Stochastic Optimization Approach Research Articles

An Integrated Stochastic Optimization and Simulation Approach to SERU vs. Assembly Line Manufacturing Systems

This research compares SERU manufacturing systems to traditional assembly lines, focusing on the impact of uncertainty in task processing time on production output. The study considers worker skill levels and team identity, using a stochastic mixed integer linear programming approach to model uncertainty and optimize workforce allocation. Discrete event simulation is then integrated to evaluate performance using five key performance indicators (KPIs). Results show that SERU systems outperform traditional lines in terms of throughput when uncertainty is considered. The integrated approach provides more reliable performance data than deterministic optimization alone. The study also highlights the advantages of SERU systems when worker skill levels and team identity are factored in. This research fills a gap in the literature by proposing a stochastic optimization approach that considers uncertainty and worker skill levels, and by integrating stochastic optimization with simulation for comprehensive analysis. This approach provides valuable guidance for production managers in optimizing production systems.

Studies on effective solar photovoltaic integration in distribution network with a blend of Monte Carlo simulation and artificial hummingbird algorithm

AbstractIn this paper, the two level stochastic optimisation approach has been suggested. In the lower level, the probability distribution functions (pdfs) for bus voltages and branch currents have been determined using the Monte Carlo simulation (MCS) to be employed in chance‐constrained probabilistic optimisation by taking into account solar radiation and power consumption uncertainties in the distribution networks (DNs). In the upper level, artificial hummingbird algorithm (AHA) handles the expected power loss minimisation subjected to chance constraints, which are related to bus voltages and branch currents, by optimising photovoltaic (PV) system capacities. This research examines the effect of uncertainties in PV system performing under diverse solar radiation and varying PV penetration level scenarios on expected power losses with stochastic DN limits. The stochastic optimisation approach has been compared with the deterministic method for observing the efficiency with optimal power usage. This research improves the knowledge base for optimal PV installation in DN by combining AHA with MCS and emphasising chance‐constrained methods. To indicate the efficacy of proposed strategy, the optimisation outcomes are tested utilising MCS under various uncertainty circumstances and DN parameters are assessed in terms of probabilities of exceeding limitations. The results are compared with the application of firefly algorithm (FA) using stochastic assessment and simulations. The simulation results show that the AHA technique outperforms the FA method in terms of effectively minimising power losses with less simulation time.

A Sample Average Approximation Approach for Stochastic Optimization of Flight Test Planning with Sorties Uncertainty

In the context of flight test planning, numerous uncertainties exist, encompassing aircraft status, number of flights, and weather conditions, among others. These uncertainties ultimately manifest significantly in the actual number of flight sorties executed, rendering high significance to engineering problems related to the execution of flight test missions. However, there is a dearth of research in this specific aspect. To address this gap, this paper proposes an opportunity-constrained integer programming model tailored to the unique characteristics of the problem. To handle the uncertainties, Sample Average Approximation (SAA) is employed to perform oversampling of the uncertain parameters, followed by the Adaptive Large Neighborhood Search (ALNS) algorithm to solve for the optimal solution and objective function value. Results from numerical experiments conducted at varying scales and validated with diverse sampling distributions demonstrate the effectiveness and robustness of the proposed methodology. By decoding the generated execution sequences, comprehensive mission planning schemes can be derived. This approach yields sequences that exhibit commendable feasibility and robustness for the flight test planning problem with sorties uncertainty (FTPPSU), offering valuable support for the efficient execution of future flight test missions.

Budget allocation problem for projects with considering risks, robustness, resiliency, and sustainability requirements

