Multi-stage stochastic engine usage optimization for fighter jet fleet using nested decomposition algorithm

A novel stochastic fractal search operator based on particle swarm optimization for constrained multi-objective optimization

Stochastic optimization of predictive maintenance scheduling for offshore wind farms

This study aims to assess the feasibility of hydrogen refueling in the Central Business District (CBD) corridors of Australia, utilizing a reinforcement-learning-based stochastic framework integrated with blockchain-enabled demand response, with the objective of ensuring reliable dispatch of hybrid PV-wind-battery-electrolyze systems. The aim is to assess the techno-economic viability amidst tariff and weather uncertainties across six locations—North Terrace (Adelaide), Elizabeth Quay (Perth), Salamanca Place (Hobart), Southbank (Melbourne), Eagle Street (Brisbane), and Martin Place (Sydney)—utilizing district-scale solar and wind projections, performance-based costing, and multi-vector integration. This contribution integrates reinforcement learning (RL) control, digitally auditable demand response (DR) settlement, and spatially resolved siting into a cohesive decision framework, validated through physics-constrained simulations and bio-inspired optimizers, facilitating geography-aware configuration options and risk-sensitive investment evaluation. The scope encompasses PV–WT–Battery, PV–Battery, and WT–Battery configurations; electrolyze and tank dimensioning; demand scenarios; and sensitivity-robustness assessments. Highlights indicate that PV–WT–Battery consistently reduces lifespan metrics while achieving RF = 100 %. Elizabeth Quay represents the cost frontier (NPC ≈ $28.04 ×10 ³; LCOE ≈ $0.01747/kWh; LCOH ≈ $0.603/kg), with Eagle Street in proximity, North Terrace and Southbank at moderate elevations, and Martin Place at the upper limit; wind-dominant Salamanca Place displays a configuration inflection where 750 kW PV surpasses 1000 kW due to wind-solar covariance and part-load penalties. Reinforcement learning combined with dynamic pricing reduces LCOH variability by synchronizing electrolyze setpoints, compressor operations, and battery-tank buffers during low-marginal-cost periods, while blockchain settlement provides verifiable green-hydrogen credentials. Demand elasticity assessments reveal that −15 % scenarios yield around 10–12 % decreases in NPC/LCOE/LCOH and surpluses of about 25–30 %, whereas + 15 % scenarios result in cost increases of approximately 5–10 %. The grouping of hydrogen valleys near ports and transit hubs improves utilization and financial viability; alternative logistics (LH₂, LOHC) and subterranean storage expand site possibilities for densely populated urban areas. The strategic considerations support PV-biased trihybrids in the sun-drenched western and subtropical regions, diversified portfolios for Adelaide, Melbourne, and Sydney, and optimized wind-driven operations in Hobart, providing a replicable framework for achieving verifiable, net-zero-aligned HRS in Australian cities. Results are applicable across various climates, precinct types, and market conditions.

Enhancing stochastic optimization of wind-PV-storage systems: A scenario reconstruction approach with source-load matching and temporal characteristics

Novel energy management and harnessing wind power for sustainable electric mobility of multi-micro grid system

Robust sizing of battery energy storage for off-grid electric vehicle charging using forecast-driven stochastic optimization

Consensus fixing for two-stage stochastic optimization – applied to stochastic prize collecting TSP

