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Keywords = routing and assignment algorithms

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29 pages, 1316 KB  
Article
DNSGA-II-ALNS: A Warm-Start Evolutionary Algorithm for Dynamic Multi-Objective Optimization of Heterogeneous Vehicle Routing with Time Windows
by Jiahao Tian, Mingyin Zou, Zhifei Li, Song Li and Xiongbing Ye
Appl. Sci. 2026, 16(17), 8572; https://doi.org/10.3390/app16178572 (registering DOI) - 28 Aug 2026
Abstract
Dynamic heterogeneous vehicle routing with time windows requires reoptimization whenever customer arrivals and network disruptions change the decision space and the set of feasible routes. A reoptimized plan is useful in practice only if it does not rewrite the schedule that crews are [...] Read more.
Dynamic heterogeneous vehicle routing with time windows requires reoptimization whenever customer arrivals and network disruptions change the decision space and the set of feasible routes. A reoptimized plan is useful in practice only if it does not rewrite the schedule that crews are already executing. This paper presents DNSGA-II-ALNS, an epoch-based dynamic multi-objective evolutionary algorithm. It couples an event-conditioned warm-start projection with an exact marginal assignment cost, feasibility-aware destroy-and-repair search and NSGA-II selection. The projection is not claimed to be a new optimization paradigm: it is a deterministic map between consecutive decision spaces that is defined even when a customer arrival changes their dimension, that introduces no constraint violation, and that leaves every customer unaffected by the event on its current vehicle. The algorithm is compared with seven alternatives under a paired protocol. All 56 Solomon instances are used with ten independent runs, and every method sees the same stored event stream for a given instance and run, a population of 50 and 8000 objective evaluations per epoch. The main empirical finding concerns plan stability. DNSGA-II-ALNS reassigns 11.1% of the persisting customers after an event, whereas a cold restart reassigns 89.2%, and the two groups do not overlap on any of the 56 instances. The reduction is not accompanied by a loss of solution quality, since the eight methods differ by at most 2.6% in total distance and 0.6% in makespan and all of them serve every customer within its time window. In front quality, the algorithm is not separated from the best-ranked method by the applied tests: it obtains the second-best Friedman mean rank (3.000 against 2.446), and the difference is smaller than the Nemenyi critical difference of 1.403. Advantages over the cold restart, MOPSO-ALNS and a memory-MOEA/D control are statistically significant with rank-biserial effect sizes of 0.84–0.87, while the comparisons with MODE-ALNS and the memory-NSGA-II control are not significant. An ablation indicates that the destroy-and-repair operators govern front quality, exceeding a routing-specific genetic control by 6.8–8.7% and a generic real-coded control by 15.9–26.4%. Quality is retained up to 200 customers at a fixed fleet density, but the mean response time rises from 33 to 716 s per epoch, which limits applicability to real-time dispatching. The contribution is accordingly operational rather than a new optimization methodology: comparable front quality at an order of magnitude less plan churn. Full article
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35 pages, 44245 KB  
Article
A Simulation-Based Dynamic Path Planning Approach for Low-Altitude Unmanned Aerial Vehicles in Inspection Scenarios
by Changqi Yang, Hongjie Hu and Yi Ai
Drones 2026, 10(9), 644; https://doi.org/10.3390/drones10090644 - 25 Aug 2026
Viewed by 130
Abstract
Traditional target-oriented task allocation and path planning methods often struggle to balance real-time responsiveness to dynamic task alterations with multi-UAV cooperative operations in complex urban environments under meteorological disturbances. To address these challenges, this paper proposes a dynamic path planning method for low-altitude [...] Read more.
