Search Results (122)

An ongoing challenge in pelagic oceanography and limnology is to quantify and understand the distribution of suspended particles and particle aggregates with sufficient temporal and spatial fidelity to understand their dynamics. These particles include biotic (mesoplankton, organic fragments, fecal pellets, etc.) and abiotic (dusts, precipitates, sediments and flocks, anthropogenic materials, etc.) matter and their aggregates (i.e., marine snow), which form a large part of the total particulate matter > 200 μm in size in the ocean. The transport of organic material from surface waters to the deep-sea floor is of particular interest, as it is recognized as a key factor controlling the global carbon cycle and hence, a critical process influencing the sequestration of carbon dioxide from the atmosphere. Here we describe the development of an oceanographic instrument, the Pelagic Laser Tomographer (PLT), that uses high-resolution optical technology, coupled with post-processing analysis, to scan the 3D content of the water column to detect and quantify 3D distributions of small particles. Existing optical instruments typically trade sampling volume for spatial resolution or require large, complex platforms. The PLT addresses this gap by combining high-resolution laser-sheet imaging with large effective sampling volumes in a compact, deployable system. The PLT can generate spatial distributions of small particles (~100 µm and larger) across large water volumes (order 100–1000 m³) during a typical deployment, and allow measurements of particle patchiness over spatial scales to less than 1 mm. The instrument’s small size (6 kg), high resolution (~100 µm in each 3000 cm² tomographic image slice), and analysis software provide a tool for pelagic studies that have typically been limited by high cost, data storage, resolution, and mechanical constraints, all usually necessitating bulky instrumentation and infrequent deployment, typically requiring a large research vessel. Full article

The classic set covering problem (SCP) is an NP-hard binary integer optimization problem with diverse business and industrial applications. Its primary goal is to consolidate resources by selecting a minimal cost subset of columns in a matrix that covers all required rows. Traditionally, conflicts between selected resources were resolved after generating a solution, often adding managerial effort and inefficiency. Recently, two papers have tried to handle conflict constraints explicitly as part of the SCP solution generation process. This paper focuses on SCPs with soft conflict constraints (SCP-SCC), where violations are allowed but with penalties, and proposes a simple hybrid solution approach that combines a GRASP-based heuristic with Gurobi optimization. Using 360 test instances (160 from the literature and 200 new instances), this hybrid approach results in a 7.4% performance improvement over Gurobi, demonstrating the benefit of integrating heuristic and exact solution methods. In addition, classification tree analysis is applied as an attempt to identify problem features (such as conflict graph density and size) that can be used to predict when SCP-SCC instances will likely be difficult to solve to proven optimality efficiently using Gurobi. These insights provide practical guidance for operations research practitioners, enabling informed decisions among heuristic, exact, or hybrid solution approaches and improving efficiency in real-world applications. Full article

This paper investigates the planning problem of AC-integrated wind–photovoltaic–hydro–storage (WPHS) bundled transmission systems. To effectively capture the uncertainty and interdependence in renewable power outputs, a Copula-enhanced distributionally robust optimization (DRO) framework is developed, enabling a unified treatment of stochastic and correlated renewable generation within the system planning process. First, a location and capacity planning model based on DRO for WPHS generation bases is formulated, in which a composite-norm ambiguity set is constructed to describe the uncertainty of renewable resources. Second, the Copula function is employed to characterize the nonlinear dependence structure between wind and photovoltaic (PV) power outputs, providing representative scenarios and initial probability distribution (PD) support for the construction of a bivariate ambiguity set that embeds coupling information. The resulting optimization problem is solved using the column and constraint generation (C&CG) algorithm. In addition, an evaluation metric termed the transmission corridor utilization rate (TCUR) is proposed to quantitatively assess the efficiency of external AC transmission planning schemes, offering a new perspective for the evaluation of regional power transmission strategies. Finally, simulation results validate that the proposed model achieves superior performance in terms of system economic efficiency and TCUR. Full article

Against the backdrop of China’s dual-carbon goals, traditional road transportation has relatively high carbon emissions and is in urgent need of a low-carbon transition. The intermittency of photovoltaic (PV) power generation and the stochastic nature of electric vehicle (EV) charging demand introduce significant uncertainty for PV-energy storage-charging systems in highway service areas. Existing approaches often struggle to balance economic efficiency and reliability. This study develops a min-max-min robust optimization model for a full-route PV-energy storage-charging system. A box uncertainty set is used to characterize uncertainties in PV output and EV load, and a tunable uncertainty parameter is introduced to regulate risk. The model is solved using a column-and-constraint generation (C&CG) algorithm that decomposes the problem into a master problem and a subproblem. Strong duality, combined with a big-M formulation, enables an alternating iterative solution between the master problem and the subproblem. Simulation results demonstrate that the proposed algorithm attains the optimal solution and, relative to deterministic optimization, achieves a desirable trade-off between economic performance and robustness. Full article