Efficiently operating a single microgrid (MG) is increasingly challenging due to volatile electricity demand and intermittent renewable generation. Traditional static networks often fail to adapt to these fluctuations, compromising reliability. Incorporating these uncertainties into planning is essential for developing resilient optimization models that can withstand the stochastic nature of decentralized energy systems. This study proposes a dynamic reconfiguration strategy for interconnected microgrids that reroutes households based on real-time supply and demand. A stochastic nonlinear optimization model was developed to maximize load factors and flatten peaks while accounting for current-dependent power and distribution losses. The Sample Average Approximation (SAA) method was used to handle uncertainty, converting probabilistic variables into a robust deterministic equivalent that prioritizes electrical proximity during reconfiguration. The model was validated using a composite dataset spanning nearly two years of hourly load and renewable profiles. A total of 600 stochastic scenarios were considered and analyzed to represent an empirical distribution of real-world uncertainty while preserving key temporal correlations. Performance was tested under N-1 and N-2 contingency events, in which one or more microgrids are deactivated, to evaluate system resilience. Results indicate that while a single active MG improves the load factor, it also increases operational instability and objective function variance. Conversely, a three-MG configuration enhances system stability and predictability. Economically, the mesh architecture allows for temporary MG deactivation to reduce maintenance and fuel costs without compromising service. The proposed strategy achieves 100% resilience, ensuring uninterrupted service even under severe constraints.

Seasonal influenza epidemics exhibit complex transmission dynamics influenced by time-varying extrinsic factors such as social behavior and seasonal effects. Estimating changes in transmission rates is critical to enable accurate forecasting of the epidemic curve. This study presents a framework for detecting changepoints in the transmission parameter ([Formula: see text]), applied as a piecewise constant function within a deterministic compartmental model. Using hospitalized case data from four recent influenza A seasons in Ireland (2019/2020 and 2022-2025), we applied iterated filtering and kernel density estimation to identify season-specific and cross-seasonal changepoint structures. The algorithm integrates stochastic search, local perturbation, and resampling to infer the most plausible changepoint configurations. Results reveal consistent changepoint patterns across seasons, particularly during periods of increased social mixing, such as the December holiday period. A universal changepoint model was also developed, enabling medium-term forecasting and scenario planning. This approach offers a robust method for capturing abrupt shifts in transmission and may be applicable to other dynamical systems.

In multimodal freight logistics the assignment of uncertain customer orders under carbon emission constraints presents a complex and important challenge. This study develops a high dimensional stochastic optimization model that aims to maximize the expected profit of order transportation by considering transportation costs and penalties caused by exceeding carbon limits. To solve this problem efficiently an intelligent optimization approach is proposed which integrates a probability guided adaptive large neighborhood search with a scenario generation technique. This method improves computational efficiency by identifying key scenarios and prioritizing influential order combinations during the search process. Experimental results indicate that the proposed approach yields improvements over the tested conventional methods in both solution quality and computational speed within the scope of our simulated scenarios. It demonstrates robust performance and stability in handling high-dimensional uncertainty, offering practical insights for sustainable logistics planning. The experimental findings indicate that the proposed method improves objective performance by over 10% on average while reducing computational time by more than 80% specifically when compared to the baseline random sampling-based intelligent neighborhood optimization algorithm used in this study. These results highlight the effectiveness of the approach in addressing high-dimensional stochastic logistics optimization under environmental constraints.

With the widespread application of the Internet of Things (IoT), computing tasks on the terminal side have surged. Traditional cloud computing models, constrained by high network latency and overloaded central servers, can no longer effectively meet the dual requirements of real-time responsiveness and energy efficiency. The cloud–edge–device collaborative architecture, by enabling distributed resource scheduling, offers a promising solution to reduce both latency and energy consumption. However, optimizing carbon emissions under dynamic operating conditions remains a pressing and unresolved challenge. This paper proposes a carbon-aware dynamic scheduling framework for cloud–edge–device systems, which accounts for the stochastic nature of task arrivals, heterogeneous computing capabilities, and varying carbon intensity across devices and locations. A multi-layer carbon emission model is developed, and the long-term carbon minimization objective is formulated as a stochastic optimization problem. Using the Lyapunov drift-plus-penalty method, the problem is transformed into a tractable deterministic optimization framework, upon which a Carbon-Efficient Computation Offloading (CECO) algorithm is designed. CECO jointly optimizes local computation frequency, data transmission rate, and edge resource allocation to dynamically balance task queue stability and carbon emission intensity. Theoretical analysis and simulation results validate that the proposed algorithm significantly reduces system-level carbon emissions while maintaining quality of service, demonstrating strong potential for enabling green computing in intelligent distributed environments.

