Stochastic Optimization Approach Research Articles

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.

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.

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

Stochastic optimization of solar-based distributed energy system: An error-based scenario with a day-ahead and real-time dynamic scheduling approach

Distributed energy systems (DES) have garnered global attention as a promising solution for the expansion of renewable energy sources. However, stochastic uncertainty in renewable sources poses significant challenges in the collaboration optimization of system design and operation. In this study, a comparison analysis was conducted to assess the effectiveness of the conventional distribution-based scenario generation (DS) method for stochastic optimization of a distributed energy system in residential buildings. The results revealed that the DS method inaccurately captured extreme scenarios and exhibited limitations in operation optimization, leading to significant performance evaluation bias. To address these challenges, a novel stochastic optimization approach was developed based on error-based scenarios and a day-ahead and real-time dynamic scheduling strategy (ES-DRS). This approach incorporated solar energy prediction errors to more accurately characterize extreme scenarios, while also considering dynamic dual-scale meteorological boundary condition for rolling operation optimization. Furthermore, the buffer storage and coverage periods in ES-DRS were investigated and discussed during dynamic scheduling. Results demonstrated that when the buffer storage and coverage period were set at 36.22 kWh in summer and 24 h, respectively, the DES with ES-DRS achieved optimal multi-objective performance. This resulted in an annual total cost of 3.21 × 104 USD and CO2 emission of 5.82 tons, representing reductions of 26.45% and 61.06%, respectively, compared to the conventional strategy. Overall, this research contributes to advancing uncertainty analysis and scenario-based optimization in DES, highlighting the potential benefits of adopting the ES-DRS approach to maximize overall performance from both economic and environmental perspectives.

3-D UAV Small Cell Base Station Positioning and Resource Allocation in Cellular Network: A Stochastic Optimization Approach

3-D UAV Small Cell Base Station Positioning and Resource Allocation in Cellular Network: A Stochastic Optimization Approach

A fuzzy interval optimization approach for p-hub median problem under uncertain information.

Stochastic and robust optimization approaches often result in sub-optimal solutions for the uncertain p-hub median problem when continuous design parameters are discretized to form different environmental scenarios. To solve this problem, this paper proposes a triangular fuzzy number model for the Non-Strict Uncapacitated Multi-Allocation p-hub Median Problem. To enhance the quality and the speed of optimization, a novel optimization approach, combining the triangular fuzzy number evaluation index with the Genetic-Tabu Search algorithm, is proposed. During the iterations of the Genetic-Tabu Search algorithm for finding the optimal solution, the fitness of fuzzy hub schemes is calculated by considering the relative positional relationships of triangular fuzzy number membership functions. This approach directly addresses the triangular fuzzy number model and ensures the integrity of information in the p-hub problem as much as possible. It is verified by the classic Civil Aeronautics Board and several self-constructed data sets. The results indicate that, compared to the traditional Genetic Algorithm and Tabu Search algorithm, the Genetic-Tabu Search algorithm reduces average computation time by 49.05% and 40.93%, respectively. Compared to traditional random, robust, and real-number-based optimization approaches, the proposed optimization approach reduces the total cost in uncertain environments by 1.47%, 2.80%, and 8.85%, respectively.

Valuing Combinations of Flexible Planning, Design, and Operations in Water Supply Infrastructure

AbstractUncertainty arising from climate change poses a central challenge to the long‐term performance of many engineered water systems. Water supply infrastructure projects can leverage different types of flexibility, in planning, design, or operations, to adapt infrastructure systems in response to climate change over time. Both flexible planning and design enable future capacity expansion if‐and‐when needed, with flexible design proactively incorporating physical design changes that enable retrofits. All three forms of flexibility have not previously been analyzed together to explicitly assess their relative value in mitigating cost and water supply reliability risk. In this paper, we propose a new framework to evaluate combinations of flexible planning, design, and operations. We develop a nested stochastic dynamic optimization approach that jointly optimizes dam development and operating policies under dynamic climate uncertainty. We demonstrate this approach on a reservoir project near Mombasa, Kenya. Our results find that flexible operations have the greatest potential to reduce costs. Flexible design and flexible planning can amplify the value of flexible operations under higher discounting scenarios and when initial infrastructure capacities are undersized. This approach provides insight on the climate change and techno‐economic conditions under which flexible planning, design, and operations can be best leveraged individually or in combination to reduce climate change uncertainty risks in water supply infrastructure projects.