Traditional target-oriented task allocation and path planning methods often struggle to balance real-time responsiveness to dynamic task alterations with multi-UAV cooperative operations in complex urban environments under meteorological disturbances. To address these challenges, this paper proposes a dynamic path planning method for low-altitude Unmanned Aerial Vehicles (UAVs) tailored for urban inspection missions. Integrating an improved Discrete Particle Swarm Optimization (DPSO) algorithm with a decoupled Soft Actor–Critic (SAC) and B-spline smoothing framework, the proposed approach optimizes upper-level task allocation and lower-level trajectory planning within a 3D joint meteorological-obstacle feasible region. For task scheduling, an improved DPSO algorithm embedded with a spatial topology guidance mechanism dynamically coordinates task flows governed by Poisson processes. effectively addressing the spatial blindness and fragmented route assignments typical of conventional discrete optimization. Concurrently, local trajectory replanning executes receding-horizon spatial exploration via SAC deep reinforcement learning, followed by B-spline refinement to strictly enforce UAV kinematic limits, systematically bridging continuous-space exploration with low-level flight compliance to overcome the kinematic infeasibility common in pure learning-based models. Validated through extensive Monte Carlo comparative simulations (N=50) and further verified by a high-fidelity AirSim dynamic physics engine, the results demonstrate that: (1) The improved DPSO constrains the average response latency for high-priority emergency tasks to within 40 s even under 50 concurrent dynamic tasks. (2) The lower-level replanning achieves an average execution time of 3.60±0.18 s and a path success rate of 95.8±1.2%, in numerical tests, while maintaining a 96.2% kinematic feasibility rate under realistic rigid-body inertia and aerodynamic drag. While the current 3.60 s latency presents a potential bottleneck for millisecond-level dynamic emergency reactions, the developed framework offers a highly effective and safe closed-loop dynamic scheduling solution that lays a rigorous computational foundation for low-altitude urban inspections. Full article
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29 pages, 731 KB  
Article
ICBBA-ACO-Based Multi-Robot Task Allocation for Smart Charging Stations
by Meiyu Chang, Zhaoyu Ku, Xuanyu Xing, Tianhao Wang and Huajun Dong
Machines 2026, 14(8), 953; https://doi.org/10.3390/machines14080953 - 21 Aug 2026
Viewed by 244
Abstract
Smart charging stations require mobile charging robots to respond to dynamically arriving charging requests with heterogeneous priorities, varying travel costs, and uneven workloads while maintaining online scheduling feasibility. Conventional single-layer approaches often optimize task assignment or route ordering separately, which limits their ability [...] Read more.
Smart charging stations require mobile charging robots to respond to dynamically arriving charging requests with heterogeneous priorities, varying travel costs, and uneven workloads while maintaining online scheduling feasibility. Conventional single-layer approaches often optimize task assignment or route ordering separately, which limits their ability to coordinate allocation quality, route efficiency, and workload regulation under real-time constraints. This study proposes a hierarchical improved consensus-based bundle algorithm–ant colony optimization (ICBBA-ACO) framework for dynamic multi-robot task allocation. The upper ICBBA layer combines deterministic task clustering, intra-cluster greedy bundling, conflict resolution, and feedback-guided workload-aware reassignment, while the lower ACO layer refines the visiting order of unstarted tasks under fixed ownership using the same normalized four-objective scheduling cost. Complete decision time is evaluated separately against a 200ms online requirement, and estimated motion energy is retained only as a distance-derived auxiliary indicator. In a five-method comparison over 100 paired scenarios, ICBBA-ACO achieves a mean composite objective of J=0.663052, a mean decision time of 33.07ms, and 100% deadline compliance. GA-MRTA obtains a lower unconstrained mean objective of J=0.615790, but requires approximately 2199.30ms on average and satisfies the 200ms requirement in only 8.89% of the evaluated updates. Thus, ICBBA-ACO provides the lowest mean objective among the compared methods that maintain full deadline compliance, demonstrating a favorable quality–runtime trade-off within the tested operating range. ROS-based engineering verification further completes all 15 repeated trials and all 48 verification tasks with no recorded invariant violations. Full article
(This article belongs to the Section Robotics, Mechatronics and Intelligent Machines)
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42 pages, 823 KB  
Article
Hierarchical Scheduler with Adaptive Time-Budget Reallocation for Time-Triggered Edge-Fog-Cloud Architectures
by Omar Hekal, Josepaul Paulachan, Daniel Onwuchekwa and Roman Obermaisser
Future Internet 2026, 18(8), 441; https://doi.org/10.3390/fi18080441 - 18 Aug 2026
Viewed by 209
Abstract
The lack of determinism restricts the integration of safety-critical applications into Edge–Fog–Cloud (EFC) architectures. Existing EFC schedulers are typically designed for dynamic, best-effort operation based on unmanaged resource allocation and elastic virtualization. This paradigm introduces unbounded queueing, resource contention, and timing jitter, making [...] Read more.