Budget Allocation Problem (BAP) for projects is considered one of the critical risks that necessitate the completion of projects in the shortest possible duration. This aspect is significant in extensive projects such as national endeavors directly impacting people's livelihoods. This research focuses on introducing Sustainable, Robust, Resilient, and Risk-averse Budget Allocation for Projects (S3RBAP). A hybrid robust stochastic optimization approach was employed, incorporating Weighted VaR (WVaR) and the minimum function as risk criteria to ensure the robustness of the objective function. This model is designed to minimize the weighted expected value, WVaR, and the minimum progress function, thereby promoting the 3R and sustainability framework to tackle budget fluctuations and enhance project viability. The case study revolves around the construction of national projects in Iran. Ultimately, the project's required budget was allocated within the budgetary constraints. Sensitivity analysis found that the integration of 3R and sustainability led to a 13.5 % reduction in the progress function compared to scenarios without these principles. Furthermore, increasing the conservatism coefficient to 20 % decreased the progress function to −0.58 %. Reducing the resiliency coefficient had an adverse effect by disrupting the budget allocation process. The computational time is increased gradually with the escalation of problem complexity, while the progress function decreases due to the increased number of projects. The findings demonstrate that using an exponential function promotes risk aversion, whereas a sine function encourages risk-seeking behaviour within this research context.

A Retrospective Approximation Approach for Smooth Stochastic Optimization

Stochastic Gradient (SG) is the de facto iterative technique to solve stochastic optimization (SO) problems with a smooth (nonconvex) objective f and a stochastic first-order oracle. SG’s attractiveness is due in part to its simplicity of executing a single step along the negative subsampled gradient direction to update the incumbent iterate. In this paper, we question SG’s choice of executing a single step as opposed to multiple steps between subsample updates. Our investigation leads naturally to generalizing SG into Retrospective Approximation (RA), where, during each iteration, a “deterministic solver” executes possibly multiple steps on a subsampled deterministic problem and stops when further solving is deemed unnecessary from the standpoint of statistical efficiency. RA thus formalizes what is appealing for implementation—during each iteration, “plug in” a solver—for example, L-BFGS line search or Newton-CG—as is, and solve only to the extent necessary. We develop a complete theory using relative error of the observed gradients as the principal object, demonstrating that almost sure and L1 consistency of RA are preserved under especially weak conditions when sample sizes are increased at appropriate rates. We also characterize the iteration and oracle complexity (for linear and sublinear solvers) of RA and identify a practical termination criterion leading to optimal complexity rates. To subsume nonconvex f, we present a certain “random central limit theorem” that incorporates the effect of curvature across all first-order critical points, demonstrating that the asymptotic behavior is described by a certain mixture of normals. The message from our numerical experiments is that the ability of RA to incorporate existing second-order deterministic solvers in a strategic manner might be important from the standpoint of dispensing with hyper-parameter tuning. Funding: R. Pasupathy received financial support from the Office of Naval Research [Grants N000141712295 and 13000991]. R. Bollapragada received financial support from the Lawrence Livermore National Laboratory and the National Science Foundation [Grant NSF DMS 2324643].

Comparing resilience strategies for a multistage green supply chain to mitigate disruptions: A two-stage stochastic optimization model

Supply chain disruptions, notably exemplified by the COVID-19 pandemic, have substantial impacts, requiring effective resilience strategies. This study introduces a comprehensive multi-stage, multi-period green supply chain design model, incorporating six resilience strategies to tackle downstream and upstream disruptions. A rigorous two-stage stochastic optimization approach is employed to manage parameter uncertainties and disruptions. The objectives include minimizing disruption costs and CO2 emissions, for a chain that operates under cap-and-trade emission regulation. The findings, derived from a numerical experiment and sensitivity analysis, offer the optimal supply chain structure and effective resilience strategies to mitigate disruptions. The demand structure for essential and non-essential products during disruptions are explored, emphasizing proactive resource allocation. In particular, the impact of facility capacity reductions underscores the importance of capacity management. Sensitivity analyses reflect the trade-offs involved in capacity management strategies, emphasizing the critical need to maintain an optimal level of capacity to prevent service level degradation. Additionally, examination of carbon abatement regulations reveals the intricate balance between environmental responsibility and economic efficiency. In summary, this study addresses supply chain disruptions and offers actionable insights for supply chain managers and policy makers. The research highlights the importance of specific and data-driven resilience strategies to optimize supply chain performance in face of disruptions.

