Two-stage Robust Optimization Research Articles

Two-stage robust optimization of a virtual power plant considering a refined demand response

Two-stage robust optimization of a virtual power plant considering a refined demand response

Uncertain Parameters Adjustable Two-Stage Robust Optimization of Bulk Carrier Energy System Considering Wave Energy Utilization

Within the 21st century, in the Maritime Silk Road, wave energy, a clean renewable source, is drawing more interest, especially in areas with power shortages. This paper investigates wave energy in ships, particularly in a hybrid electric bulk carrier, by designing a system that supplements the existing power setup with oscillating buoy wave energy converters. The system includes diesel generators (DGs), a wave energy generation system, heterogeneous energy storage (consisting of battery storage (BS) and thermal storage (TS)), a combined cooling heat and power (CCHP) unit, and a power-to-thermal conversion (PtC) unit. To ensure safe and reliable navigation despite uncertainties in wave energy output, onboard power loads, and outdoor temperature, a robust coordination method is adopted. This method employs a two-stage robust optimization (RO) strategy to coordinate the various onboard units across different time scales, minimizing operational costs while satisfying all operational constraints, even in the worst-case scenarios. By applying constraint linearization, the robust coordination model is formulated as a mixed-integer linear programming (MILP) problem and solved using an efficient solver. Finally, the effectiveness of the proposed method is validated through case studies and comparisons with existing ship operation benchmarks, demonstrating significant reductions in operational costs and robust performance under various uncertain conditions. Notably, the simulation results for the Singapore–Trincomalee route show an 18.4% reduction in carbon emissions compared to conventional systems.

Equity-driven facility location: A two-stage robust optimization approach

Equity-driven facility location: A two-stage robust optimization approach

Distributed peer-to-peer energy sharing framework in multi-energy microgrids: A two-stage robust optimization approach with multi-interval uncertainty

Distributed peer-to-peer energy sharing framework in multi-energy microgrids: A two-stage robust optimization approach with multi-interval uncertainty

An Extended C&CG Algorithm for Solving Two-Stage Robust Optimization of Economic and Feasible Scheduling

An Extended C&CG Algorithm for Solving Two-Stage Robust Optimization of Economic and Feasible Scheduling

Towards efficient energy hubs: Two-stage robust optimization with compressed air storage, electric vehicles and renewable energy integration

Towards efficient energy hubs: Two-stage robust optimization with compressed air storage, electric vehicles and renewable energy integration

Two-stage robust optimization approach for enhanced community resilience under tornado hazards

Two-stage robust optimization approach for enhanced community resilience under tornado hazards

Two-stage robust optimization of hydrogen microgrid in plateau tourist cities —taking Yunnan Lijiang as an example

Hydrogen energy, as a vital supplement to renewable energy, contributes significantly to the system's energy storage benefits. In this work, we build and optimize a hydrogen energy microgrid for the plateau tourist city of Lijiang, taking into account the city's unique geographic and climatic circumstances, with the goal of investigating the potential role of hydrogen energy in the regional energy structure and its economics. The study uses a two-stage robust optimization method to change the microgrid's configuration and operation strategy. The system uses a set of alkaline (ALK) electrolyzers, prioritizes wind turbine (WT) and photovoltaic (PV) production, as well as considers three hydrogen use pathways: hydrogen peaking, hydrogen transportation (HEV), hydrogen sales. The oxygen produced by the P2G technology can be used to refill portable oxygen cylinders, which will provide additional cash for highland attractions. The performance of this microgrid system was experimentally evaluated under different operating scenarios through simulation. The results show that the system is able to meet the daily power demand of about 920 residents in the ancient city area, supply 16 hydrogen-energy buses in a single day, and provide 694 kg oxygen. Furthermore, the single-day operational cost analysis reveals that using hydrogen energy saves the microgrid 25.72% in running expenses compared to a traditional microgrid. The use of data-driven uncertainty sets reduces operating costs by 20.82% compared to standard microgrids. This paper presents an innovative hydrogen microgrid design strategy for highland tourist communities, proving the benefits of hydrogen energy in facilitating a regional low-carbon transition.