The lack of determinism restricts the integration of safety-critical applications into Edge–Fog–Cloud (EFC) architectures. Existing EFC schedulers are typically designed for dynamic, best-effort operation based on unmanaged resource allocation and elastic virtualization. This paradigm introduces unbounded queueing, resource contention, and timing jitter, making standard schedulers unsuitable for hard-deadline workloads. Moreover, most approaches focus on computational placement, while communication is abstracted or treated as a secondary cost term. As a result, bounded-latency routing and deterministic task execution are rarely co-optimized under a unified timing model. This paper addresses these gaps by utilizing a managed Time-Triggered Edge–Fog–Cloud (TTEFC) architecture that supports safety-critical workloads, orchestrates IEEE Time-Sensitive Networking (TSN) for local intra-domain communication, and uses IETF Deterministic Networking (DetNet) for routed inter-domain paths. On this infrastructure, a hierarchical genetic algorithm (HGA) is proposed to jointly schedule partition-to-execution-location allocation, partition execution order, inter-partition route selection, and negotiated per-partition time budgets that act as temporal boundaries for parallel partition-level optimizers. An adaptive slack reallocation operator redistributes unused temporal slack from over-satisfied partitions to budget-violating partitions, improving feasibility convergence. Experiments on synthetic DAG workloads with 100–500 tasks compare the proposed HGA against HEFT and round-robin baselines. These baselines are included as scoped external references to contextualize the end-to-end scheduling performance of the proposed method. Ablation results show that slack reallocation improves partition-budget feasibility, reaches feasible budget assignments earlier, and produces tighter budget–makespan alignment than feedback-free and static-budget variants. An automotive-characteristic DAG case study further evaluates the method on an application-oriented workload under the same timing and communication assumptions. Full article
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29 pages, 660 KB  
Article
The Collaborative Green Vehicle Routing Problem with Time-Dependent Travel Speeds
by Juan Li, Yang Yu, Min Huang and Xingwei Wang
Mathematics 2026, 14(16), 2933; https://doi.org/10.3390/math14162933 - 13 Aug 2026
Viewed by 186
Abstract
This study investigates the collaborative green vehicle routing problem with time-dependent travel speeds (CGVRP-TD), which integrates horizontal collaboration among multiple depots with time-dependent traffic conditions. The problem jointly optimizes customer allocation, vehicle routing, and departure-time decisions to minimize transportation-related carbon emissions subject to [...] Read more.
This study investigates the collaborative green vehicle routing problem with time-dependent travel speeds (CGVRP-TD), which integrates horizontal collaboration among multiple depots with time-dependent traffic conditions. The problem jointly optimizes customer allocation, vehicle routing, and departure-time decisions to minimize transportation-related carbon emissions subject to vehicle capacity and customer time-window constraints. We formulate the CGVRP-TD as a mixed-integer programming model and develop a two-phase adaptive large neighborhood search algorithm with embedded departure-time optimization. The first phase explores routing and customer-assignment decisions using problem-specific operators, including two speed-related removal operators, while the second phase applies exact departure-time optimization to fixed routes. Computational experiments show that the proposed algorithm obtains high-quality solutions efficiently and that both departure-time optimization and speed-related operators contribute to emission reduction. The results further demonstrate that combining horizontal collaboration with time-dependent travel-speed information can substantially reduce transportation emissions while preserving on-time service. We also discuss emission-savings allocation mechanisms for sustaining collaboration among participating depots. Full article
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26 pages, 675 KB  
Article
Reinforcement Learning-Based Day-to-Day Route Choice Models Under Full and Partial Information Conditions: A Theoretical and Experimental Research
by Yuance Yang, Ning Jia, Nianlu Ren, Hongye Fan and Zhanghao Lei
Mathematics 2026, 14(16), 2910; https://doi.org/10.3390/math14162910 - 12 Aug 2026
Viewed by 314
Abstract
Learning behavior plays an important role in the day-to-day route choice process, which is essentially a repeated decision-making process. This paper proposes two learning models for the day-to-day route choice process, one for the full-information (FI) condition and one for the partial-information (PI) [...] Read more.