Designing a resilient reverse network to manage the infectious healthcare waste under uncertainty: A stochastic optimization approach

The global expansion of healthcare facilities has resulted in increased levels of infectious-hazardous waste, posing serious threats to the environment and public health. Existing waste management systems can become overwhelmed during health crises, such as epidemics or natural disasters, exacerbating the problem. This study formulates a mixed-integer linear programming model for developing a resilient infectious waste management reverse network during the outbreak of the COVID-19 pandemic. Health crisis are unpredictable in nature and it is almost impossible to predict their exact behavior. Therefore, in this paper, the uncertainty of ambiguous parameters is considered using a scenario-oriented approach. To make the proposed model resilient, three strategies, including establishing new collection centers, overtime, and cooperation with third-party logistics, are introduced. The results derived from running the developed model in GAMS software using the case study data showed that the active collection center cannot serve the network alone, and to make the network more resilient, the strategy of establishing a new collection center should be selected. The findings validate the model’s utility in designing a resilient waste management network during a health crisis, emphasizing the importance of resilience in infectious healthcare waste management networks.

Dispatch strategies for large-scale heat pump based district heating under high renewable share and risk-aversion: A multistage stochastic optimization approach

Heat pumps play an essential role in decarbonizing the heating sector, and their adoption is projected to rise significantly. The high share of large-scale heat pumps in district heating exposes heating utilities to uncertainty in electricity markets. This challenge is further exacerbated by 1) future high share of renewable energy resulting in increased uncertainty of electricity prices, and 2) introduction of voluntary energy bids for balancing energy markets (or regulation market). Despite the importance of this issue, little research has been conducted to address it. Therefore, this paper investigates the optimal dispatch of large-scale heat pump based district heating by adopting multi-stage stochastic optimization approach to minimize the total expected heat generation cost, taking sequential electricity markets prices as stochastic. We also evaluate the impact of high renewable energy penetration on this optimal dispatch strategy. Furthermore, we include the risk preference of district heating operator by using conditional value at risk in the objective function. We conclude that heat pump should be coupled with flexible technologies like electric boilers as more renewable energy and balancing market trading increases flexible units' dispatch. Also, most of the heat produced (50%) in our case study is used flexibly via thermal storage. We find more renewable could lead to negative expected costs and voluntary bids in balancing market further reduces the expected cost by 28–59%. Furthermore, trading risk increases significantly with renewable energy penetration, which can be mitigated to a limited extent by bidding in up and down balancing market. Risk aversion shifts trading from intraday to day-ahead market and promotes heat pump dispatch.

Advanced OCTA imaging segmentation: Unsupervised, non-linear retinal vessel detection using modified self-organizing maps and joint MGRF modeling

Background and Objective:This paper proposes a fully automated and unsupervised stochastic segmentation approach using two-level joint Markov-Gibbs Random Field (MGRF) to detect the vascular system from retinal Optical Coherence Tomography Angiography (OCTA) images, which is a critical step in developing Computer-Aided Diagnosis (CAD) systems for detecting retinal diseases. Methods:Using a new probabilistic model based on a Linear Combination of Discrete Gaussian (LCDG), the first level models the appearance of OCTA images and their spatially smoothed images. The parameters of the LCDG model are estimated using a modified Expectation Maximization (EM) algorithm. The second level models the maps of OCTA images, including the vascular system and other retina tissues, using MGRF with analytically estimated parameters from the input images. The proposed segmentation approach employs modified self-organizing maps as a MAP-based optimizer maximizing the joint likelihood and handles the Joint MGRF model in a new, unsupervised way. This approach deviates from traditional stochastic optimization approaches and leverages non-linear optimization to achieve more accurate segmentation results. Results:The proposed segmentation framework is evaluated quantitatively on a dataset of 204 subjects. Achieving 0.92 ± 0.03 Dice similarity coefficient, 0.69 ± 0.25 95-percentile bidirectional Hausdorff distance, and 0.93 ± 0.03 accuracy, confirms the superior performance of the proposed approach. Conclusions:The conclusions drawn from the study highlight the superior performance of the proposed unsupervised and fully automated segmentation approach in detecting the vascular system from OCTA images. This approach not only deviates from traditional methods but also achieves more accurate segmentation results, demonstrating its potential in aiding the development of CAD systems for detecting retinal diseases.

