Stochastic Robust Optimization Research Articles

Robust two‐level market coordinated transaction optimal model and benefit allocation strategy for a novel shared‐energy aggregator

AbstractShared‐energy storage (SES) can break the energy interaction barrier between the demand side and the supply side, which is becoming an option for improving the flexibility of energy systems. This study designed a novel structure for the shared‐energy aggregator (SEA), incorporating a microgrid (MG), prosumer and SES. Then, a two‐level market transaction optimization model for SEA, considering the robust stochastic optimization method, is proposed; namely, at the day‐ahead stage, a robust stochastic operation optimization model is constructed to achieve the dispatching plan from the demand side under the objective of achieving the minimum energy consumption cost for the prosumer, and at the real‐time market stage, a robust stochastic operation optimization model from the supply side is constructed to arrange the optimal dispatching strategy under the objective of the maximum aggregator benefits of MG and SES. Finally, an industrial park micro‐grid in Qinghai Province, China, is selected as an example for analysis.

Data-driven optimization for seismic-resilient power network planning

Many regions of the planet are exposed to seismic hazards that can cause devastating consequences on power systems. Due to these systems’ crucial role, the evaluation and planning for their safe and reliable operation are paramount. This paper develops a novel data-driven optimization framework to assess the power network’s seismic resilience and plan cost-effective investments for its enhancement. Under a robust optimization scheme, an earthquake attacker–defender model finds the worst-case realization of random earthquake network contingencies within an uncertainty set defined with a large number of scenarios generated by state-of-the-art engineering methods. Moreover, data-driven stochastic-robust optimization is employed in a two-stage seismic-resilient power network planning model, leveraging multiple seismic sources’ distributional information. Transmission line expansions and siting and sizing of battery energy storage systems are decided in the first stage, while the second stage decides operational variables. Experiments on a 281-node Chilean power system provide insights for seismic-resilient planning and demonstrate the efficiency of the proposed approach.

Net-zero, resilience, and agile closed-loop supply chain network design considering robustness and renewable energy.

The Net-zero, Resilience, and Agile Closed-Loop Supply Chain Network (NZRACLSCND) concept integrates net-zero, resiliency, and agility in a circular economy. Regarding net-zero, this research embeds renewable energy like solar energy and hybrid trucks to supply energy for facilities and transportation of goods and products between components. Applying redundancy, multi-source, and flexible capacity as resiliency strategies is suggested to cope with the demand disruption. Satisfaction demand level is utilized for the agile approach. This research proposes Robust Stochastic Optimization (RSO), including the weighted expected value and maximum CO2 for NZRACLSCND. This study locates and determines the flow of CLSC in the home appliance industry by considering NZRA, robustness, and risk against demand disruption. CO2 emission using the NZRA concept is 233.33% less than without considering NZRA concepts. In addition, the conservative coefficient, agile coefficient, decreased CO2 coefficient, and the model scale are analyzed. The results show that when the conservative coefficient increases, the risks of CO2 emission increase. In addition, when the agile coefficient increases, as a result, CO2 emission increases. Finally, when the decreased CO2 coefficient and the model scale increase, we can see that CO2 emission and cost are increased.

Day-ahead bidding and dispatch strategy of novel battery charging and swapping station under multiple uncertainties

The novel battery charging and swapping station (NBCSS) has great operational flexibility due to its integration of wind power, photovoltaic power, gas turbine and energy storage. This paper presents a day-ahead bidding and dispatch strategy of NBCSS under multiple uncertainties, which consists of battery demand, market price, renewable energy and load. Firstly, the optimized backup method is used to address the uncertainty of battery demand. Then, a two-stage stochastic robust optimization model is further applied to address the uncertainties of market price, renewable energy and load. The model’s goal is to minimize the total operational cost in the worst-case scenario, which is limited by the corresponding uncertainty set. Especially, to control the conservatism of the model, the total adjustable budget and temporal adjustable budget of uncertainties are considered together. Next, the two-stage model is solved efficiently based on the strong duality theory and column-and-constraint generation (C&CG) method. Finally, case studies are given to verify the effectiveness and performance of the proposed model. The results demonstrate that the NBCSS can be efficiently deployed, enabling market arbitrage and reducing the overall cost. Additionally, the conservatism of the proposed model can be adjusted according to the budgets of uncertainties.