Service area design and allocation problem for electric bike sharing system under demand uncertainty

ABSTRACT Currently, the electric bike sharing system (EBSS) has gained popularity due to its efficiency and eco-friendliness. However, limited battery capacity of electric bikes (EBs) complicates the system design. To address this, we propose a service area design and allocation model incorporating hybrid stations, aiming to maximize daily net profit. Two cases are explored to address demand uncertainty. First, an expected value model is established, where demand is described probabilistically. Second, demand uncertainty is addressed by modeling random variables as uncertain parameters within an uncertainty set. A two-stage robust optimization model is developed, which maximizes the net profit in the worst-case scenario. We design a row generation approach to solve adjustable two-stage robust programs. Numerical experiments with data from the Daha EBSS in Yangzhou, China, demonstrate the model applicability. Moreover, the proposed algorithm outperforms the existing scenario-based approach in terms of both solution quality and computational efficiency.

A two-stage robust optimization model for emergency service facilities location-allocation problem under demand uncertainty and sustainable development

Under the backdrop of frequent emergencies, the rational layout of emergency service facilities (ESF) and the effective allocation of emergency supplies have emerged as crucial in determining the timeliness of post-disaster response. By adequately accounting for potential uncertainties and carrying out comprehensive pre-planning, the robustness of location-allocation decisions can be significantly improved. This paper delves into the ESF network design problem under demand uncertainty and formulates this problem as a two-stage robust optimization model. The presented model defines a generalized budget uncertainty set to capture victims’ uncertain demand and minimizes the sum of the costs involved in the two stages. The objective function integrates the input cost in the preparedness phase, the deprivation cost from the victims’ perspective and the environmental impact cost responding to sustainable development in the response phase, which respectively correspond to the comprehensive optimization of the deployment of ESF, the distribution of emergency supplies and the implementation of sustainable measures. Subsequently, we employ the column and constraint generation (C&CG) algorithm to solve the proposed model and take the COVID-19 epidemic in Wuhan as a case to verify the effectiveness of the model and algorithm. Finally, we examine the influence of demand uncertainty and environmental impact cost on the optimal solution, yielding valuable managerial insights.

A Two-Stage Robust Optimization Strategy for Long-Term Energy Storage and Cascaded Utilization of Cold and Heat Energy in Peer-to-Peer Electricity Energy Trading

This study addresses the optimization of urban integrated energy systems (UIESs) under uncertainty in peer-to-peer (P2P) electricity trading by introducing a two-stage robust optimization strategy. The strategy includes a UIES model with a photovoltaic (PV)–green roof, hydrogen storage, and cascading cold/heat energy subsystems. The first stage optimizes energy trading volume to maximize social welfare, while the second stage maximizes operational profit, considering uncertainties in PV generation and power prices. The Nested Column and Constraint Generation (NC&CG) algorithm enhances privacy and solution precision. Case studies with three UIESs show that the model improves economic performance, energy efficiency, and sustainability, increasing profits by 1.5% over non-P2P scenarios. Adjusting the robustness and deviation factors significantly impacts P2P transaction volumes and profits, allowing system operators to optimize profits and make risk-aligned decisions.

Capacity configuration optimization of electricity heat hydrogen regional integrated energy system considering supply-demand uncertainties.

Rationally configuring the capacity of the electricity heat hydrogen regional integrated energy system is conducive to improving its economy and energy utilization efficiency. In view of the dual effects of the uncertainties of energy supply and demand in system configuration on power supply reliability and wind power consumption, a min-max-min two-stage robust optimization configuration model aiming at the minimum sum of system investment and operating cost is established for achieving an optimal capacity configuration of multi-vector technologies involved in it. On the basis of typical scenarios, a box-type uncertainty set independent of a probability distribution is used to describe the uncertainty of wind power and demand and the robustness constraint is formed. An innovative parameter, named the uncertainty adjustment parameter, is introduced into the box-type uncertainty set to avoid sacrificing economic benefits caused by too conservative configuration scheme. In this paper, the column and constraint generation algorithm and strong duality theory are used to decompose the original problem into the linearized master problem and subproblem, which can improve the solving speed. Finally, an integrated energy system in the north of China is taken as a case study. The results demonstrate that the proposed model effectively addresses the uncertainty problems of wind power and demand, leading to improved reliability and wind power integration performance. By changing the uncertainty adjustment parameter, the conservativeness of the configuration scheme can be flexibly adjusted. The effectiveness and applicability of the proposed model and solution algorithm are verified.