Deterministic Multi-Objective Optimization of Analog Circuits

Stochastic optimization approaches benefit from random variance to produce a solution in a reasonable time frame that is good enough for solving the problem. Compared with them, deterministic optimization methods feature faster convergence rates and better reproducibility but may get stuck at a local optimum that is insufficient to solve the problem. In this paper, we propose a group-based deterministic optimization method, which can efficiently achieve comparable performance to heuristic optimization algorithms, such as particle swarm optimization. Moreover, the weighted sum method (WSM) is employed to further improve our deterministic optimization method to be multi-objective optimization, making it able to seek a balance among multiple conflicting circuit performance metrics. With a case study of three common analog circuits tested for our optimization methodology, the experimental results demonstrate that our proposed method can more efficiently reach a better estimation of the Pareto front compared to NSGA-II, a well-known multi-objective optimization approach.

Prescriptive analytics for low and high water management in German waterways

Abstract The real-time management of multi-purpose storage reservoirs aims at an efficient operation of existing hydraulic infrastructure. This management process can be structured as a prescriptive analytics setup that considers both current and predicted system states to recommend actions and outline potential implications. In application to a reservoir and river system, it combines hydrological modelling components for the system schematization, observations and data assimilation for the identification of the current system state, meteorological and hydrological predictions as well as optimization-based techniques to support decision-making regarding reservoir operations. In this paper, we present the application of such a framework to the short-term management of the Eder and Diemel storage reservoirs. These reservoirs are operated by the German Federal Waterways and Shipping Administration (WSV) with the primary goal to support navigation in the River Weser during low flow periods. In addition, partially conflicting objectives such as flood protection, energy generation and recreation are considered. The implementation includes an explicit consideration of forecast uncertainty and its impact on the decision-making by using probabilistic forecasts in combination with a multi-stage stochastic optimization approach. We demonstrate the applicability of the approach based on low and high water use cases. Special attention is paid on the benefits of the probabilistic forecast in combination with the multi-stage stochastic optimization versus a deterministic setup. It provides an explicit translation of the forecast uncertainty in the decision variables, in this case the reservoir releases helping the operators to better anticipate the range of future release decisions. Furthermore, the stochastic approach is expected to provide more stable decisions in an operational setting, based on more stable forecasts by considering various possible realizations of the future instead of picking a single one, which gets random after 4–5 days.

Environmentally sustainable inventory control for perishable products: A bi-objective reorder-level policy

In order to improve sustainability and transparency in the decision making for inventory control, this paper presents a reorder-level model that considers product perishability. Conversely to most inventory control policies, the classical economic perspective is paired with an environmental one for a stochastic bi-objective optimization approach to reduce inventory logistics emissions and costs. In order to contrast stockouts, lost-sale costing and a service level constraint are integrated for a more comprehensive approach. Results show how the two objectives may be in contrast, and how Pareto-efficient solutions can help to analyze and select the proper trade-offs during decision making. Experiments indicate, for a case-study application, how the most relevant aspects affecting system performance are product shelf life and the possible need of temperature control during storage. Moreover, considering multiple sustainability perspectives in inventory management can help businesses consolidate and future-proof their operations, as well as meet environmental standards and customer demand for greener products and processes.

Multi-objective stochastic scheduling of inpatient and outpatient surgeries

AbstractWith the advancement of surgery and anesthesiology in recent years, surgical clinical pathways have changed significantly, with an increase in outpatient surgeries. However, the surgical scheduling problem is particularly challenging when inpatients and outpatients share the same operating room blocks, due to their different characteristics in terms of variability and preferences. In this paper, we present a two-phase stochastic optimization approach that takes into account such characteristics, considering multiple objectives and dealing with uncertainty in surgery duration, arrival of emergency patients, and no-shows. Chance Constrained Integer Programming and Stochastic Mixed Integer Programming are used to deal with the advance scheduling and the allocation scheduling, respectively. Since Monte Carlo sampling is inefficient for solving the allocation scheduling problem for large size instances, a genetic algorithm is proposed for sequencing and timing procedures. Finally, a quantitative analysis is performed to analyze the trade-off between schedule robustness and average performance under the selection of different patient mixes, providing general insights for operating room scheduling when dealing with inpatients, outpatient, and emergencies.