Two-stage stochastic robust optimization scheduling of electric–thermal microgrid with solid electric thermal storage

During the periods of high heat load (HL) demand in winter, the increased heat output of combined heat and power units (CHPs) can significantly compress the electric power regulation range, thereby posing a threat to the safety of the power system. The solid electric thermal storage (SETS) can be employed as the regulating resource for both electric and thermal systems, expanding the dispatch space of microgrids to promote renewable energy consumption. In this paper, a two-stage stochastic robust optimization scheduling model of an electric–thermal microgrid with SETS is proposed, and the electric–thermal bi-directional regulation characteristics of SETS are considered. First, a SETS operation model based on the heat transfer characteristics of the homogeneous material-type thermal storage unit is established. Second, a regional thermal inertia model under a constant-flow variable-temperature system is established, which integrates HL at different locations to the heat source, avoiding the calculation of variation in water temperature, thus reducing the calculation difficulty. Finally, the two-stage stochastic robust optimization scheduling model of an electric–thermal microgrid with SETS is established. The model decouples the power and heat generation of CHP through the bi-directional regulation function of SETS. Case studies demonstrate the validity and effectiveness of the proposed scheduling model.

Aggregator-Network Coordinated Peer-to-Peer Multi-Energy Trading via Adaptive Robust Stochastic Optimization

Aggregator-Network Coordinated Peer-to-Peer Multi-Energy Trading via Adaptive Robust Stochastic Optimization

Optimization of intermodal routes for reefer containers under double uncertainty

Aiming at the influence of demand uncertainty and stochastic carbon trading price on the choice of intermodal transportation route for reefer containers, a hybrid robust stochastic optimization model with minimum economic cost is established, and a Monte Carlo sampling-based catastrophic adaptive genetic algorithm is designed to test the reasonableness and validity of the model. The results show that: influenced by the regret value constraint, the robust optimization of demand uncertainty will increase the total cost of reefer container multimodal transportation, while the increase of carbon trading price stochasticity doesn’t necessarily mean the increase of cost, and the reasonable setting of carbon trading price stochasticity and the trade-off between the maximum regret value and the economic cost, so that the cold-chain logistics and transportation enterprises can easily deal with the fluctuation of the demand of the freight transportation market, and also respond to the low-carbon requirements.

A data-driven robust optimization in viable supply chain network design by considering Open Innovation and Blockchain Technology

The research proposes a new method for Viable Supply Chain Network Design (VSCND) that incorporates Open Innovation (OI) and Blockchain Technology (BCT). A robust stochastic optimization and Conditional Value at Risk (CVaR) in the cost function is utilized to develop the model. This model's objective function incorporates the expected value, maximum cost, and CVaR cost. The OI and BCT platforms are suggested for an antifragile policy against disruption. In addition, CO2 emissions and energy consumption are proposed as sustainability requirements. Eventually, minimum demand satisfaction and resilience facilities by incorporating capacity based on specific scenarios are added to the model for an agile strategy. This research entails several parties, including vendors supplying the primary components and manufacturers creating products based on customer preferences. OI and BCT platforms aim to receive demand based on customer specifications and facilitate rapid transactions between components. Risk-averse decision-makers utilize a polyhedral Data-Driven Robust Optimization (DDRO) approach to manage uncertainty and flexible sets. Incorporating OI and BCT as antifragility instruments resulted in a 0.2% cost reduction for VSCNDOIBCT compared to when OI and BCT were not considered. This research suggests that integrating OI and BCT positively affects SC performance overall. The decreasing rate, DDRO coefficient, agility rate, demand variation, and problem size were subjected to a sensitivity analysis.

Hybrid robust-stochastic optimal scheduling for multi-objective home energy management with the consideration of uncertainties

Home energy management systems (HEMS) have transformed the traditional structure of electricity consumption on the customer side and facilitate real-time interaction between the customers and the grid. However, the HEMS scheduling is currently challenged by a variety of uncertainties, including photovoltaic (PV) output, electric vehicle (EV) charging/discharging behavior, and real-time pricing (RTP), which can seriously impact home equipment scheduling and critical objectives like total cost and users' comfort. Therefore, a hybrid robust-stochastic (HRS) optimization approach for multi-objective home energy management with the consideration of uncertainties and users' comfort has been proposed in this paper. Firstly, a detailed classification and modeling of the loads in the household are carried out to facilitate the exchange between the user-side resources and the grid in a benchmark based on RTP. Then the stochastic charging/discharging behavior of EV is modeled by stochastic optimization (SO) methods, and uncertainties in PV production and RTP are modeled by robust optimization (RO) methods, making full use of the flexibility of various uncertainty parameters. Meanwhile, the users' requirements for comfort are considered, and a multi-objective function for the economy and comfort of the HEMS is established. Finally, the effectiveness of the proposed method has been verified by case studies. The results show that the proposed HRS is effective to deal with different levels of the uncertainty parameters and ensures the users' comfort requirements in home energy system. Moreover, the users can make trade-offs between various levels of robust decisions according to their needs of economic and comfort level, thus obtaining a variety of electricity consumption decisions.

