Two-stage Heuristic Algorithm Research Articles

Real-time scheduling and routing of shared autonomous vehicles considering platooning in intermittent segregated lanes and priority at intersections in urban corridors

Anticipating the forthcoming integration of shared autonomous vehicles (SAVs) into urban networks, the imperative of devising an efficient real-time scheduling and routing strategy for these vehicles becomes evident if one is to maximize their potential in enhancing travel efficiency. In this study, we address the problem of jointly scheduling and routing SAVs across an urban network with the possibility of platooning the vehicles at intersections to reduce their travel time. We argue that this is especially useful in large urban areas. We introduce a novel vehicle scheduling and routing method that allows a specific number of SAVs to converge at the intersections of urban corridors within designated time intervals, facilitating the formation of SAV platoons. Dedicated lanes and signal priority control are activated to ensure that these platoons go through the corridors efficiently. Based on the above concept, we propose a linear integer programming model to minimize the total travel time of SAVs and the delays experienced by the conventional vehicles due to SAV priority, thereby optimizing the overall performance of the road network. For large instances, we develop a two-stage heuristic algorithm to solve it faster. In the first stage, leveraging an evaluation index that manifests the compatibility of each vehicle-to-request combination, we allocate passenger requests to a fleet of SAVs. In the second stage, a customized genetic algorithm is designed to coordinate the paths of various SAVs, thus achieving the desired vehicle platooning effect. The optimization method is tested on a real-world road network in Shanghai, China. The results display a remarkable reduction of 15.76 % in the total travel time of the SAVs that formed platoons. The overall performance of the road network could be improved with the total travel time increase of conventional vehicles significantly smaller than the reduction observed in SAVs’ total travel time.

Optimal decision-making of post-disaster emergency material scheduling based on helicopter–truck–drone collaboration

In the last decades, natural disasters, such as earthquakes and landslides, have occurred frequently, seriously threatening the safety of people’s lives and property. How emergency material is scheduled and delivered efficiently to the affected sites after a disaster has become a critical issue in emergency management. Current studies on emergency material scheduling mainly focus on truck or helicopter transport. Inspired by the success of employing drones in commercial logistics, this work investigates the emergency material scheduling issue based on the cooperative transport of drones, helicopters, and trucks. Specifically, this paper considers the limited transport capacity, road conditions in the early stage of the disaster rescue, and affected sites restricted by road conditions that can only be served by helicopters or drones. The studied problem is formulated as a mixed integer programming model, and a two-stage heuristic algorithm is developed to solve the model. For the proposed model, instances of different sizes are generated, and extensive experiments are performed to test the efficiency of the proposed algorithm. The comparison between the solutions obtained by the two-stage algorithm and Gurobi Solver for the small instances validates the effectiveness of the proposed heuristic algorithm. Experimental results for the larger instances show that the proposed two-stage algorithm can effectively solve the problem of emergency material scheduling. Sensitivity analysis of ten typical instances is performed to provide managerial insights. Finally, a case study of the Sichuan earthquake and the visualization of transport routes are presented. The model and solving approach proposed in this work can provide essential decision references for emergency management decision-making.

Order Distribution and Routing Optimization for Takeout Delivery under Drone–Rider Joint Delivery Mode

Order distribution and routing optimization of takeout delivery is a challenging research topic in the field of e-commerce. In this paper, we propose a drone–rider joint delivery mode with multi-distribution center collaboration for the problems of limited-service range, unreasonable distribution, high delivery cost, and tight time windows in the takeout delivery process. The model is constructed with the minimum delivery cost and the overall maximum customer satisfaction as the objective function, and a two-stage heuristic algorithm is designed to solve the model. In the first stage, Euclidean distance is used to classify customers into the regions belonging to different distribution centers, and the affinity propagation (AP) clustering algorithm is applied to allocate orders from different distribution centers. The second stage uses an improved tabu search algorithm for route optimization based on specifying the number of rider and drone calls. This paper takes China’s Ele.me and Meituan takeout as the reference object and uses the Solomon data set for research. The experimental results show that compared with the traditional rider delivery mode, the drone–rider joint delivery mode with multiple distribution center collaboration can effectively reduce the number of riders used, lower the delivery cost, and improve the overall customer satisfaction.