Aiming at multi-agent interest demands and environmental benefits, a distributionally robust game-theoretic optimization algorithm based on a green certificate–carbon trading mechanism is proposed for uncertain microgrids. At first, correlated wind–solar scenarios are generated using Kernel Density Estimation and copula theory and the probability distribution ambiguity set is constructed combining 1-norm and $\infty$-norm metrics. Subsequently, with gas turbines, renewable energy power producers, and an energy storage unit as game participants, a two-stage distributionally robust game-theoretic optimization scheduling model is established for microgrids considering wind and solar correlation. The algorithm is constructed by integrating a non-cooperative dynamic game with complete information and distributionally robust optimization. It minimizes a linear objective subject to linear matrix inequality (LMI) constraints and adopts the column and constraint generation (C&CG) algorithm to determine the optimal output for each device within the microgrid to enhance its overall system performance. This method ultimately yields a scheduling solution that achieves both equilibrium among multiple stakeholders’ interests and robustness. The simulation result verifies the effectiveness of the proposed method. Full article

The continuous growth of electric vehicle (EV) penetration offers electric vehicle aggregators (EVAs) opportunities to increase revenue by participating in both the energy market and the frequency regulation (FR) market. However, the uncertainty of user behavior poses challenges for formulating effective scheduling strategies. To address these issues, this paper first establishes a charging probability prediction model that considers battery state, travel distance, and user driving habits. Subsequently, a distributionally robust optimization (DRO) model is adopted to characterize the uncertainties associated with EV clusters, and the Column-and-Constraint Generation (C&CG) algorithm is employed to decompose the original model into a master–subproblem framework for solution. Finally, the proposed scheduling strategy for EVAs is validated within the PJM market framework. The results demonstrate that simultaneous participation in the energy and FR markets can significantly enhance the operational revenue of EVAs, achieving a total daily revenue of USD 547.47 compared to USD 427.35 from coordinated charging only. Moreover, the scheduling strategy based on the DRO model achieves a trade-off between economic efficiency and risk resilience, yielding a higher average daily revenue with lower volatility (standard deviation of USD 40.46) compared to Stochastic Optimization (UD 500.98 and USD 49.57, respectively). Full article

With the continuously rising penetration rate of variable renewable energy (VRE), issues related to power balance and frequency stability in power systems have become increasingly prominent. Battery energy storage systems (BESS) with grid-forming capabilities are regarded as an effective solution for providing rapid frequency support. However, the stochastic fluctuations of VRE output also lead to time-varying system inertia, which undoubtedly increases the complexity of energy storage planning. To address these problems, this study constructs a bi-level robust planning model for grid-forming energy storage considering frequency security constraints. First, a frequency response model for grid-forming BESS is established. By accurately describing the delay characteristics of different resources in frequency response, dynamic frequency security constraints (FSC) that can be embedded into the planning model are constructed. Subsequently, the study proposes an evaluation method for the spatial distribution of power system inertia, providing a basis for the optimal siting of BESS in the grid. On this basis, a bi-level robust planning model, considering VRE uncertainty, is constructed, which embeds an operational simulation model and incorporates FSC. To achieve an effective solution of the model, FSC is transformed into a second-order cone form, and a nested column-and-constraint generation (C&CG) algorithm is employed for solving. Simulation results on the modified NPCC-140 bus system verify the effectiveness of the proposed model. While reducing the total cost by 15.9%, this method effectively ensures the dynamic frequency security of the power system, improves the spatial distribution of inertia and significantly enhances the system’s ability to accommodate VRE. Full article

Trails in heritage sites are useful ways to engage visitors with the place. Sensory trails proposed in this paper, engaged with the sensory walking method, are designed purposefully to engage the multi-sensory features onsite with prompts to link to the historic sensory elements that have historic and cultural meanings to the heritage sites. Two questions are asked: (1) What process can we follow to design sensory heritage trails? (2) What criteria can be used to evaluate and guide the sensory features on site and from historic documentations? Taking design research as the overarching methodology, this paper reflects on the creation of two sensory trails, Sensing Beyond the Roundhouse and Sensing Around the Anglesey Column, following the Double Diamond framework developed by UK Design Council. An iterative design framework was developed, beginning with the identification of constraints and sensory opportunities through site observations, document analysis, and stakeholder interviews, which leads to interpretations of sensory features to shape storylines and route planning informed by user analysis. It is followed by representing the trails through sensory maps and other low-cost creative formats and then validating proposed trails with communities and stakeholders via pilot walks and feedback sessions. Four criteria are generated to assess sensory features based on engagement and authenticity: their contribution to the authentic historic atmosphere of the site; their ability to trigger imagination and evoke nostalgia; their distinctiveness and relevance to the site’s heritage narratives; and their capacity to encourage physical interaction and embodied engagement. The discussion part argues that sensory trails can be used as place-based strategies to inform urban planning and development around the heritage site through three pathways: catalyst for improvements and developments, connect isolated heritage sites, generate place-based knowledge. Full article

