystals by optimization of a forward model of multi-reflection Bragg coherent diffraction imaging (MR-BCDI) data. The method flexibly accounts for geometric factors that arise when making BCDI measurements, is amenable to efficient inversion with modern optimization toolkits, and allows for globally constraining a single image reconstruction to multiple Bragg peak measurements. This is enabled by a forward model that emulates the multiple Bragg peaks of a MR-BCDI experiment from a single estimate of the 3D crystal sample. We present this forward model, we implement it within the stochastic gradient descent optimization framework, and we demonstrate it with simulated and experimental data of nanocrystals with inhomogeneous internal lattice displacement. We find that utilizing a global optimization approach to MR-BCDI affords a reliable path to convergence of data which is otherwise challenging to reconstruct.

Stochastic Framework for Optimal Control of Planetary Reentry Trajectories Under Multilevel Uncertainties

We present a novel stochastic optimal control framework that accounts for various types of uncertainties, with application to reentry trajectory planning. The formulation of the optimal trajectory control problem is presented in the context of an indirect method where a functional objective associated with the terminal vehicle speed is to be minimized. Uncertain input parameters in the optimal trajectory control model, including aerodynamic parameters and initial and terminal conditions, are modeled as aleatory random variables, while the statistical parameters of these aleatory distributions are themselves random variables. The parametric and model uncertainties are simultaneously propagated through an extended polynomial chaos expansion (EPCE) formalism. Several metrics are described to evaluate response statistics and presented as insightful tools for robust decision making. Specifically, the response probability density function (PDF) reflecting influence of both epistemic and aleatory uncertainties is obtained. By sampling over the random variables representing model error, an ensemble of response PDFs is generated and the associated failure probability is estimated as a random variable with its own polynomial chaos expansion. Besides, the sensitivity index functions of response PDF with respect to the statistical parameters are evaluated. Coupling parametric and model uncertainties within the EPCE framework leads to a robust and efficient paradigm for multilevel uncertainty propagation and PDF characterization in general optimal control problems.