Efficient inventory management for perishable goods is a critical operational challenge for retailers due to the complexities introduced by limited shelf-life and uncertain demand. This paper presents a two-stage stochastic programming model tailored for optimising perishable goods distribution in retail networks, explicitly addressing last-in-first-out customer preferences, demand uncertainty and fixed shelf-life. The model integrates operational objectives including cost minimisation, demand satisfaction, and waste reduction through scenario-based stochastic optimisation. Due to computational complexity in solving large-scale stochastic problems, we introduce heuristic and approximation methodologies for improved scalability. Specifically, we develop three approaches: a Demand-Based Fractional Allocation heuristic fairly distributing goods among locations, a Ranked Greedy Allocation heuristic prioritising stores based on profitability, and a Scenario Reduction method using Weighted K-means clustering to manage scenario complexity efficiently. These heuristics are evaluated using synthetic datasets and real-world-inspired instances from the M5 forecasting competition dataset, covering various demand patterns including intermittent and smooth series. Results indicate that scenario reduction via Weighted K-means significantly improves computational efficiency (up to 90 % reduction in computation time for short shelf-lives) while maintaining high solution accuracy for smooth demands (average optimality gap 1.37 % ). The greedy heuristic effectively minimises waste for intermittent demands, highlighting the need for testing general allocation approaches considering diverse demand patterns.

This study explores sustainable energy management approaches for a smart distribution network that combines multiple infrastructures, such as electric vehicle charging stations, hydrogen refueling facilities for fuel cell vehicles, and renewable energy systems integrated with hydrogen storage. These components are managed in a coordinated manner to satisfy both operational requirements and security criteria defined by the distribution system operator. A key feature of the hydrogen storage unit is its dual functionality, as it not only stores electrical energy but also supplies hydrogen to end users. The primary objective is to reduce overall energy losses within the distribution system. To accomplish this, the research considers several important factors, including AC power flow modeling, grid voltage operational and security constraints, system flexibility, environmental restrictions, operational characteristics of electric vehicles charging and hydrogen stations, and performance models of renewable energy systems coupled with hydrogen storage. Furthermore, the proposed framework accounts for uncertainties related to load demand, renewable generation, and variations in the number of electric vehicles by applying a scenario-based stochastic optimization technique. The findings demonstrate significant enhancements in both system performance and security. In particular, the proposed method decreases voltage deviations, power losses, and peak load capacity by approximately 24.4%, 32.8%, and 38.3%, respectively, compared to conventional load flow analyses. Moreover, voltage security within the network is improved by nearly 10.2%, confirming the efficiency of the proposed integrated energy management strategy.

Slope stability analysis is a crucial task in the design of geotechnical structures. In many computational methods, such as those combining displacement-based finite element methods and strength reduction techniques, no assumptions are made a priori about the shape or position of the failure mechanism. This is usually considered to be a positive feature but there are situations where the ability to control the search domain for the critical slip surface might be of interest. These are the cases where the critical slip surface converges towards a local (unintended) one, or when it is necessary to determine the factor of safety for slopes with varying inclinations such as the upstream and downstream slopes of embankment dams. This article presents the Finite Element Limit Equilibrium Method (FELEM), which integrates stress states computed by the finite element method along a predefined trial slip surface to determine the factor of safety. This method is combined with a swarm-based metaheuristic optimization algorithm to identify the critical slip surface with the lowest factor of safety. The combined approach is tested on two numerical examples, addressing issues such as discretization error, optimization procedure settings, and non-associated plastic flow. Finally, the combination of FELEM and the optimization algorithm is applied to a boundary value problem of a newly designed embankment dam. Slope stability is evaluated independently for both the upstream and downstream slope, each with a different inclination. Computations are performed for the hydrostatic and steady-state seepage conditions.