Robust planning for distributed energy storage systems considering location marginal prices of distribution networks

Energy storage plays an important role in integrating renewable energy sources and power systems, thus how to deploy growing distributed energy storage systems (DESSs) while meeting technical requirements of distribution networks is a challenging problem. This paper proposes an area-to-bus planning path with network constraints for DESSs under uncertainty. First, a distribution location marginal price (DLMP) formulation with maximum fluctuation boundaries of uncertainties is designed to select vulnerable areas exceeding voltage limits and higher line losses that occur in distribution networks. Different from simple multi-scenario power flow calculation and sensitivity analysis, DLMP with time and regional characteristics could be more intuitive to reflect line losses and voltage limits of distribution networks through price signals. After that, a two-stage stochastic robust optimization based planning method is developed to determine locations and capacities of DESSs in vulnerable areas. To make the uncertainty problem more tractable, stochastic scenarios are used to portray upper and lower boundaries of uncertainties, which avoids too-conservative decisions for robust optimization. Finally, numerical tests are implemented to testify the reasonability and validity of the proposed area-to-bus planning path under uncertainty. Compared with the DESSs planning framework without DLMP, the costs of DESSs are observably reduced with DLMP. With same budgets of uncertainty, investment costs of DESSs for the stochastic robust optimization with 30 and 50 scenarios are 3.91% and 4.45% lower than classical adaptive robust optimization (ARO).

A viable supply chain by considering vendor-managed-inventory with a consignment stock policy and learning approach

Inventory management challenges are optimizing inventory levels, minimizing stockouts, and streamlining the supply chain process for the vendor and the customer. The study tries to improve these challenges by proposing a new Viable Supply Chain (VSC) incorporating Vendor-Managed-Inventory (VMI) with a Consignment Stock (SC) policy for managing inventory between SC components. These strategies access the inventory level of the customer in the vendor, and if the items are sold, the customer pays the vendor for the inventory that was sold. The Robust Stochastic Optimization (RSO) with Conditional Value at Risk (CVaR) as risk criteria is utilized to solve the model. The objective function of this model combines the expected value, maximum, and CVaR of cost. To promote viability against disruption, sustainability requirements such as CO2 emissions and energy consumption are considered. An agile approach that includes a learning factor is suggested. In addition, a resiliency strategy by addressing order disruption requirements is proposed. The case study of this research is a small healthcare industry that prepares drug products. It is one of the largest industries with high sales and added value. The results show that the inclusion of VMI and CS in the main problem-solving approach resulted in a 14.8 % cost reduction compared to the scenario where VMI and CS were not considered. Finally, sensitivity analysis is performed on CVaR confidence, conservatism coefficient, learning rate, agility rate and scale of the main problem.

Robust stochastic optimization of needle configurations for robotic HDR prostate brachytherapy.

Ideally, inverse planning for HDR brachytherapy (BT) should include the pose of the needles which define the trajectory of the source. This would be particularly interesting when considering the additional freedom and accuracy in needle pose which robotic needle placement enables. However, needle insertion typically leads to tissue deformation, resulting in uncertainty regarding the actual pose of the needles with respect to thetissue. To efficiently address uncertainty during inverse planning for HDR BT in order to robustly optimize the pose of the needles before insertion, that is, to facilitate path planning for robotic needleplacement. We use a form of stochastic linear programming to model the inverse treatment planning problem. To account for uncertainty, we consider random tissue displacements at the needle tip to simulate tissue deformation. Conventionally for stochastic linear programming, each simulated deformation is reflected by an addition to the linear programming problem which increases problem size and computational complexity substantially and leads to impractical runtime. We propose two efficient approaches for stochastic linear programming. First, we consider averaging dose coefficients to reduce the problem size. Second, we study weighting of the slack variables of an adjusted linear problem to approximate the full stochastic linear program. We compare different approaches to optimize the needle configurations and evaluate their robustness with respect to different amounts of tissuedeformation. Our results illustrate that stochastic planning can improve the robustness of the treatment with respect to deformation. The proposed approaches approximating stochastic linear programming better conform to the tissue deformation compared to conventional linear programming. They show good correlation with the plans computed after deformation while reducing the runtime by two orders of magnitude compared to the complete stochastic linear program. Robust optimization of needle configurations takes on average 59.42s. Skew needle configurations lead to mean coverage improvements compared to parallel needles from 0.39 to 2.94 percentage points, when 8mm tissue deformation is considered. Considering tissue deformations from 4 to 10mm during planning with weighted stochastic optimization and skew needles generally results in improved mean coverage from 1.77 to 4.21 percentagepoints. We show that efficient stochastic optimization allows selecting needle configurations which are more robust with respect to potentially negative effects of target deformation and displacement on the achievable prescription dose coverage. The approach facilitates robust path planning for robotic needleplacement.

