Search Results (28)

Offshore engineering microgrids integrate renewable generation, energy storage, and large marine test loads. Frequent start-stop transients of test loads, strong wind/PV fluctuations, and saline–humid conditions accelerate equipment aging and threaten power quality, while conventional dispatch neglects battery degradation, converter stress, and test-load energy recovery. This paper develops a data-driven distributionally robust economic dispatch method combining: (i) a priority-based dynamically weighted multi-functional battery coordination model unifying test-load surge suppression, renewable smoothing, and price arbitrage, with its coordinated reference embedded as a tracking constraint with an explicit two-level reserved margin; (ii) a two-stage Wasserstein distributionally robust optimization with adaptive ambiguity radii on standardized forecast errors and an improved column-and-constraint generation algorithm covering the full vertex set of the standardized uncertainty box; and (iii) a life-cycle-cost-aware objective with linearized battery degradation and converter power-variation stress under a dual time-scale (1 h day-ahead/15 min intraday) framework. Case studies on grid-connected and islanded offshore engineering microgrids show that multi-functional coordination lowers the post-storage maximum load ramp rate from 23.57 to 19.31 kW/min (−18.1%) and its standard deviation from 6.25 to 5.79 kW/min (−7.3%) at an operating-cost increase of 126.4 CNY/day, while reducing downstream renewable power fluctuation by 41.0% and recovering 102.0 kWh/day of test-load regenerative energy. The distributionally robust schedule attains a first-stage cost of 9492.5 CNY and, over 1000 independent realizations, reduces the out-of-sample mean cost from 9656.1 CNY (deterministic) to 9397.3 CNY and the 95% conditional value at risk (CVaR95) from 9940.5 to 9552.1 CNY, versus 10,698.3 CNY for a box-robust schedule with equivalent 95% coverage. The life-cycle-cost-aware dispatch reduces equivalent battery capacity fade by 37.1% and converter power-variation stress by 32.5% at +1.76% operating cost, while maintaining energy-based supply reliability at 99.79–100%. When the four mechanisms operate simultaneously, the maximum post-storage ramp is 19.31 kW/min against 23.57 kW/min for the unintegrated baseline (−18.1%), and removing the distributionally robust layer from the integrated schedule raises the out-of-sample CVaR95 of the recourse cost from 68.8 to 609.2 CNY/day. All optimization results are reproduced by two independent MILP solvers, with objectives agreeing within 2 × 10⁻⁹. Full article

The increasing penetration of renewable energy integration poses a threat to the safe, reliable operation of coupled electricity and heating systems under uncertain power supply. Additionally, there are limitations on the sharing of private data between the two system operators, while managing uncertainty escalates the intricacy of this issue. Therefore, we propose a risk-quantified distributed optimal dispatch model for combined electricity and heating systems. We utilize moment-based distributionally robust chance constraints to describe the uncertain risk caused by the stochastic wind power output. The adaptive penalty factor-based alternating direction method of multipliers is employed to decouple the centralized model in a distributed manner. A second-order cone programming problem can be derived to enhance a more tractable reformulation. Multidimensional risk indices are proposed to quantify the operational risk, achieving a balance between the controllable risk and the economical dispatch. Finally, numerical results, based on the Barry Island system, validate the effectiveness and feasibility of the proposed approach while selecting risk coefficient $\epsilon =0.1$ to achieve the optimal distributed risk operation. © 2017 Elsevier Inc. All rights reserved. Full article

Due to its significant importance in many disciplines, distributed optimization under uncertainty has become an active research field over the past decade. This paper presents a cross-paradigm review of this development. We organize the literature around three approaches ordered by how much is known about the uncertainty: robust optimization, which uses set or support information; distributionally robust optimization, which uses partial distributional knowledge; and stochastic programming, which uses an estimated or specified distribution. These are regions of a spectrum rather than disjoint classes, and formulations that combine them are noted where they arise. For each approach, we examine modeling frameworks and distributed algorithmic adaptations, together with representative applications across different domains. We synthesize methodological trends, compare algorithmic properties, and identify open challenges for scalable distributed algorithms under uncertainty. Key findings include the widespread adaptation of classical algorithms, particularly the alternating direction method of multipliers (ADMM), across all uncertainty paradigms, alongside an evolution toward data-driven and adaptive methods for real-time uncertainty handling. We also highlight that many advanced centralized techniques for optimization under uncertainty remain only partially adapted to distributed settings, representing a significant research opportunity. Of the 112 reviewed studies falling within the 2015–2025 eligibility window, 59.8% address power and energy systems, 12.5% federated and distributed learning, and 5.4% robotics and autonomous systems, while other application domains contribute only isolated studies. The paper concludes with critical gaps and future directions spanning distributed reformulations, machine learning integration, multi-stage optimization, privacy-preserving computation, and cross-domain methodological unification. Full article