Planning renewables in distribution system with electric vehicles to improve hosting capacity and energy losses: Two-stage stochastic optimization framework

Excessive penetration of renewables in distribution system can create several operational issues. One of the technologies that can maximize accommodation of renewables is electric vehicles (EVs). However, along with EVs additional measures are required while maximizing hosting capacity (HC) to avoid negative impact on system and account for uncertain parameters. In this regard, this paper proposes a two-stage stochastic optimization approach for planning of renewables in distribution system integrated with EVs. In the first stage, capacity of renewables is determined while maximizing HC whereas in the second stage operating strategy of EVs, renewables and grid power is evaluated to minimize expected energy losses. The proposed framework includes uncertainties in load demand, renewables and EVs characteristics through stochastic programming approach. The optimization problem is formulated as second order cone programming problem. The proposed model is tested on modified IEEE-33 bus and real-life 108-bus Indian distribution systems with different charging/discharging patterns and penetration rates of EVs. Moreover, an economic based cost analysis to compare planning cost and EV charging cost is also provided. Simulation results reveal that in 33-bus system with 500 EVs, the HC with vehicle-to-grid capability (V2G) is higher as compared to uncoordinated and coordinated charging by 29.86% and 6.36% respectively, while in 108-bus system with 1000 EVs, it is higher by 18.51% and 5.69% respectively. Further, the energy losses with V2G are 27.54% and 1.36% less in 33-bus system and 7.31% and 3.22% less in 108-bus system as compared to uncoordinated and coordinated charging respectively.

Multistage Stochastic optimization for mid-term integrated generation and maintenance scheduling of cascaded hydroelectric system with renewable energy uncertainty

The uncertainties resulting from the escalating penetration of renewable energy resources pose severe challenges to the efficient operation of modern power systems. Hydroelectricity is characterized by its flexibility, controllability, and reliability, and thus becomes one of the most ideal energy resources to hedge against such uncertainties. This paper studies the mid-term integrated generation and maintenance scheduling of a cascaded hydroelectric system (CHS) consisting of multiple cascaded reservoirs and hydroelectric units. To precisely describe the mid-term water regulation policies, the hydraulic coupling relationship and water-energy nexus of CHS are incorporated into the proposed optimization model. The uncertainties of natural water inflow and the power outputs of wind/solar energy generation are taken into consideration and captured via a stochastic process modeled by a scenario tree. A multistage stochastic optimization (MSO) approach is developed to coordinate the complementary operations of multiple energy resources, by optimizing the mid-term water resource management, generation scheduling, and maintenance scheduling of CHS. The proposed MSO model is formulated as a large-scale mixed-integer linear program that presents significant computational intractability. To address this issue, a tailored Benders decomposition algorithm is developed. Two real-world case studies are conducted to demonstrate the capability and characteristics of the proposed model and algorithm. The computational results show that the proposed MSO model can exploit the flexibility of hydroelectricity to efficiently respond to variable wind and solar power, and reserve water resources for the generation in peak months to reduce the consumption of fossil fuel. The proposed solution approach also exhibits promising computational efficiency when handling large-scale models.

Data-driven Wasserstein distributionally robust dual-sourcing inventory model under uncertain demand

Dual-sourcing inventory management, which is aimed at replenishing inventory through two supply sources, has been extensively incorporated across various industries as it can mitigate supply chain related operational risks. Given the practical relevance of this framework, many dual-sourcing inventory models based on stochastic and robust optimization approaches have been developed. However, these approaches encounter challenges such as the curse of dimensionality or solution conservativeness. In this study, we developed a data-driven distributionally robust optimization model for dual-sourcing inventory management under uncertain demand conditions, in which partial information regarding the distribution of the uncertain demand is available. A tractable model was constructed to solve the problem, and an optimal solution was derived in a closed-form expression. Numerical experiments were conducted to evaluate the performance of the proposed model in comparison with benchmark models in terms of the order-, stock-, and rolling-horizon-related parameters and demand distributions. The results demonstrated the benefit of adopting the dual-sourcing strategy in inventory management based on the distributionally robust optimization approach. In addition, the proposed model outperformed the benchmark models in terms of mitigating the bullwhip effect.