Designing a sustainable disruption-oriented supply chain under joint pricing and resiliency considerations: A case study

Supply chains must adopt an appropriate mechanism to deal with interrelated risks. Sustainable development's economic, environmental and social aspects are critical concerns of supply chains. This study presents a three-objective model to design a forward supply chain network considering interrelated operational and disruptive risks. Several mitigative and preventive resilience strategies are implemented to cope with mentioned risks. Also, the optimal prices for products and parts are determined via a joint pricing strategy to enhance supply chain's profitability in disruption incidence. A stochastic robust optimization method is employed to deal with parameters’ uncertainty. The proposed model is applied to an industry of manufacturing chemical processing equipment to validate the formulation and derive practical insights. Results revealed that simultaneously managing disruption risks and uncertainties can improve sustainability goals and reduce the costs associated with risk exposure and protection in the under-study supply chain.

Data-driven stochastic robust optimization of sustainable utility system

Sustainable utility systems reduce reliance on fossil fuels by using renewable energy sources. Multi-scale uncertainties associated with renewable energy and utility systems pose challenges to the modeling and optimization of sustainable utility systems. This study proposes a sustainable retrofit framework for utility systems based on a data-driven stochastic robust optimization approach. Kernel density estimation and fuzzy clustering were employed to capture the uncertainty features in a holistic framework. A life cycle assessment approach was used to calculate the global warming potential (GWP) of the sustainable utility system, and a multi-objective environmental and economic optimization model was developed. A nested decomposition-based algorithm was proposed to solve a large-scale mixed-integer nonlinear programming problem. Finally, a case study of an industrial utility system was conducted to demonstrate the effectiveness of the proposed method. The optimization results show that the proposed method reduces GWP by 9 % after introducing renewable energy and achieves a balance between economic and environmental performance.

Antifragile, sustainable, and agile supply chain network design by considering resiliency, robustness, risk, and environmental requirements.

This research suggests an Antifragile, Sustainable and Agile Supply Chain Network Design (ASASCND) as a new network design that integrates these concepts considering resiliency, robustness, risk, and environmental requirements. The cost function combines a novel method with robust stochastic optimization and Entropic Value atRisk (EVaR). This model combines expected value, maximum and EVaR of cost as an objective function. This research adds antifragility by the effect of learning on variable parameters, sustainability by considering the environmental and social issues, resiliency and agility by flexible capacity, and multi-resource and demand satisfaction constraints to the model. The case study is in the automotive industry. This model compares the main problem by considering antifragility without thinking about antifragility. The ASASCND cost is - 0.3% less than without considering antifragility. In addition, when the conservatism coefficient grows, the cost function increase. In addition, the antifragility coefficient and the confidence level affect positively, and the agility coefficient negatively affects the cost function. Expanding the model scale changes the cost function and time computation because the antifragility coefficient changes variable cost. Finally, managerial insights and practical implications are explained.

Stochastic-robust planning optimization method based on tracking-economy extreme scenario tradeoff for CCHP multi-energy system

The load tracking performance of combined cooling, heating, and power multi-energy system (CCHP-MES) greatly depends on the equipment capacity configuration. And the frequent fluctuations in the source-load uncertainty puts higher demands on the load tracking ability of CCHP-MES. For this reason, this paper proposes a novel tracking-economy extreme scenario tradeoff model by comparing the differences between tracking ability and economic benefit. The corresponding extreme scenarios based on these two objectives are characterized and the concept of uncertainty adjustment parameter is introduced to weigh the preference of extreme scenarios. On this basis, a multi-objective two-stage stochastic-robust optimization approach is developed, where the first stage optimizes the investment cost and the second stage optimizes the operating cost. Case study using typical load demand and renewable energy data in Nanjing verify the efficacy of the optimization model. The results indicate that the proposed tracking-economy extreme scenario can better characterize the frequent fluctuations of uncertainties compared to the traditional definition of extreme scenario. The equipment capacity configuration obtained under tracking-economy extreme scenario tradeoff model can better cope with the uncertainty fluctuations under extreme weather. Depending on different optimization preference, the economic robustness and tracking robustness can be improved by 13.80% and 36.06%, respectively.