Learning behavior plays an important role in the day-to-day route choice process, which is essentially a repeated decision-making process. This paper proposes two learning models for the day-to-day route choice process, one for the full-information (FI) condition and one for the partial-information (PI) condition. Both models are developed based on attraction-based reinforcement learning theory but with different learning mechanisms. In our FI model, travelers learn by comparing different paths, while in our PI model, travelers’ route choice decision is modeled by long-term cost minimization and a policy-based reinforcement algorithm. Both models are rooted in individual strategy updating and are theoretically linked to classical network flow assignment theory: we establish that individual-level invariance of choice probabilities is sufficient for aggregate stationarity consistent with Wardrop equilibrium, and provide an explicit stability condition for the FI dynamics. To validate the models, laboratory experiments under FI and PI conditions were designed and conducted. The experimental data confirm the presence of learning behavior and show that the proposed models achieve better predictive performance than several behavioral benchmarks, including EWA, Q-learning, mixed logit, and a Selten variant. Moreover, an interesting phenomenon was found in the FI experimental dataset: even though FI was provided, some subjects still made decisions hinging on their own experience. Our findings would benefit traffic information services and traffic administration. Full article
(This article belongs to the Special Issue AI, Machine Learning and Optimization)
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36 pages, 2389 KB  
Article
Optimization of Multimodal Public Transit Networks Considering Spatial Equity
by Meina Zheng, Feng Liu and Xiucheng Guo
Systems 2026, 14(8), 947; https://doi.org/10.3390/systems14080947 - 5 Aug 2026
Viewed by 330
Abstract
Public transport equity is usually assessed after a network has been designed rather than treated as a requirement that shapes the design itself. This study develops an equity-oriented optimization framework for hierarchical multimodal transit networks in which a fixed rail backbone, main-bus routes, [...] Read more.
Public transport equity is usually assessed after a network has been designed rather than treated as a requirement that shapes the design itself. This study develops an equity-oriented optimization framework for hierarchical multimodal transit networks in which a fixed rail backbone, main-bus routes, and feeder-bus routes are designed jointly. The model minimizes an integrated objective combining total system cost and the modal accessibility gap between public transport and private cars, while spatial equity is imposed as a binding constraint through two alternative Gini-based standards: a demand-proportional (horizontal) index and a need-sensitive (vertical) index. The problem is solved by a genetic algorithm that embeds a strategy-based passenger assignment with crowding effects and tracks the best-so-far solution across generations. Experiments on Mandl’s benchmark network across eight scenarios, combining the two equity standards with four threshold levels, yield average travel times of 11.8–13.9 min. The two standards produce structurally different networks, and stricter equity does not necessarily degrade performance: the strictest need-sensitive scenario attains the lowest average travel time, although it also records the largest modal gap relative to cars. The framework thus supports scenario-based comparison, in which the equity formulation and threshold serve as explicit policy levers rather than fixed technical bounds. Full article
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27 pages, 1467 KB  
Article
Towards Carbon-Efficient Urban Logistics: A Constructive Routing Framework for Heterogeneous Courier Fleets
by Metin Özşahin
Mathematics 2026, 14(15), 2730; https://doi.org/10.3390/math14152730 - 1 Aug 2026
Viewed by 289
Abstract
The increasing demand for urban last-mile delivery services has intensified the need for routing approaches that simultaneously address operational efficiency and environmental sustainability. This study introduces the Green Multi-Courier Delivery Routing Problem (GMCDRP), a heterogeneous routing and assignment problem involving pedestrian couriers, electric [...] Read more.