Against the backdrop of the global low-carbon transition, power-to-ammonia (PtA) has emerged as a pivotal direction for large-scale energy storage. Distributionally robust optimization can effectively address uncertainties in energy systems; however, traditional distributionally robust dispatch models generally suffer from over-conservatism that leads to increased operational costs, and existing PtA studies mostly focus on scenario-based adaptations of established optimization tools, lacking mechanistic and methodological innovations tailored to the electricity–hydrogen–ammonia coupling characteristics. To address these issues, this paper proposes a distributionally robust chance-constrained economic dispatch model (WMDRCC) based on the Wasserstein metric and first-order moment information, and introduces a logical mapping relationship that links hydrogen storage capacity with the operating modes of ammonia synthesis. This mechanism enables real-time optimization of the H₂/N₂ feed ratio, mitigates hydrogen source fluctuations, and avoids reactor instability and cost-ineffective shutdowns. Furthermore, by integrating Conditional Value at Risk (CVaR), duality theory, and big-M linearization, the complex robust chance-constrained problem is reformulated into a computationally tractable mixed-integer linear programming (MILP) model. Numerical results on the IEEE 33-bus system demonstrate that, compared with a distributionally robust model based solely on the Wasserstein distance, the proposed method effectively reduces system operating costs under the tested 24 h daily scenarios, while simultaneously improving renewable energy accommodation and reducing network losses, thereby providing a novel dispatch scheme for PtA systems that balances both economic efficiency and robustness. Full article

Production scheduling in sustainable manufacturing systems must cope with processing time uncertainty while maintaining operational efficiency and controlling operational costs. This paper proposes a Distributionally Robust Optimization (DRO) model for the permutation flow shop scheduling problem with sequence-dependent setup times (PFSP-SDST), where uncertain processing times are represented through multiple scenarios and evaluated under ambiguous probability distributions. An exact solution approach is developed for small-scale instances. For medium and large-scale problems, the Greedy Randomized Adaptive Search Procedure (GRASP), the proposed Hybrid GRASP (HGRASP), Ant Lion Optimizer (ALO) and Slime Mold Algorithm (SMA) are adapted and compared. Computational experiments show that most methods closely reproduce the exact benchmark solutions on small instances. For large-scale problems, the Friedman test reveals significant differences in both solution quality ($p=9.91 \times {10}^{-6}$) and computational time ($p=3.49 \times {10}^{-6}$). Post hoc comparisons indicate that ALO and SMA achieve the best solution quality performance and are statistically indistinguishable from each other, while SMA obtains the most favorable computational time rank. These findings indicate favorable performance of the population-based metaheuristics under the adopted experimental settings for the considered distributionally robust flow shop scheduling problems under processing time uncertainty. The proposed DRO framework offers a practical approach for generating reliable schedules while reducing operational costs in Industry 4.0 manufacturing systems. Full article