The rapid growth of electric vehicles (EVs) and renewable distributed generators (DGs) is transforming microgrid (MG) operation and introducing significant uncertainty into energy management. This study proposes a stochastic energy management (SEM) framework for a grid-connected microgrid integrating photovoltaic (PV) systems, wind turbines (WTs), battery storage (BS), and EV charging stations. Uncertainties in renewable generation, load demand, and electricity prices are modeled using a data-driven probabilistic scenario generation approach based on probability density functions and a roulette-wheel sampling mechanism, followed by fast-forward scenario reduction. The resulting optimization problem is formulated as a mixed-integer nonlinear programming model and tested on the IEEE 33-bus distribution system. Simulation results demonstrate that coordinated battery storage operation significantly enhances microgrid performance. In particular, the optimized scheduling strategy reduces operational costs by approximately 16.26% compared with scenarios without storage. In addition, battery integration improves voltage profiles, reduces system losses during peak demand periods, and mitigates stress on distribution infrastructure by lowering the maximum transformer loading from 3.69MW to 2.96MW. The findings highlight the importance of explicitly modeling operational uncertainty and demonstrate that stochastic optimization can provide more reliable and cost-effective energy management strategies for microgrids with high renewable penetration and significant EV integration.

This study presents a hybrid reinforcement learning-assisted distributionally robust optimization (RL-DRO) framework for resilient and low-carbon energy system operation under uncertainty. The proposed model integrates a multi-agent reinforcement learning structure with a Wasserstein-metric distributionally robust formulation to capture both adaptive decision-making and conservative risk management. Reinforcement learning agents, representing distributed subsystems such as renewable generators, storage units, and flexible loads, are trained to minimize a composite objective combining expected cost and risk, while the DRO layer ensures robustness against distributional ambiguity. A case study on a renewable-dominated microgrid demonstrates that the RL-DRO framework converges smoothly within 4000 training iterations, achieving a 9.7 % reduction in expected cost and a 28 % improvement in robustness compared with stochastic optimization. The optimal ambiguity radius balances efficiency and resilience, while renewable curtailment and storage utilization exhibit clear compensatory dynamics across uncertainty scenarios. Emission trajectories show an exponential decay from 200 to 140 tCO[Formula: see text] across learning epochs, confirming the model's ability to internalize environmental objectives. Overall, the RL-DRO architecture unifies data-driven learning and mathematical robustness, enabling distributed agents to achieve stable coordination and sustainable operation under high renewable penetration. The framework establishes a practical foundation for intelligent, risk-aware, and carbon-efficient decision-making in modern power systems.

The article reveals the conceptual foundations of forming flexible logistics infrastructure for the needs of rapid reconstruction of Ukraine. The author proposes a transition from static capital-intensive facilities to a network of mobile railway hubs based on passive damping shielding technology, which allows gravitational unloading of gondola cars on any track section without constructing trestles. A stochastic model for economic optimization of the hub network has been developed, taking into account shortage risks, preservation of railway asset resources, and minimization of logistics costs under multiple demand scenarios. Practical calculations are provided for typical conditions of gravel and sand unloading, confirming the technical feasibility of the concept «Anywhere Logistics». The research results prove that mobile hubs provide an 87 % reduction in capital costs, reduction of deployment time to 1 hour, and increased flexibility of the logistics system with minimal impact on track infrastructure resources.A stochastic optimization model of a mobile hub network showed that a system with mobile elements provides 53.1 % lower total logistics costs compared to a traditional system with stationary terminals due to a significant reduction in the distance of «last mile» road transportation and the creation of an «Anywhere Logistics» approach.Mobile railway hubs for unloading bulk and construction cargo will quickly pay for themselves due to a significant reduction in road transportation costs. Further development of the concept «Anywhere Logistics» may be in the direction of adapting mobile railway logistics hubs to US conditions, which opens up significant opportunities for optimizing supply chains, but requires taking into account the specific legal and technological field of this country. The practical value of the method has been proven through a comparative analysis with traditional technologies based on the criteria of capital expenditure, deployment time, system flexibility and total cost of ownership.

