Rui Xu

Entropy-based fault diagnosis depends on signal representation and the properties captured by each entropy measure. We evaluated dual-view complementary multiscale entropy fusion (DCMEF), which combines RMS-normalized raw vibration with a normalized logarithmic Hilbert envelope. Three entropy measures at five fixed scales produce 30 candidate features, with imputation, selection, and classifier tuning confined to grouped training folds. In an exploratory comparison against 20 representations across four selected tasks and three classifiers, DCMEF achieved the highest observed accuracy in nine of 12 settings and tied for highest in three. A separate view ablation found that the full bank outperformed raw-only features in two settings, tied in five, and underperformed in five; relative to envelope-only, it outperformed in ten and tied in two. Thus, raw-vibration features were useful across these settings, whereas adding envelope features had inconsistent effects. Independent evaluation is needed to assess performance beyond the selected tasks.

This study investigates a dynamic parallel-machine scheduling problem with human–robot collaboration (DPMS-HRC), where dynamically arriving jobs are assigned to eligible workstations and processed by workers, robots, or human–robot collaboration based on real-time system states. Worker-involving modes improve operational flexibility but may increase actual processing times and cause uneven fatigue distribution due to fatigue accumulation. To coordinate production responsiveness and fatigue management, a weighted objective combining average flow time and the worker fatigue balance index is minimised. A mixed-integer nonlinear programming (MINLP) formulation is developed to model dynamic job arrivals, alternative processing modes, worker–robot allocation, and fatigue-dependent processing times. An action-masked and potential-shaped multi-agent proximal policy optimisation (AMPS-MAPPO) algorithm is then designed. Action masking restricts policy sampling to structurally feasible job-mode-resource combinations, while time-scaled potential shaping provides dense feedback for long-horizon learning. Experiments on dynamic instances of different scales show that AMPS-MAPPO achieves millisecond-level online inference, reduces average flow time by 40.98% relative to the best dispatching-rule benchmark and by 8.17–20.92% relative to deep reinforcement learning baselines, and obtains the lowest overall worker fatigue balance index among the compared deep reinforcement learning algorithms.

This paper investigates a new transportation problem arising in automotive parts milk-run logistics under a business contract in which the payment for each vehicle is determined by the maximum direct shipment cost among its assigned suppliers, plus a fixed stop-off charge for each additional supplier. The company determines the supplier groups, whereas the carriers arrange the visiting sequences, which do not affect the payment. We formulate this allocation problem as the Bin Packing Problem with Conflicts and Item-dependent Bin Costs (BPPCI), in which suppliers are treated as items and vehicles as bins, with the objective of minimizing total transportation cost under the contract subject to capacity and conflict constraints. We develop a mixed-integer linear programming model and two lower bounds, together with a hybrid metaheuristic that combines prefiltering, variable neighborhood descent, and reactive search within a greedy randomized adaptive search procedure. Computational experiments on 400 benchmark instances show that the proposed algorithm achieves an average gap of 4.91% relative to the tighter of the two lower bounds, with an average runtime of a few seconds. Component analysis examines the contributions of the main algorithmic components to solution quality and computational time. Three company cases involving 24, 53, and 106 suppliers show cost reductions of 12.76%, 11.19%, and 10.28%, respectively, relative to the corresponding manual plans.

The rapid development of shared delivery, parcel lockers, and community pickup services has enabled customers to receive orders at multiple alternative service locations. In such scenarios, the fixed-location assumption adopted in traditional electric vehicle routing problems is no longer appropriate. This paper investigates the Electric Vehicle Routing Problem with Time Windows and Flexible Service Locations (EVRPTW-FSL), in which customers can be served at one selected location from a candidate set, while each service location may accommodate multiple customers subject to capacity limits. A mixed-integer optimization model is developed to jointly determine service location assignments, vehicle routing, and charging decisions under vehicle capacity, battery range, partial recharging, and customer time-window constraints. To balance operational efficiency and customer convenience, the objective minimizes the total travel cost and the customer deviation cost incurred when a customer is assigned to an alternative service location rather than the original service location. To solve this NP-hard problem, a Modified Adaptive Large Neighborhood Search with Fix-and-Optimize mechanism (MALNS-FO) is proposed, incorporating specialized operators such as location association destroy, location similarity destroy, and route reconstruction repair, as well as a fix-and-optimize mechanism. Computational experiments demonstrate that the proposed method consistently outperforms benchmark approaches in solution quality and computational efficiency. Results further show that introducing flexible service locations can significantly reduce fleet usage and routing cost by consolidating spatially dispersed demand. Moreover, moderate customer flexibility provides substantial operational benefits while maintaining acceptable service deviation levels.