Mobile crowd sensing (MCS) is an emerging sensing paradigm that leverages mobile devices for large-scale data collection, where an MCS platform recruits workers to perform time-sensitive sensing tasks. In practice, worker travel times are inherently uncertain due to dynamic urban environments—traffic congestion, road closures, and unplanned detours cause actual delays to deviate from historical patterns. However, existing worker recruitment methods typically optimize expected-case performance based on static historical distributions, providing no robustness guarantee under distribution shift. To address these challenges, this paper proposes DRO-IGR, a worker recruitment framework based on Distributionally Robust Optimization (DRO) and an Iterative Greedy Recruitment algorithm. The framework introduces a DRO Probability Estimation Engine that treats each worker’s true delay distribution as lying within a Wasserstein ambiguity set centered on its empirical history, with a radius that adapts to data sparsity, behavioral variability, and task importance. Strong duality reduces the resulting worst-case optimization to an efficient one-dimensional convex search. Driven by these robust probability estimates, a marginal-gain scoring rule iteratively selects worker–task pairs that maximize importance-weighted robust utility per unit cost. Extensive experiments on three synthetic spatial distributions and the real-world T-Drive Beijing taxi dataset show that, compared to existing approaches, DRO-IGR completes more tasks, achieves a higher total importance sum, and attains greater utility within the same budget constraint. Full article

The electrification of urban transport has made battery electric buses (BEBs) an important option for reducing carbon emissions and improving urban air quality. However, the high investment cost of charging infrastructure and the uncertainty in effective usable battery capacity at the day-ahead scheduling stage—caused by accumulated degradation, heterogeneous operating conditions, and imperfect state estimation—create major challenges for charging infrastructure siting and daily bus operations. This study proposes a joint optimization model for infrastructure siting and BEB charging scheduling, in which effective capacity uncertainty is handled using a distributionally robust optimization (DRO) framework. To solve the resulting mixed-integer nonlinear program efficiently, we develop a matheuristic decomposition method that integrates Adaptive Large Neighborhood Search (ALNS) with small gaps relative to a relaxation-based lower bound. Computational experiments based on real-world bus route data indicate that the proposed framework obtains high-quality solutions with small gaps relative to a relaxation-based lower bound, performs better than representative benchmark heuristics, and scales well to large instances. Full article

This study develops an advanced optimization framework for heating, ventilation, and air conditioning (HVAC) systems in multi-zone buildings with highly dynamic and uncertain internal heat loads. Unlike conventional models that assume static occupancy, the proposed approach captures time-varying, spatially heterogeneous thermal disturbances driven by occupant activity. The building is modeled as a coupled cyber-physical system integrating multi-zone thermal dynamics, nonlinear HVAC energy consumption, and behavior-driven heat generation. To address uncertainty, a distributionally robust optimization framework based on Wasserstein ambiguity sets is employed, enabling reliable performance without requiring precise probability distributions. In addition, a physics-informed reinforcement learning mechanism is incorporated to derive adaptive control policies while ensuring thermodynamic feasibility. A multi-zone coordination strategy is further introduced to manage spatial thermal interactions and maintain stable comfort across different areas. Case study results demonstrate that the proposed method reduces peak energy consumption by 28–32%, decreases comfort violation rates by 65–75%, and improves thermal stability, with temperature variance reduced by over 60% compared to baseline strategies. Full article

The large-scale integration of renewable energy necessitates enhanced flexibility in power grids. As aggregators, electric vehicle charging stations (EVCSs) can provide potential grid services via vehicle-to-grid (V2G) technology. Against the challenge from the intertwined uncertainties of transmission system operation and renewable energy output limit, the private ownership of EVCSs limit their practical implementation. To exploit the flexibility of EVCSs to cope with the system operational uncertainties, this paper proposes a novel multi-stage coordination framework for EVCS flexibility utilization, based on a demand response incentive mechanism. The framework explicitly incorporates the operational constraints and charging/discharging strategies of EVCSs into the demand response clearing and dispatch mechanism. Specifically, adaptive robust optimization (ARO) and distributionally robust optimization (DRO) are employed to model the heterogeneous uncertainties of transmission operational requirements and renewable energy output, respectively. The model is solved in a distributed manner using the alternating direction method of multipliers (ADMM), with a tailored column-and-constraint generation (C&CG) algorithm developed to solve the regional problems. Simulation results confirm that the proposed method improves both economic efficiency and renewable energy accommodation. Full article