The strong uncertainty of renewable energy poses significant reliability and safety challenges for the coordinated operation of multi-integrated energy systems (MIES). To address this, a data-driven two-stage distributed robust collaborative optimization scheduling model for MIES is proposed, based on a spatiotemporal fusion conditional diffusion model (STF-CDM). First, to more accurately capture the uncertainty in renewable energy output, the model utilizes a scenario set generated by the STF-CDM model and reduced via the K-means clustering algorithm as the initial renewable energy scenarios for the distributed robust optimization set. The STF-CDM model employs a Temporal module component (TMC) unit composed of Transformer time-series modules and a Spatial module component (SMC) unit composed of CNN neural networks for feature extraction and fusion of time-series and spatial-series data. Second, a benefit allocation method based on multi-energy trading contribution rates is proposed to achieve equitable distribution of cooperative gains. Finally, to protect participant privacy and enhance computational efficiency, an alternating direction multiplier method (ADMM) coupled with parallelizable column and constraint generation (C&CG) is employed to solve the energy trading problem. The case analysis results demonstrate that the STF-CDM model proposed in this study exhibits superior performance in addressing the uncertainty of renewable energy output. Concurrently, the asymmetric Nash game mechanism and the ADMM-C&CG solution algorithm proposed in this study achieve a fair and reasonable distribution of benefits among all participants when handling energy transactions and cooperative gains. This is accomplished while ensuring system robustness, economic efficiency, and privacy. Full article

Building a sustainable and resilient humanitarian logistics system is essential for reducing disaster losses and supporting long-term socio-economic recovery. Following a major disaster, rapidly organizing casualty evacuation while maintaining system robustness is a fundamental component of sustainable emergency management. This study develops a two-stage robust optimization model for designing a sustainable humanitarian logistics network that simultaneously accounts for two critical post-disaster uncertainties: (i) interruption risks at temporary medical points and (ii) uncertain casualty demand. By explicitly differentiating deprivation costs between mild and serious injuries, the model quantifies human suffering in monetary terms, thereby integrating social and economic sustainability considerations into the optimization framework. A customized column-and-constraint generation (C&CG) algorithm with proven finite convergence is proposed to ensure tractability and practical applicability. Using the 2008 Wenchuan earthquake as a real-world case study, involving 10 affected areas and 10 candidate temporary medical points, the results demonstrate that the proposed approach yields evacuation plans that remain feasible under all tested worst-case realizations, substantially reducing deprivation costs compared with existing benchmarks. The findings highlight that strategically increasing the capacity of key temporary medical nodes enhances the sustainability and resilience of the emergency medical system, offering evidence-based insights for designing sustainable and robust disaster-response strategies. Full article

As ports evolve to meet sustainability targets, seamless coordination between road and rail operations becomes fundamental to success. This study addresses the Train Loading Planning Problem (TLPP) which focuses on assigning outbound containers to train wagons under slot, weight, and pattern constraints aiming to examine its broader systemic implications. A compact mixed-integer programming formulation is developed and enhanced through a column-generation approach that efficiently prices feasible wagon plans. The optimization module is embedded within a discrete-event simulation of terminal processes including yard handling, gate operations, and train timetables. The study tests a TLPP-based rail planning algorithm within a DES of terminal and hinterland operations to quantify the impact under realistic variability. Using operational data from the Port of Valencia, realistic planning scenarios are evaluated across varying demand mixes and train frequencies. Results indicate that integrating rail capacity with optimized wagon loading reduces set-up time by 20%, delivery lead time by 54%, container dwell time by 80%, and greenhouse gas emissions by 54% compared with a trucking forwarding baseline, while maintaining throughput and alleviating congestion at terminal gates and yards. From a computational perspective, the column-generation approach achieves improved runtimes to the compact MIP and scales linearly to the number of variables. The proposed framework delivers ready to use load plans and practical insights for the deployment of additional rail capacity, supporting sustainable logistics in port environments. Full article