A Novel Chaotic Elite Adaptive Genetic Algorithm for Task Allocation of Intelligent Unmanned Wireless Sensor Networks

In recent times, the progress of Intelligent Unmanned Wireless Sensor Networks (IUWSNs) has inspired scientists to develop inventive task allocation algorithms. These efficient techniques serve as robust stochastic optimization methods, aimed at maximizing revenue for the network’s objectives. However, with the increase in sensor numbers, the computation time for addressing the challenge grows exponentially. To tackle the task allocation issue in IUWSNs, this paper introduces a novel approach: the Chaotic Elite Adaptive Genetic Algorithm (CEAGA). The optimization problem is formulated as an NP-complete integer programming challenge. Innovative elite and chaotic operators have been devised to expedite convergence and unveil the overall optimal solution. By merging the strengths of genetic algorithms with these new elite and chaotic operators, the CEAGA optimizes task allocation in IUWSNs. Through simulation experiments, we compare the CEAGA with other methods—Hybrid Genetic Algorithm (HGA), Multi-objective Binary Particle Swarm Optimization (MBPSO), and Improved Simulated Annealing (ISA)—in terms of task allocation performance. The results compellingly demonstrate that the CEAGA outperforms the other approaches in network revenue terms.

Data-driven source-load robust optimal scheduling of integrated energy production unit including hydrogen energy coupling

A robust low-carbon economic optimal scheduling method that considers source-load uncertainty and hydrogen energy utilization is developed. The proposed method overcomes the challenge of source-load random fluctuations in integrated energy systems (IESs) in the operation scheduling problem of integrated energy production units (IEPUs). First, to solve the problem of inaccurate prediction of renewable energy output, an improved robust kernel density estimation method is proposed to construct a data-driven uncertainty output set of renewable energy sources statistically and build a typical scenario of load uncertainty using stochastic scenario reduction. Subsequently, to resolve the problem of insufficient utilization of hydrogen energy in existing IEPUs, a robust low-carbon economic optimal scheduling model of the source-load interaction of an IES with a hydrogen energy system is established. The system considers the further utilization of energy using hydrogen energy coupling equipment (such as hydrogen storage devices and fuel cells) and the comprehensive demand response of load-side schedulable resources. The simulation results show that the proposed robust stochastic optimization model driven by data can effectively reduce carbon dioxide emissions, improve the source-load interaction of the IES, realize the efficient use of hydrogen energy, and improve system robustness.

Optimal scheduling of ethylene plants under uncertainty: An unsupervised learning-based data-driven strategy

Ethylene cracking furnaces are core units that determine the yield of key products, and its cycle scheduling optimization is of great significance to improve the efficiency of the whole plant. However, uncertainties in cracking batch durations may lead to sub-optimal or ineffective scheduling arrangements. This paper develops a novel data-driven stochastic robust optimization strategy to achieve the optimal scheduling of cracking furnaces under uncertainty. The proposed stochastic robust optimization model applies machine learning methods to extract data information and is represented as a bilevel problem: the outer layer is a two-stage stochastic programming, where typical scenarios are clustered by a three-level data mining approach; the inner layer is robust optimization, whose uncertainty set is constructed by an efficient kernel-based approach. An actual ethylene cracking system is investigated and the results show that the proposed method achieves the highest daily profit, performing well in data coverage (92.3%) and change rate (0.826%). Moreover, the sensitivity analysis for the number of clusters and regularization parameter values is performed.

A Robust Stochastic Programming Model for the Well Location Problem: The Case of The Brazilian Northeast Region

Slow-onset disasters, such as drought, are usually more destructive in the long term since they affect the productive capacity of a community, thereby preventing it from recovering using its resources. This requires the leaders and planners of drought areas to establish the best strategies for effective drought management. In this direction, the present work develops a robust stochastic programming approach for the problem of locating artesian wells for the relief of drought-affected populations under uncertainty. Our model considers different demand scenarios and proposes a novel perspective which considers both social and hydrogeological aspects for the location choice, aiming to maximize the affected area’s satisfaction through its prioritization using a composite drought risk index as well as to maximize the probability of success in water prospecting. We present a case study of our robust stochastic optimization approach for the Brazilian Semiarid Region using demand points from the database of Operação Carro-Pipa. Our findings show that a robust solution has a better expected value for the objective function considering all scenarios, so it can help decision makers to plan facility location and demand allocation under demand uncertainty, pointing out the best solution according to their degree of risk aversion.