The increasing demand for urban last-mile delivery services has intensified the need for routing approaches that simultaneously address operational efficiency and environmental sustainability. This study introduces the Green Multi-Courier Delivery Routing Problem (GMCDRP), a heterogeneous routing and assignment problem involving pedestrian couriers, electric bicycles, and motorized vehicles under capacity, distance, and service-time constraints. To solve the problem, a state-aware constructive heuristic named Emission-Minimizing Green Routing (EMGRO) is proposed. Unlike conventional metaheuristics that evaluate emissions after route generation, EMGRO integrates emission awareness directly into the assignment process by considering the real-time operational state of each courier and prioritizing the lowest-emission feasible alternative. The proposed method is evaluated using 20 large-scale scenarios derived from the real road network of Adana, Türkiye, each containing up to 1000 delivery requests. Its performance is compared with Genetic Algorithm (GA), Ant Colony Optimization (ACO), and Particle Swarm Optimization (PSO) approaches. Experimental results demonstrate that EMGRO achieves the lowest average emission per delivered package (0.512 g CO2/package), outperforming ACO, PSO, and GA by 47.9%, 44.1%, and 41.9%, respectively, while maintaining identical delivery coverage. Furthermore, EMGRO generates solutions within seconds, providing substantial computational advantages over population-based metaheuristics. The findings indicate that embedding environmental considerations directly into the decision-making process can significantly improve both sustainability and computational efficiency in heterogeneous urban delivery systems. Full article
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31 pages, 2548 KB  
Article
Outbound Path Optimization for Sustainable China–Europe Railway Express Operations Considering Cargo Consolidation and Departure-Time Matching
by Fenling Feng, Wenli Sun and Meng Qi
Sustainability 2026, 18(15), 7719; https://doi.org/10.3390/su18157719 - 30 Jul 2026
Viewed by 269
Abstract
In outbound China–Europe Railway Express (CR Express) operations, dispersed cargo access, transshipment-node activation, order consolidation path assignment, block train line selection, and departure-time matching are strongly coupled, directly affecting the economic performance, timeliness, and block train operation efficiency of transport plans. Existing studies [...] Read more.
In outbound China–Europe Railway Express (CR Express) operations, dispersed cargo access, transshipment-node activation, order consolidation path assignment, block train line selection, and departure-time matching are strongly coupled, directly affecting the economic performance, timeliness, and block train operation efficiency of transport plans. Existing studies have mainly focused on the local optimization of consolidation paths, train routes, or departure times. At the same time, insufficient attention has been paid to the bilevel combinatorial structure between node activation and order path assignment. To address this issue, this study proposes an outbound path optimization model for the CR Express considering cargo consolidation, and develops a graph-guided adaptive large neighborhood search (Gra-ALNS) algorithm. The algorithm is organized around a bilevel search structure of node activation and order path assignment. At the upper level, a transport organization graph is constructed, and graph convolutional network (GCN) embeddings are integrated with cargo-access reachability to generate H-node scores, which guide the search for promising transshipment-node activation combinations. At the lower level, outbound generalized paths are used as the basic search units, and upper confidence bound (UCB)-based operator selection, local exact refinement, and cross-ε-grid elite-solution warm starts are combined to optimize order consolidation paths, block train line selection, and departure-time matching. Numerical results show that the proposed Gra-ALNS outperforms conventional adaptive large neighborhood search (ALNS) in computational efficiency and multi-objective solution-set quality. Activating transshipment nodes can reduce the transport cost and in-transit time cost of some orders, but may increase fixed train operating cost and reduce average load factors. The findings provide methodological support for outbound cargo organization optimization, transshipment-node configuration, and block train operation planning of the CR Express. By improving cargo consolidation efficiency, coordinating departure-time matching, and revealing the trade-off between temporal accessibility and train-loading efficiency, this study provides a decision-support reference for a more efficient and sustainable CR Express freight organization. Full article
(This article belongs to the Section Sustainable Transportation)
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39 pages, 4277 KB  
Article
Adaptive Large Neighborhood Search Algorithm for Electric Vehicle Routing Problem with Capacitated Charging Stations and Queueing
by Zhuoti Huang, Senlai Zhu and Yuming Wang
Sustainability 2026, 18(15), 7580; https://doi.org/10.3390/su18157580 - 25 Jul 2026
Viewed by 308
Abstract
With growing emphasis on green and low-carbon development and rising urban delivery demand, electric vehicles (EVs) have been increasingly adopted in logistics distribution systems. However, their limited driving range, relatively long charging durations, and the limited capacity of charging stations pose substantial challenges [...] Read more.