Optimal resource allocation and operation for smart energy hubs considering hydrogen storage systems and electric vehicles

Energy hubs (EHs) have substantially paved the way for the coordinated operation of various energy carriers, converters, and storage. However, the establishment of optimal planning and operation of the EH include several challenges, e.g., the stochastic nature of non-dispatchable generation assets, obtaining a satisfactory performance from the storage assets with reasonable energy and power density costs, and long-term load growth. Accordingly, this paper proposes a two-stage stochastic optimal resource allocation and operation approach for multiple smart energy hubs-based microgrids. The first stage optimizes the location of each EH and different assets' capacities. On the other hand, the second stage optimizes the charging/discharging rates of each asset and parking lot power. These microgrids combine renewable energy sources. Moreover, for research gap and unlike existing research, the cooperative operation of hybrid storage systems (i.e., solar-powered compressed air energy storage, hydrogen storage systems, battery energy storage systems, thermal energy storage systems) along with plug-in electric vehicles (PEV) has been investigated. Furthermore, annual load growth and price-based demand response (PBDR) are employed in this study. The simulation results demonstrate that the controlled charging/discharging of the PEVs reduces the total annualized cost by 5.49%, while the operation and emission costs are reduced by 21.3% and 19.86%, respectively. Furthermore, employing PBDR has led to a reduction of 10.1% in capital and operational costs.

Stochastic Optimization Approaches for an Operating Room and Anesthesiologist Scheduling Problem

Improving Operating Room, Surgery, and Anesthesiologist Scheduling Using Stochastic and Robust Optimization Efficient planning and scheduling of operating room (OR) activities is crucial for managing costs and delivering high-quality surgical care. However, this task is extremely complex for several reasons. First, it requires coordinating multiple resources, such as ORs and anesthesiologists. Second, in addition to limited OR capacity and time, there is a significant shortage of anesthesiologists required to perform surgeries. Third, surgery durations are uncertain and difficult to predict. Ignoring such uncertainty may lead to substantial overtime, idling, and surgery delays, among other schedule deficiencies. Thus, hospital managers could benefit greatly from advanced methodologies to improve OR utilization, surgical care, and quality as well as to minimize OR operational costs. In “Stochastic Optimization Approaches for an Operating Room and Anesthesiologist Scheduling Problem,” M. Y. Tsang, K. S. Shehadeh, F. E. Curtis, B.R. Hochman, and T. E. Brentjens propose computationally tractable stochastic programming and distributionally robust optimization methodologies for an integrated allocation, assignment, sequencing, and scheduling problem under uncertainty involving multiple ORs, anesthesiologists, and surgery types. Using real-world surgery data and a case study from a health system in New York, they conduct extensive experiments demonstrating the computational efficiency of the proposed methodologies, allowing for their implementation in practice. Moreover, they show the negative consequences of adopting the existing non-integrated approaches and provide valuable practical insights.

Optimal investment problem for a hybrid pension with intergenerational risk-sharing and longevity trend under model uncertainty

This paper studies the optimal investment problem for a hybrid pension plan under model uncertainty, where both the contribution and the benefit are adjusted depending on the performance of the plan. Furthermore, an age and time-dependent force of mortality and a linear maximum age are considered to capture the longevity trend. Suppose that the plan manager is ambiguity averse to the financial market and is allowed to invest in a risk-free asset and a risky asset. The plan manager aims to find optimal investment strategies and optimal intergenerational risk-sharing arrangements by minimizing the unstable contribution risk, the unstable benefit risk and the discontinuity risk under the worst-case scenario. By applying the stochastic optimal control approach, robust optimal strategies are derived under the worst-case scenario for a penalized quadratic cost function. Through numerical analysis and three special cases, we find that the intergeneration risk-sharing is achieved in our collective hybrid pension plan effectively. And it also shows that when people live longer, postponing the retirement seems a reasonable way to alleviate the stress of the aging problem.