The green vehicle routing problem with private capacitated alternative fuel stations (GrVRP-PCAFS) extends the traditional green vehicle routing problem by considering capacitated refueling stations, where a limited number of vehicles can refuel simultaneously and additional vehicles must wait. This feature presents new challenges for route planning, as waiting times at stations must be managed while keeping route durations within limits and reducing total travel distance. This article presents METS, a novel memetic algorithm (MA) with separate constraint-based tour segmentation (SCTS) and a local search procedure tailored for solving GrVRP-PCAFS. METS balances exploration and exploitation through three key components. For exploration, the SCTS strategy splits giant tours to generate diverse solutions, and the search process is guided by a comprehensive fitness evaluation function to dynamically control feasibility and diversity to produce solutions that are both diverse and near-feasible. For exploitation, the local search procedure incorporates tailored move operators with constant-time evaluation mechanisms, enabling efficient examination of large solution neighborhoods. Experimental results demonstrate that METS discovers 31 new best-known solutions out of 40 instances in existing benchmark sets, achieving substantial improvements over current state-of-the-art methods. Additionally, a new large-scale benchmark set based on real-world logistics data is introduced to facilitate future research.

With the escalating environmental crisis, electric vehicles have emerged as a key solution for emission reductions in logistics due to their low-carbon attributes, prompting significant attention and extensive research on the electric vehicle routing problem (EVRP). However, existing studies often overlook charging infrastructure (CI) capacity constraints and fail to fully exploit the synergistic potential of heterogeneous energy replenishment infrastructures (HERIs). This paper addresses the EVRP with HERIs under various capacity constraints (EVRP-HERI-CC), proposing a mixed-integer programming (MIP) model and a hybrid ant colony optimization (HACO) algorithm integrated with a variable neighborhood search (VNS) mechanism. Extensive numerical experiments demonstrate HACO’s effective integration of problem-specific characteristics. The algorithm resolves charging conflicts via dynamic rescheduling while optimizing charging-battery swapping decisions under an on-demand energy replenishment strategy, achieving global cost minimization. Through small-scale instance experiments, we have verified the computational complexity of the problem and demonstrated HACO’s superior performance compared to the Gurobi solver. Furthermore, comparative studies with other advanced heuristic algorithms confirm HACO’s effectiveness in solving the EVRP-HERI-CC. Sensitivity analysis reveals that appropriate CI capacity configurations achieve economic efficiency while maximizing resource utilization, further validating the engineering value of HERI networks.

Motivated by observing real-world instances of multi-aisle automated storage and retrieval systems (AS/RSs) with shared storage, we introduced a new optimization problem called the parallel crane scheduling (PCS) problem. Unlike the single crane scheduling (SCS) problem, the decisions of the PCS problem include not only the request sequencing and storage/retrieval location selection, but also assigning requests to cranes. The PCS problem better reflects the real-life situation, but it is more complex, since these three decisions are interrelated and interact with one another. In this study, since the empty location vacated by any retrieval operation is instantly available, we introduced a new dynamic programming model combined with a mixed-integer linear programming model to describe this complex problem. Considering the feature of location-dependent processing time, we transformed the PCS problem into a variant of the unrelated parallel machine scheduling problem. We developed an apparent tardiness cost-based construction heuristic and an ant colony system algorithm with a problem-specific local optimization. Our experiments demonstrated that the proposed algorithms provide excellent performance, along with the insight that globally scheduling multiple aisles could be considered to reduce the total tardiness when designing an operation scheme for multi-aisle AS/RSs.

Inspired by long-distance road transport in industrial logistics in China, this paper studies a simultaneous loading scheduling and vehicle routing problem over a multi-workday planning horizon. Industrial cargo often requires specialized facilities, and these facilities vary in performance and quantity and are subject to available time constraints. Consequently, achieving coordinated optimization of vehicle routing and loading scheduling becomes a significant challenge in practice. We describe the studied problem as a multi-trip vehicle routing problem with time windows and resource synchronization on heterogeneous facilities. First, we develop a mixed integer programming model in a multi-workday setting to minimize the total travel distance and the number of vehicles. Moreover, a three-phase heuristic approach is developed. An initial solution is constructed using a sequential strategy in the first phase, and then an adaptive large neighbourhood search and a post-optimization procedure based on ejection chains are, respectively, designed to optimize the two hierarchical objective functions. Finally, extensive computational experiments are conducted to demonstrate the effectiveness of the proposed method. Specifically, the research results indicate that in long-distance road transport in industrial scenarios, expanding the planning horizon from a single workday to a multi-workday period could significantly reduce logistics operational costs and improve service quality.

This paper introduces Split Delivery Clustered Vehicle Routing Problem with Soft cluster conflicts and Customer-related costs (SDCVRPSC) arising in automotive parts of milk-run logistics with supplier cluster distribution in China. In SDCVRPSC, customers are divided into different clusters that can be visited by multiple vehicles, but each vehicle can only visit each cluster once. Penalty costs are incurred when traveling between clusters. The transportation cost of a route is calculated as the maximum direct shipment cost between customers on the route plus the total drop costs. The SDCVRPSC aims to minimize the sum of transportation costs and penalty costs by determining the assignment of customers to vehicles and the visiting order of clusters. We propose an integer linear programming model and a two-level variable neighborhood descent algorithm (TLVND) that includes two-stage construction, intensification at cluster and customer levels, and a perturbation mechanism. Experimental results on designed SDCVRPSC benchmark instances demonstrate that TLVND outperforms the Gurobi solver and two adapted algorithms at the business operation level. Moreover, a real case study indicates that TLVND can bring significant economic savings compared to expert experience decisions. TLVND has been integrated into the decision support system of the case company for daily operations.