With growing emphasis on green and low-carbon development and rising urban delivery demand, electric vehicles (EVs) have been increasingly adopted in logistics distribution systems. However, their limited driving range, relatively long charging durations, and the limited capacity of charging stations pose substantial challenges to real-world electric delivery operations. When multiple vehicles arrive at a station with a limited number of chargers, queueing delays may disrupt subsequent customer service and increase total operating costs. To address this issue, this study investigates an electric vehicle routing problem with capacitated charging stations and queueing delays. A mixed-integer linear programming model is formulated, and an enhanced adaptive large neighborhood search (ALNS) algorithm is developed to efficiently solve medium- and large-scale instances. In the proposed model, each vehicle visit to a charging station is represented as a charging event, while finite station capacity is enforced through charging-event assignment and temporal non-overlap constraints. Computational results show that the enhanced ALNS matches the proven optimal solution for the 10-customer instance. For the 15- and 20-customer instances, the best objective values obtained by the enhanced ALNS were 0.39% and 4.84% lower than the corresponding time-limited Gurobi incumbents, respectively. For the 30-, 50-, and 100-customer instances, the enhanced ALNS consistently generates feasible solutions within the prescribed computational budget, whereas Gurobi does not obtain a feasible incumbent within substantially longer time limits. Compared with the baseline ALNS, the enhanced version generally achieves lower mean objective values and more favorable convergence behavior. Sensitivity analyses further show that increasing the number of chargers and improving the charging rate can reduce queueing delays and total charging duration. The proposed approach provides practical decision support for reliable and sustainable urban electric freight operations. Full article
(This article belongs to the Special Issue Sustainable Transportation and Logistics Optimization)
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23 pages, 2428 KB  
Article
Heterogeneous Conditional Counter-Inspection: Configurable Error Control and Weak-Filter Recovery for 5G Network Intrusion Detection
by Khaoula Tahori, Imade Fahd Eddine Fatani, Mohamed Moughit and Hicham Magri
Future Internet 2026, 18(7), 381; https://doi.org/10.3390/fi18070381 - 22 Jul 2026
Viewed by 410
Abstract
Intrusion detection systems for 5G networks are typically reported at a single operating point, obscuring the trade-off between missed attacks and false alarms that governs real deployments. Building on a lightweight conditional counter-inspection pipeline, in which a global classifier is selectively validated by [...] Read more.
Intrusion detection systems for 5G networks are typically reported at a single operating point, obscuring the trade-off between missed attacks and false alarms that governs real deployments. Building on a lightweight conditional counter-inspection pipeline, in which a global classifier is selectively validated by curriculum-biased experts under a unanimous dissent rule, we remove the constraint that all components share one learning algorithm, assigning decision trees, random forests, extremely randomized trees, and histogram-based gradient boosting independently to the global (G), malicious-biased (EM), and benign-biased (EB) roles. Across two datasets of contrasting difficulty, 5G-NIDD and UNSW-NB15, all 14 evaluated tree-based configurations reduce missed attacks, by 36.5–79.6% on 5G-NIDD, confirming that the recovery effect is a property of the architecture rather than of decision trees. The expert assignment also selects which error the system controls: the same pipeline can be steered toward fewer false alarms, fewer missed attacks, or higher aggregate F1 without retraining the first stage. The mechanism also rescues a weak linear filter: on 5G-NIDD it cuts false positives and false negatives by 92.8% and 95.8%, and on UNSW-NB15 it raises F1 from 0.903 to 0.934 while reducing missed attacks by 35.5%. These results reframe the pipeline as a configurable validation layer matched to a deployment’s cost structure. We further show, through direct measurement on both datasets, that the conditional routing evaluates at most four of seven models per record, keeping classifier inference below 0.1 ms per record and leaving the detection stage a small contributor to overall processing cost. Full article
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28 pages, 2837 KB  
Article
Towards Intelligent Aerial Logistics: A UAV Routing Algorithm for Industrial Transportation Networks
by Konstantinos Kolonas, Stavros T. Ponis, Michalis Fragkoulakis and Athanasios Vourdanos
Future Transp. 2026, 6(4), 151; https://doi.org/10.3390/futuretransp6040151 - 13 Jul 2026
Viewed by 278
Abstract
The emergence of unmanned aerial vehicles (UAVs) introduces new opportunities for the design of intelligent and flexible transportation systems beyond traditional road-based logistics. This study investigates the integration of UAVs as an alternative transportation mode within industrial environments, focusing on the rapid delivery [...] Read more.