The growing scale and complexity of industrial infrastructure make efficient and reliable inspections a critical challenge. Inspection task demands often vary dynamically, requiring efficient and demand-responsive inspection strategies to ensure stable operation. However, existing UAV inspection approaches typically deploy UAV base stations (UAV-BSs) based on fixed inspection frequencies, which are inadequate for adapting to such dynamic demands and may reduce inspection efficiency. Moreover, these approaches often rely on historical inspection data, whose empirical distributions may deviate from the true distributions, thereby compromising solution robustness. To address these issues, this paper proposes a two-stage distributionally robust optimization (TDRO) framework for joint UAV-BS deployment and inspection routing in dynamic environments. The framework accounts for uncertainties in both inspection frequency and distributional perturbations. Uncertainty sets constructed based on probability metrics are employed to capture deviations between empirical and true distributions, forming the foundation of the two-stage distributionally robust optimization model. The resulting model is solved using column-and-constraint generation (C&CG) integrated with column generation (CG), yielding robust deployment decisions and an effective trade-off between total system cost and inspection efficiency. Simulation results show that the framework effectively addresses inspection frequency uncertainty, reducing the total objective by 5.50% on average, with a further 2.16% reduction when distributional perturbations are considered. Full article

Spacecraft pursuit–evasion in contested environments is complicated by strategic incompleteness: the evader can switch maneuvering modes and deploy multi-domain countermeasures that degrade the pursuer’s perception, leading to non-stationary information and distributionally ambiguous interference statistics. A dynamic time-window Nash equilibrium framework is developed for linearized Local Vertical Local Horizontal (LVLH) relative motion under interference-induced uncertainty. Perceptual degradation is modeled via an evidence–theoretic belief representation, and the Jensen–Shannon (JS) divergence is introduced to quantify discrepancies between nominal and interference-corrupted beliefs. The divergence metric drives an adaptive time-window partitioning policy and an uncertainty-aware running cost that balances nominal performance objectives with robustness regularization during high-degradation intervals. In each time window, sufficient conditions are provided for the existence of a local Nash equilibrium, and equilibrium strategies are characterized by the Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation. A global consistency result is established: assuming state continuity, additive cost decomposition, and dynamic-programming compatibility at window boundaries, concatenating the window-wise equilibria yields a Nash equilibrium over the entire horizon. Unlike conventional receding-horizon differential games with a fixed replanning grid, the proposed policy partitions the horizon online in response to perceptual-degradation events and stitches adjacent windows through a continuation value. This boundary stitching enables the global consistency guarantee under additive costs and state continuity. To hedge against ambiguity in interference intensity, a variational distributionally robust optimization (DRO) problem with moment-constrained ambiguity sets is formulated, and the dual worst-case distribution is derived. The resulting Karush–Kuhn–Tucker (KKT) system is reformulated as a finite-dimensional variational inequality, for which an accelerated Alternating Direction Method of Multipliers (ADMM) operator-splitting solver is proposed for efficient real-time computation. Numerical simulations validate the framework and demonstrate improved robustness and computational scalability under time-varying interference compared with fixed-window baselines. Full article

Shared energy storage provides a promising solution for the operation of microgrid clusters. This paper explores a hybrid electric–hydrogen shared energy storage model within microgrid clusters, aiming for clean energy generation and economical energy supply despite renewable energy’s unpredictability and complex stakeholder interactions. First, the proposed method features a shared energy storage operator that hosts electric storage and power-to-gas, enabling multi-microgrids energy sharing. To address market dynamics, a hybrid game theory approach using Nash bargaining and Stackelberg games is employed to manage interactions among the shared energy storage operator, microgrid operators, and internal end-users, while accounting for their differing interests. Second, to address uncertainty in renewable energy output, a distributionally robust optimization model is implemented with conditional value at risk, focusing on risk in extreme scenarios. The Adaptive Alternating Direction Method of Multipliers algorithm and Karush–Kuhn–Tucker conditions are used to solve the optimal decision scheme for each entity. Finally, a case study is used to verify the model’s effectiveness. Simulation results show that hybrid electric–hydrogen energy sharing improves resource utilization, leading to significant revenue increases for microgrids and higher profitability for shared energy storage operator. The game-theory-based approach ensures equitable revenue distribution and a 9.86% increase in coalition revenue. It provides a flexible approach to balance economic efficiency and system robustness by allowing decision-makers to adjust risk preference parameters and use historical sample data for informed decision-making. Full article