The reliable ship fleet planning problem for liner shipping services

The reliable ship fleet planning problem for liner shipping services

Research on Two-Stage Robust Optimization of Reverse Logistics Network for Power Batteries

Research on Two-Stage Robust Optimization of Reverse Logistics Network for Power Batteries

Two-stage robust optimization for the integrated dynamic berth allocation and quay crane scheduling problem under uncertainty

A container port is an important cargo transit node that links the land and maritime regions, with berth allocation and quay crane scheduling tasks. Often, bad weather and delays in loading information make vessels’ navigation uncertain. Therefore, in contrast to the classical berth allocation and quay crane assignment and scheduling problem, which minimizes the makespan, this study proposes a novel two-stage robust mixed-integer linear programming model for the integrated dynamic berth allocation and time-variant quay crane scheduling problem to minimize the total departure time, under uncertainties of vessel arrival time and container demand. An extended column constraint generation algorithm with a variable reduction strategy is designed to solve the model. Extensive computational experiments are performed to verify the effectiveness of the proposed model and algorithm. The conclusions drawn from this study could provide operational guidance for container operators to deal with uncertainties.

Machine learning enabled uncertainty set for data-driven robust optimization

Machine learning enabled uncertainty set for data-driven robust optimization

Study on two-stage robust optimal configuration of integrated energy system considering CCUS and electric hydrogen production

Study on two-stage robust optimal configuration of integrated energy system considering CCUS and electric hydrogen production

Two-stage optimization strategy for the active distribution network considering source-load uncertainty

This study aims to advance the development of the active distribution network (ADN) by optimizing resource allocation across different stages to enhance overall system performance and economic benefits. First, an ADN optimization model is constructed based on a two-stage robust optimization approach. The first stage focuses on determining optimal decision variables within the uncertainty set, while the second stage adjusts control variables based on the initial stage decisions. This model effectively addresses source-load uncertainties while preserving the flexibility and adaptability of decision-making solutions. Additionally, this study explores uncertainty models that incorporate correlation factors. The IEEE33-node model is employed to validate the effectiveness and superiority of the proposed optimization strategy through numerical simulations. Simulation results demonstrate that Model 3 comprehensively accounts for photovoltaic and wind turbine generator planning by optimizing their capacity configurations, leading to a 23% increase in distributed generation (DG) penetration. During high-load periods (e.g., 13:00 and 16:00), DG output reaches 47% and 50% of the demand load, underscoring the critical role of DG in supporting the power grid during peak hours. Overall, the proposed two-stage optimization strategy considers source-load uncertainties, significantly reducing economic costs, enhancing DG output, and improving overall system performance. In scenarios with correlated uncertainties, the optimized results exhibit greater accuracy and reliability, providing robust support for the planning and operation of practical distribution networks.

Two-stage distributionally robust optimization operation of virtual power plant considering the virtual energy storage of electric vehicles

Virtual Power Plant (VPP) is a key to aggregate various distributed energy sources. With the vigorous rise of various distributed energy sources, the direct access of large-scale electric vehicle load will increase the complexity of VPP coordinated operation. Hence, this paper proposes a VPP optimization method for Electric Vehicle Virtual Energy Storage (EV-VES). Firstly, the travel characteristics of electric vehicles are analyzed, and EV-VES model is established to coordinate and manage the charge-discharge behavior of EV. Secondly, the “carbon charge rate” model of energy storage (ES) is introduced to establish the relationship between carbon emission and electricity price, and the VPP operation model considering the “carbon charge rate” of energy storage is established. Finally, the two-stage robust optimization operation model of VPP is constructed, Wasserstein distance is used to describe the confidence set of uncertain probability distribution of wind power generation and load, and the uncertainty of system source and load are described by the confidence set. The Column and Constraint Generation (C&CG) algorithm was used to determine the optimal operational benefit solution. The effectiveness of the proposed VPP optimal operation model was validated through case study.

A low-carbon driven price approach for energy transactions of multi-microgrids based on non-cooperative game model considering uncertainties

A low-carbon driven price approach for energy transactions of multi-microgrids based on non-cooperative game model considering uncertainties