The emergence of unmanned aerial vehicles (UAVs) introduces new opportunities for the design of intelligent and flexible transportation systems beyond traditional road-based logistics. This study investigates the integration of UAVs as an alternative transportation mode within industrial environments, focusing on the rapid delivery of critical spare parts in large-scale production facilities. A two-stage optimization framework is developed, combining demand pre-processing with a routing algorithm that determines fleet utilization and delivery schedules under operational constraints. The proposed framework utilizes a data pre-processing stage, which converts enterprise resource planning order records into delivery-ready item data, with a mixed-integer linear programming (MILP) routing model that assigns eligible spare parts to UAV trips and determines the use of a fixed fleet under payload, dimensional, service-time, and battery-related constraints. The approach is evaluated using real annual order data from a metal-industry plant, combined with simulated intra-day arrival profiles due to the absence of exact order-placement timestamps in the ERP records. The results indicate that UAV-based transportation can serve a substantial share of internal demand while achieving shorter delivery-response times for the modeled UAV layer under the simulated dispatch instances and significantly lower direct energy-related transportation costs compared with the existing pickup-based process. The results highlight the role of UAVs as a complementary transportation layer in controlled industrial networks, supporting the transition toward more responsive and intelligent future transportation systems. Full article
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42 pages, 3542 KB  
Article
A Risk-Averse Two-Stage Stochastic Programming Model for Emergency UAV Task Allocation
by Shumeng Xu, Lili Wan, Jiahui Huang, Qingyang Zhang, Zhenyu Yuan and Zhan Wang
Drones 2026, 10(7), 529; https://doi.org/10.3390/drones10070529 - 12 Jul 2026
Viewed by 352
Abstract
As UAVs are increasingly used in emergency rescue, task allocation under uncertainty still faces tail delay risk. Existing studies mainly optimize expected cost and pay insufficient attention to task temporal relations and delay losses under extreme scenarios. To address this issue, this study [...] Read more.
As UAVs are increasingly used in emergency rescue, task allocation under uncertainty still faces tail delay risk. Existing studies mainly optimize expected cost and pay insufficient attention to task temporal relations and delay losses under extreme scenarios. To address this issue, this study develops a risk-averse two-stage stochastic programming model that incorporates the precedence relation between reconnaissance and delivery tasks, UAV routes, and task execution sequences into a unified decision process. The first stage determines task assignment, route selection, and visit order, while the second stage evaluates waiting, delay, and recourse costs under stochastic scenarios. A Mean-CVaR risk measure is adopted to characterize both average performance and tail risk. To solve the resulting multi-scenario risk-averse model, this study develops a problem-tailored Enhanced BD framework based on the classical Benders decomposition structure. The proposed framework integrates partial scenario embedding, heuristic warm start, and dynamic cut-pool management to strengthen early master problem information, improve feasible-route search, and control the growth of scenario-wise cuts. Numerical experiments based on a Nanjing emergency rescue instance evaluate the model and algorithm in terms of solution performance, acceleration ablation, optimized scheduling results, and parameter sensitivity. The results show that the proposed model can identify tail delay risk concentrated at a small number of demand points and downstream nodes in task chains. Across ten independent replications, Enhanced BD achieves a higher convergence success rate and lower final BD Gap than Basic BD in the medium-sized and largest tested instances. Parameter analysis shows that moderate risk aversion improves out-of-sample performance, whereas excessive risk aversion or resource allocation may reduce overall scheduling efficiency. The proposed method improves tail risk identification and solution capability for emergency UAV task allocation under time uncertainty and provides a methodological reference for risk-aware UAV emergency scheduling. Full article
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19 pages, 1162 KB  
Article
Spatially Constrained Evacuation Route Optimization for LPG Leakage Accidents in Chemical Industrial Parks
by Xinhui Wang
Processes 2026, 14(13), 2222; https://doi.org/10.3390/pr14132222 - 7 Jul 2026
Viewed by 346
Abstract
In chemical industrial parks, evacuation during LPG tank leakage is governed not only by travel distance but by the loss of safe corridors, failed exits, and congestion induced by spatially coupled vapor exposure, explosion overpressure, and thermal radiation. Existing consequence assessment studies usually [...] Read more.