Uncertainty in optimization models often causes awkward properties in their deterministic equivalent formulations (DEFs), even for simple linear models. Chance-constrained programming is a reasonable tool for handling optimization problems with random parameters in objective functions and constraints, but it assumes that the distribution of these random parameters is known, and its DEF is often associated with the complicated computation of multiple integrals, hence impeding its extensive applications. In this paper, for optimization models with chance constraints, the historical data of random model parameters are first exploited to construct an adaptive approximate density function by incorporating piecewise linear interpolation into the well-known histogram method, so as to remove the assumption of a known distribution. Then, in view of this estimation, a novel confidence set only involving finitely many variables is constructed to depict all the potential distributions for the random parameters, and a computable reformulation of data-driven distributionally robust chance constraints is proposed. By virtue of such a confidence set, it is proven that the deterministic equivalent constraints are reformulated as several ordinary constraints in line with the principles of the distributionally robust optimization approach, without the need to solve complicated semi-definite programming problems, compute multiple integrals, or solve additional auxiliary optimization problems, as done in existing works. The proposed method is further validated by the solution of the stochastic multiperiod capacitated lot-sizing problem, and the numerical results demonstrate that: (1) The proposed method can significantly reduce the computational time needed to find a robust optimal production strategy compared with similar ones in the literature; (2) The optimal production strategy provided by our method can maintain moderate conservatism, i.e., it has the ability to achieve a better trade-off between cost-effectiveness and robustness than existing methods. Full article

This study develops a tri-level adversarial robust optimization framework for cyber–physical scheduling in smart grids, addressing the intertwined challenges of coordinated cyberattacks, defensive resource allocation, and stochastic operational uncertainties. The upper level represents the attacker’s objective to maximize system disruption and conceal detection, the middle level models the defender’s optimization of detection and redundancy deployment under budgetary constraints, and the lower level performs economic dispatch given tampered data and uncertain renewable generation. The model integrates Distributionally Robust Optimization (DRO) based on a Wasserstein ambiguity set to safeguard against worst-case probability distributions, ensuring operational stability even under unobserved adversarial scenarios. A hierarchical reformulation using Karush–Kuhn–Tucker (KKT) conditions and Mixed-Integer Second-Order Cone Programming (MISOCP) transformation converts the nonconvex tri-level problem into a tractable bilevel surrogate solvable through alternating direction optimization. Numerical case studies on multi-node systems demonstrate that the proposed method reduces system loss by up to 36% compared to conventional stochastic scheduling, while maintaining 92% dispatch efficiency under high-severity attack scenarios. The results further reveal that adaptive defense allocation accelerates robustness convergence by over 50%, and that the risk–reward frontier stabilizes near a Pareto-optimal equilibrium between cost and resilience. This work provides a unified theoretical and computational foundation for adversarially resilient smart grid operation, bridging cyber-defense strategy, uncertainty quantification, and real-time economic scheduling into one coherent optimization paradigm. Full article

Thise article examines the reliable online detection and IDS/IPS intrusion prevention in dynamic corporate networks problems, where traditional signature-based methods fail to keep pace with new and evolving attacks, and streaming data is susceptible to drift and targeted “poisoning” of the training dataset. As a solution, we propose a hybrid neural network system with adaptive online training, a formal minimax false-positive control framework, and a robustness mechanism set (a Huber model, pruned learning rate, DRO, a gradient-norm regularizer, and a prioritized replay). In practice, the system combines modal encoders for traffic, logs, and metrics; a temporal GNN for entity correlation; a variational module for uncertainty assessment; a differentiable symbolic unit for logical rules; an RL agent for incident prioritization; and an NLG module for explanations and the preparation of forensically relevant artifacts. In this case, the applied components are connected via a cognitive layer (cross-modal fusion memory), a Bayesian-neural network fuser, and a single multi-task loss function. The practical implementation includes the pipeline “novelty detection → active labelling → incremental supervised update” and chain-of-custody mechanisms for evidential fitness. A significant improvement in quality has been experimentally demonstrated, since the developed system achieves an ROC AUC of 0.96, an F1-score of 0.95, and a significantly lower FPR compared to basic architectures (MLP, CNN, and LSTM). In applied validation tasks, detection rates of ≈92–94% and resistance to distribution drift are noted. Full article