A stochastic data-driven Bayesian optimization approach for intensified ethanol–water separation systems

The optimization of advanced intensified distillation operation systems is crucial for achieving sustainability in the chemical industry. In this paper, we present a stochastic data-driven Bayesian optimization approach for the design and operation of ethanol distillation separation systems. The proposed optimal design methodology does not require a first-principles mathematical model to draw optimal operating conditions. The approach involves an initial sampling of input/output system measurements, followed by the construction of an approximate input/output Gaussian process model. The next best sampling point is then drawn using an acquisition function, and the algorithm converges when the optimization function value does not change or when the maximum number of iterations is reached. We address the optimal parametric design of advanced ethanol–water intensified distillation separation systems, assuming a mixture of the ethanol–water system is available, and almost anhydrous ethanol is required for mobility applications. We also consider the impact of noisy measurements on the optimality operating region. The proposed approach can be extended to the optimization of merged discrete and continuous systems. Bayesian optimization techniques represent black-box optimization strategies that can be employed for the continuous online optimization of intricate separation systems. These techniques aid in mitigating sustainability issues by reducing mass and energy requirements.

Combinatorial Optimization-Enriched Machine Learning to Solve the Dynamic Vehicle Routing Problem with Time Windows

With the rise of e-commerce and increasing customer requirements, logistics service providers face a new complexity in their daily planning, mainly due to efficiently handling same-day deliveries. Existing multistage stochastic optimization approaches that allow solving the underlying dynamic vehicle routing problem either are computationally too expensive for an application in online settings or—in the case of reinforcement learning—struggle to perform well on high-dimensional combinatorial problems. To mitigate these drawbacks, we propose a novel machine learning pipeline that incorporates a combinatorial optimization layer. We apply this general pipeline to a dynamic vehicle routing problem with dispatching waves, which was recently promoted in the EURO Meets NeurIPS Vehicle Routing Competition at NeurIPS 2022. Our methodology ranked first in this competition, outperforming all other approaches in solving the proposed dynamic vehicle routing problem. With this work, we provide a comprehensive numerical study that further highlights the efficacy and benefits of the proposed pipeline beyond the results achieved in the competition, for example, by showcasing the robustness of the encoded policy against unseen instances and scenarios. History: This paper has been accepted for the Transportation Science special issue on DIMACS Implementation Challenge: Vehicle Routing Problems. Funding: This work was supported by Deutsche Forschungsgemeinschaft [Grant 449261765].

Intensifying the fumigation policy to minimize the risk of mosquito-borne diseases implementing a stochastic optimization approach

This paper presents a stochastic mathematical model for the planning, dosage, and strategic scheduling of fumigation policies to reduce mosquito-borne diseases in a geographic location. Multiple scenarios were generated to account for uncertainty in the existing mosquito population based on a random normal distribution. In addition, the model includes occupational health, considering the permissible limits of each insecticide applied and their residual effect. This stochastic mathematical model applies a Pareto solution method, using a Conditional Value at Risk approach to select solutions that trade off the different objective functions. Results show that the optimal solutions found by the model provide a compromise between the expected infected people and the total cost of applying the insecticides. This methodology improves the current practice by an intensified approach that considers optimal scheduling alternatives that minimize cost while considering the permissible concentration limits to guarantee the health and comfort of the population to minimize the possible incidences of infections.

Artificial Bee Colony Algorithm with Adaptive Parameter Space Dimension: A Promising Tool for Geophysical Electromagnetic Induction Inversion

Frequency-domain electromagnetic induction (FDEMI) methods are frequently used in non-invasive, area-wise mapping of the subsurface electromagnetic soil properties. A crucial part of data analysis is the geophysical inversion of the data, resulting in either conductivity and/or magnetic susceptibility subsurface distributions. We present a novel 1D stochastic optimization approach that combines dimension-adapting reversible jump Markov chain Monte Carlo (MCMC) with artificial bee colony (ABC) optimization for geophysical inversion, with specific application to frequency-domain electromagnetic induction (FDEMI) data. Several solution models of simplified model geometry and a variable number of model knots, which are found by the inversion method, are used to create re-sampled resulting average models. We present synthetic test inversions using conductivity models based on 14 direct-push (DP) EC logs from Greece, Italy, and Germany, as well as field data applications using multi-coil FDEMI devices from three sites in Azerbaijan and Germany. These examples show that the method can effectively lead to solutions that resemble the known DP input models or image reasonable stratigraphic and archaeological features in the field data. Neighboring 1D solutions on field data examples show high coherence along profiles even though each 1D inversion is independently handled. The computational effort for one 1D inversion is less than 120,000 forward calculations, which is much less than usually needed in MCMC inversions, whereas the resulting models show more plausible solutions due to the dimension-adapting properties of the inversion method.