In chemical industrial parks, evacuation during LPG tank leakage is governed not only by travel distance but by the loss of safe corridors, failed exits, and congestion induced by spatially coupled vapor exposure, explosion overpressure, and thermal radiation. Existing consequence assessment studies usually delineate hazardous zones, while evacuation models often optimize routes on a fixed network with available exits and simplified capacity constraints; the coupling between multi-hazard consequence fields and capacity-constrained evacuation assignment remains insufficient. This study proposes a spatially constrained, congestion-aware evacuation optimization framework. ALOHA-derived AEGL exposure, vapor cloud explosion overpressure, and jet fire radiation zones are mapped onto the plant network to identify unsafe nodes, unavailable links, and failed exits. A capacity-constrained model is then established to minimize system-level RSET under an ASET constraint, and a congestion-aware ant colony algorithm balances evacuees among available exits by incorporating risk and density penalties. In a petrochemical plant case with 717 evacuees and 74 nodes, Gate 3 failure makes the nearest-exit strategy infeasible, whereas the proposed strategy reduces RSET from 560.8 to 504.9 s. The framework links accident consequence assessment with actionable evacuation routing for chemical parks. Full article
(This article belongs to the Section Process Control, Modeling and Optimization)
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47 pages, 50912 KB  
Article
Citi Bike Station Behavioral Regime Model and Its Application in Rebalancing Operations
by Simao Alice Chen
Future Transp. 2026, 6(4), 143; https://doi.org/10.3390/futuretransp6040143 - 2 Jul 2026
Viewed by 553
Abstract
Past Citi Bike rebalancing research has relied on optimization and geospatial models but has treated spatial and temporal structures separately, leaving a gap in understanding stations as long-term behavioral entities. This study exploits the frequent spatiotemporal structure in Citi Bike daily trip data [...] Read more.
Past Citi Bike rebalancing research has relied on optimization and geospatial models but has treated spatial and temporal structures separately, leaving a gap in understanding stations as long-term behavioral entities. This study exploits the frequent spatiotemporal structure in Citi Bike daily trip data and treats the station’s bike net flow rate (NFR) time-series as the study object. Stations are grouped into regimes using time-series clustering, cluster stability, and the spatial context surrounding each station. Stations were assigned operational roles based on their hourly NFRs and potential contribution to the rebalancing truck. A priority-queue-based heuristic routing (PQHR) algorithm is introduced to design a single-vehicle route that accounts for stations’ regimes, roles, rebalancing urgency, and priority during rush hours. Therefore, this study formally introduces the Station Behavior Regime Model (SBRM) that defines station regimes, rebalancing roles, and routing. The result achieved a >90% reduction in the number of stations with extreme bike accumulation or unavailability and reduced the NFR of affected stations by >30% in busy areas. The spatial context derived from station behavior modes suggests new ways to define neighborhood boundaries. The methodologies provide new avenues for rebalancing operations and routing plans across a broad range of station-centric transportation network studies. Full article
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