The increasing penetration of photovoltaic distributed generation (PV-DG) in Radial Distribution Systems (RDSs) plays a vital role in achieving sustainable energy transition objectives; however, the inherent uncertainty associated with solar irradiance and load demand poses significant challenges to optimal planning and operation. This paper presents a stochastic optimization framework for PV-DG allocation in RDSs using the Barrel Theory-Based Optimizer (BTO). Uncertainties in solar irradiance and load demand are explicitly modeled using appropriate probability density functions and efficiently represented through a higher-order Point Estimate Method (PEM), which captures the essential statistical characteristics with a limited number of representative scenarios. The proposed framework simultaneously optimizes the location and capacity of PV-DG units to minimize real power losses and enhance voltage profile performance while ensuring system operational constraints are satisfied. The effectiveness of the proposed approach is validated on the 85-bus and the IEEE 118-bus RDSs, where the BTO exhibits superior convergence characteristics and enhanced solution robustness when compared with several benchmark optimization techniques, including the well-established Differential Evolution Algorithm (DEA), the recent Crocodile Ambush Optimization (CAO, 2025), and the Schrödinger Optimizer Algorithm (SOA, 2025). For the 85-bus RDS, the impact of integrating different numbers of PV units is systematically investigated. Simulation results confirm that the proposed BTO-based stochastic planning strategy significantly improves energy efficiency, voltage regulation, and loss reduction, thereby enhancing the overall sustainability of the RDS. For the 85-node RDS, the BTO achieves a noticeable reduction in average real power losses, outperforming DEA, CAO, and SOA by 2.55%, 4.10%, and 6.74%, respectively, when three PV units are installed. Additionally, for the case of four PV units, the proposed BTO yields even greater improvements, with loss reductions of 5.12%, 7.50%, and 14.12%, respectively, compared with the same benchmark algorithms. Furthermore, for five PV units, the BTO achieves much greater reduction, outperforming DEA, CAO, and SOA by 13.05%, 6.45%, and 32.31%, respectively, when three PV units are installed.

• Deterministic and stochastic methods are studied for adjoint-based inverse modeling. • Novel stochastic update rule preserves boundary and regularity via adjoint-state. • When coupled with high-order schemes, it enhances smoothness of tuning parameter. • New method outperforms L-BFGS and N-ADAM in multi-objective inverse problems. This work explores the use of quasi-Newton and stochastic optimization methods for gradient-based inverse problems in physical modeling, focusing on their application within high-order numerical frameworks. Such problems are often characterized by the following challenges: (i) physical constraints often yield a highly non-convex design space with multiple local optima; (ii) solutions must satisfy intrinsic properties, such as boundary and regularity conditions, which are not easily enforced as explicit constraints. Conventional stochastic optimizers, such as N-ADAM, exhibit significant information loss in their update rules, leading to non-physical solutions. To overcome these limitations, we introduce a novel stochastic optimizer, V-N-ADAM-DG, which incorporates adjoint-state information into the update rule to maintain physically meaningful corrections in terms of regularity and boundary conditions. We validate our approach in the context of mean-flow reconstruction for Reynolds-averaged Navier-Stokes (RANS) simulations using a high-order discontinuous Galerkin (DG) discretization method, as proposed by Fanizza et al. (2025). The optimization framework considers both vectorial corrective terms, inferred in the momentum and energy equations, and scalar corrective terms in the Spalart-Allmaras (SA) transport equation. The V-N-ADAM-DG optimizer effectively reconstructs mean flow quantities while ensuring smooth transitions of corrective parameters at boundaries, an improvement over standard stochastic optimizers. Additionally, it facilitates a rapid decay of the optimal degrees of freedom (DOFs), leading to smoother corrections in high-order reconstructions-achieving a balance between the robustness of quasi-Newton methods (such as L-BFGS) and the flexibility of stochastic approaches. Numerical experiments across various flow configurations demonstrate that V-N-ADAM-DG consistently outperforms both L-BFGS and N-ADAM, particularly in complex inverse problems that employ multiple combined cost functions to reconstruct different physical quantities.