Designing an optimal multi-energy system with fast charging and hydrogen refueling station under uncertainties

As the demand for battery-powered and hydrogen-based electric vehicles continues to rise, the need for integrated charging and refueling systems with energy systems becomes more critical. Therefore, it is crucial to consider the stations serving diverse vehicle users during the system design process. This paper presents an optimal sizing strategy for a multi-energy system that covers clean energy sources and two energy storage technologies under the presence of a fast-charging station and a hydrogen refueling station for various types of car users. For the considered system, the optimal sizing problem aims to minimize the loss of power supply probability (LPSP) and annualized total life cycle cost (TLCC) through a two-stage stochastic programming-based multi-objective optimization approach. Using a scenario-based approach, the study considers the uncertainties associated with renewables, homeowner’s vehicle demands, and energy demands from homes and stations. Different cases are produced to evaluate the impacts of the different stations with the availability of various electric vehicle profiles under different levels of reliability. The TLCC decreases if LPSP increases in each case. Also, the cost of installing a fast charging station is significantly lower than that of a hydrogen refueling station for all LPSP limits. Moreover, the overall cost of the system design is at its lowest when homeowners’ vehicles provide vehicle-to-grid services. It is worth noting that when the station loads which come from the customers’ vehicle increase by 10%, the TLCC increases by 1.19%. Additionally, the revenue from hydrogen refueling station is approximately 70% less than the fast charging station.

Optimal operation of a hydropower plant in a stochastic environment

Given the currently changing climate conditions it is of primary importance to optimise the management of hydropower resources. This paper proposes a framework in a dynamic setting to determine the water outflow that maximises the value of a water resource for a given reservoir. The model includes two sources of uncertainty, the water inventory determined mainly by the water inflow and the electricity prices. It is implemented under the stochastic optimal control approach and calibrated using monthly data of reservoir characteristics from ResOpsUs. The results indicate that the inventory dynamics are specially important in valuing reservoir resources. The application of optimal management policies guarantees the long-term sustainability of the reservoir. The possible effects of climate change are considered in a sensitivity analysis to changes in the price and water inventory dynamics.

Risk-constrained bidding and offering strategy for sector-coupled electricity-hydrogen systems incorporating accessibility level of mobility sector

To enhance the economic viability of integrated energy systems, it is important to balance risk and reward while ensuring operational flexibility and compliance with regulatory constraints. Developing an integrated risk measurement method for energy trading in energy markets that complies with regulatory constraints adds another layer of complexity, especially when dealing with large-scale heterogeneous energy systems, such as those dominated by green hydrogen. Ensuring adherence to market regulations, grid codes, and flexible requirements requires a thorough understanding of legal frameworks and policy considerations, as well as integrating regulatory constraints into the bidding/offering strategies. To address these challenges and enable the profitable development of integrated electricity-hydrogen energy systems (IEHSs), this paper develops a risk-constrained bidding/offering self-scheduling strategy for IEHSs that allows for simultaneous trading in day-ahead energy and reserve electricity markets. The developed self-scheduling strategy regulates hydrogen and power flow in a centralized manner, taking into account the operational limits of the power sector, hydrogen fueling stations (HFSs), electric vehicle parking lots, fuel cell vehicle parking lots, and renewable energy sources. As a salient feature, the important human-related factors in the mobility sector are included in the proposed strategy to motivate private owners to collaborate with IEHSs and to accommodate the charging demand of vehicles with electricity market signals. To obtain the robust day-ahead schedule, economic risks associated with renewable power generation, calls for reserve deployment, and electricity market prices are taken into consideration. Towards this end, a stochastic adaptive robust optimization approach is proposed to control the risk of profit variability, which is solved by a nested column-and-constraint generation algorithm. The effectiveness and feasibility of the proposed strategy are verified using the modified IEEE 14-bus test system, as a standard scale of local IEHSs. The numerical results highlight the synergies impact between HFSs and the power sector, resulting in an increase in the profit of the IEHS from $101.654k to $275.078k. Furthermore, the IEHS can improve its profit margin and competitiveness by employing the tri-level stochastic adaptive robust optimization approach. This approach ensures that the IEHS is resistant to sudden changes in real-time interactions, even with an 8.14% increase in the imbalance cost.

A Multi-Objective Stochastic Optimization Approach for Planning a Multi-Energy Microgrid Considering Unscheduled Islanded Operation

A Multi-Objective Stochastic Optimization Approach for Planning a Multi-Energy Microgrid Considering Unscheduled Islanded Operation