A stochastic optimization technique for hyperparameter tuning in reservoir computing

This paper presents a new approach to reservoir computing (RC) optimization. Reservoir computing (RC) is a framework for building recurrent neural networks (RNNs) that alleviates the well-known learning difficulties in such neural networks by training only the output layer. While the weights of the input and the nonlinear hidden layers are randomly generated, the adjustment of critical hyperparameters, such as the input and the feedback scaling factor, is essential for optimal performance in RC. While recent hardware implementations of RC are crucial for high-speed processing, standard gradient-based hyperparameter optimization is often irrelevant due to potentially uncertain or time-varying internal functions and parameters. In this work, we propose and analyze a stochastic optimization approach using gradient approximations based solely on noisy measurements of the loss function to circumvent this problem. Our numerical and experimental results confirm that the proposed method can provide near-optimal RC hyperparameters with substantial complexity reduction compared to competing methods, validating its potential for RC optimization.

A decentralized dispatch model for multiple micro energy grids system considering renewable energy uncertainties and energy interactions

Micro energy grids (MEGs) play a vital role in realizing carbon neutrality and efficient utilization of renewable energy resources. This research focuses on optimizing the synergy of MEG interconnections. Given the diverse development paths of different operating entities within the system, information barriers emerge among MEGs, creating great difficulties for the collaborative system management. In response, this paper proposes a decentralized coordinated dispatch model targeting multiple stakeholders within the system. This model accounts for energy interactions between MEGs and the inherent uncertainty associated with renewable energy sources. Specifically, stochastic optimization approach was applied to characterize the uncertainty of renewable energy output by generating stochastic scenarios. Furthermore, it incorporates the analytical target cascading (ATC) method to decouple objective functions and constraints, creating autonomous scheduling sub-models for individual MEGs. This decentralized approach ensures independent modeling and coordinated problem-solving. Simulations verify that (1) the ATC-based inter-MEG energy interaction strategy effectively achieves decentralized coordinated scheduling of multiple MEGs and (2) the decentralized coordinated scheduling solution closely approximates the global optimum while considering the interest of various system entities.

Impact assessment of shared storage and peer-to-peer trading on industrial buildings in the presence of electric vehicle parking lots: A hybrid robust-CVaR analysis

Local power markets and peer-to-peer (P2P) power transaction plans between the clients have lately received attractions as a cost-effective approach to encourage flexible energy options and sharing the internal power resources. For the integration of industrial consumers (ICs) in the presence of electric vehicle parking lot, this study modeled local power markets to share the surplus power of ICs between each other. Other hands, shared storage is modeled in the proposed system to benefit consumers. In order to investigate the proposed system under uncertain conditions, a hybrid optimization method is proposed for uncertainty modeling. In this paper, the well-known uncertainty modeling tools, including the robust optimization and Conditional Value at Risk (CVaR) embedded stochastic optimization approach, are proposed to model the uncertainties. The markets price uncertainty is one of the important uncertain parameters assumed as an unknown-distribution parameter due to insufficient historical data or not following a specific distribution; thus, the risks of this parameter are modeled by robust optimization, which has no need for big historical data of uncertain parameter. The other uncertain parameter is solar irradiation. The corresponding risks of solar irradiation is modeled by CVaR modeling because of the following Beta distribution. Thus, the financial risks of different uncertain parameters can be modeled effectively using the proposed hybrid optimization framework. According to obtained results, using peer-to-peer trading reduces the operation cost by 7.94%, while using the shared storage along with peer-to-peer trading reduces the operation cost by 21.49%.