To address the uncertainty in power grid scheduling caused by the output variability of distributed energy resources (DERs) in microgrids, as well as the limitations of stochastic optimization relying on accurate probability distributions and the overly conservative nature of robust optimization leading to insufficient economic performance, this paper proposes a disseminated robust optimization method for microgrid operation that considers flexible demand-side resources. First, to address the uncertainty in the forecasting of wind and solar power scenarios, this paper launches a two-stage distributionally robust optimization (DRO) model based on a Kullback–Leibler (KL) divergence ambiguity set using a min–max–min framework. Then, the Column-and-Constraint Generation (C&CG) algorithm is employed to decouple the model for an iterative solution. Finally, simulation case studies are directed to validate the effectiveness of the proposed model. The demand response-based optimization model projected in the paper effectively enhances the flexibility of the Microgrid. Compared to robust optimization, this model reduces the daily operating cost by 2.86%. Although the cost is slightly higher (4.88%) than that of stochastic optimization, it achieves a balance between economy and robustness by optimizing the expected value under the worst-case probability distribution. Full article

With the deepening of multi-energy coupling and the integration of high proportions of renewable energy, the Park Integrated Energy System (PIES) 1demonstrates enhanced energy utilization flexibility. However, the random fluctuations in photovoltaic (PV) output also pose new challenges for system dispatch. Existing distributed robust scheduling approaches largely rely on offline predictive models and therefore lack dynamic correction mechanisms that incorporate real-time operational data. Moreover, the initial probability distribution of PV output is often difficult to obtain accurately, which further degrades scheduling performance. To address these limitations, this paper develops a PV digital twin model capable of providing more accurate and continuously updated initial probability distributions of PV output for distributed robust scheduling in PIESs. Building upon this foundation, this paper proposes a distributed robust scheduling method for the PIES based on digital twins. This approach aims to maximize the flexibility of energy utilization in PIESs and overcome the challenges posed by random fluctuations in PV output to PIES operational scheduling. First, a PIES model is established after investigating a park-level practical integrated energy system. To describe the uncertainty of PV output, a PV digital twin model that incorporates historical data and temporal features is developed. The long short-term memory (LSTM) neural network is employed for output prediction, and real-time data are integrated for dynamic correction. On this basis, error perturbations are introduced, and PV scenario generation and reduction are carried out using Latin hypercube sampling and k-means clustering. To achieve multi-energy cascade utilization, the objective of optimization is defined as the minimization of the sum of system operating cost and curtailment cost. To this end, a two-stage distributed robust optimization model is constructed. The optimal scheduling scheme was obtained by solving the problem using the column-and-constraint generation (CCG) algorithm. The proposed method was finally validated through a case study involving an actual industrial park. The findings indicate that the constructed digital twin model achieves a significant improvement in prediction accuracy compared to traditional models, with the root mean square error and mean absolute error reduced by 13.3% and 10.81%, respectively. Furthermore, the proposed distributed robust scheduling strategy significantly enhances the operational economics of PIESs while maintaining system robustness, compared to conventional methods, thereby demonstrating its practical application value in PIES scheduling. Full article

Hydrogen energy is developing rapidly, and the hydrogen-based integrated energy system (HIES) offers improved economic performance, flexibility, and environmental benefits compared with conventional power systems. However, the increasing frequency of natural disasters caused by climate change introduces significant vulnerabilities that threaten system security. Preventive scheduling provides a proactive and economical means to enhance system resilience against such uncertainties. This paper proposes a preventive scheduling model for HIES based on adaptive robust optimization (ARO) to address the uncertain impacts of natural disasters on transmission lines, pipelines, and roads. The model incorporates the operational constraints and interdependencies among multiple energy subsystems and integrates flexible scheduling strategies such as power-to-hydrogen-and-heat (P2HH) and hydrogen transportation (HT). A hybrid algorithm is developed to efficiently solve the large-scale ARO problem with numerous integer variables. Case studies performed on two test systems demonstrate that the proposed preventive scheduling model effectively reduces operational costs and load curtailments. Simulation results show that coordinating P2HH and HT reduces power, heat, hydrogen, and gas load curtailments by 14.35%, 43.39%, 49.97%, and 40.32%, respectively, as well as operational costs by 14.60%. Moreover, the proposed hybrid algorithm enhances computational efficiency, reducing solution time by 21% with only a 2% deviation from the solution obtained by the conventional C&CG–AOP algorithm. Full article

Transportation planning often involves not only shipment costs but also setup costs associated with deploying vehicles or transport resources. In many practical logistics operations, this setup cost does not remain constant but increases stepwise with the number of vehicles used, reflecting economies of scale and scheduling thresholds. To capture this realistic feature, this study investigates the transportation problem with stepwise costs, where total costs combine shipment-dependent variable costs and vehicle activation costs. We develop a mixed-integer programming (MIP) model to represent the problem and propose an efficient algorithm based on variable-splitting reformulation and a row-and-column generation scheme. This approach dynamically introduces only the necessary variables and constraints, enabling the solution of large-scale instances that are otherwise computationally challenging. Numerical experiments show that the method produces high-quality solutions much faster than direct MIP solvers. The results highlight the model’s practical value in optimizing fleet utilization and transportation cost structures in real logistics and supply chain systems. Full article