Model and Algorithm for a Two-Machine Group Scheduling Problem with Setup and Transportation Time

This paper investigates a two-machine group scheduling problem with sequence-independent setup times and round-trip transportation times, which is derived from the production management requirements of modern steel manufacturing enterprises. The objective is to minimize the makespan. Addressing limitations in prior studies, we consider a critical but largely ignored transportation method, namely round-trip transportation, and restricted transporter capacity between machines. To solve this problem, a mixed-integer programming model is first developed. Then, the problem complexity is analyzed for situations with both single and unlimited transporters. For the NP-hard case of a single transporter, we design an efficient two-stage heuristic algorithm with proven acceptable solution quality bounds. Extensive computational experiments based on steel plant data demonstrate the effectiveness of our approach in providing near-optimal solutions, and the maximum deviation between our algorithm and the optimal solution is 1.38%. This research can provide an operable optimization method that is valuable for group scheduling and transportation scheduling.

The capacity matching problem of the third-party shared manufacturing platform with capacity time windows and order splitting

The development of sharing economy and new information technologies has promoted the emergence of third-party shared manufacturing platforms (TPSMPs). In the shared manufacturing context, one main challenge to TPSMPs is the matching of manufacturing enterprises with insufficient production capacity (capacity demanders) and those with overcapacity (capacity suppliers), where available capacities of capacity suppliers are within time ranges, and orders of capacity demanders can be split. In this capacity matching problem with capacity time windows and order splitting (CMPCTW-OS), each capacity demander's order needs to be delivered on time, while each capacity supplier can also match with multiple capacity demanders and fulfil orders of the capacity demanders by sequence. A mathematical model for the CMPCTW-OS is developed to maximise the total profit of the TPSMP. Then, we design a two-stage heuristic algorithm to solve this model. In the first stage, the inserting algorithm (IA) is used to obtain an initial feasible solution. In the second stage, the iterated local search (ILS) is applied to optimise and improve the initial feasible solution. Finally, in numerical simulation experiments, the effectiveness of IA-ILS has been verified by comparison with the GUROBI solver.

Truck-drone joint path planning for post-disaster emergency material deployment considering fairness

As the expert gear of the emergency rescue system, drones are frequently utilized to distribute supplies following a calamity. The cost and effectiveness of rescue efforts as well as equitable distribution should be taken into account when allocating emergency supplies to disaster-affected areas. This work explores the emergency material allocation problem for truck-drone joint transportation with dynamic energy restrictions based on taking the fairness of emergency material allocation into consideration. In order to guarantee the equitable distribution of materials, the psychological stress experienced by the victims at each catastrophe site is measured using the relative deprivation cost. An adaptive large-scale neighborhood search method serves as the foundation for the creation of a two-stage heuristic algorithm, which reduces the overall cost of the system. The integer programming model MIP is built for this purpose. The research findings can serve as a useful guide for developing a just and effective emergency drone rescue system, and the testing results demonstrate the viability and effectiveness of the two-stage heuristic algorithm.

A cyber-physical social system for autonomous drone trajectory planning in last-mile superchilling delivery

Logistics drones are theoretically advantageous in automating last-mile delivery activities, but practically challenging in urban environments, including public concerns about risk of crashes and privacy. In view of the above concerns existing in the trajectory planning of logistics drones, this paper presents a parallel automatic delivery model following the cyber-physical social system (CPSS) for the last mile delivery of superchilling products, revealing the social value of logistics drone operations. Considering the operational constraints of logistics drone, a multi-objective optimisation model is established to balance the social value, energy efficiency and productivity of using logistics drones in the last-mile superchilling delivery. To effectively achieve the above optimisation, improved strategies, including the material exchange mechanism based on the random proportion rule and the Universe-Particle search strategy, are developed, resulting in an improved two-stage heuristic algorithm. Finally, simulation experiments are carried out in a simulated environment with 154 buildings, and compared with other frontier algorithms used for unmanned aerial vehicle (UAV) trajectory planning. The results show that the proposed framework can effectively reduce the threats to public life safety and improve the energy efficiency of logistics drones, while ensuring the productivity in the delivery process.

Optimization for Storage Scheduling of Steel Plates Based on Cloud Manufacturing Platform

With the development of cloud manufacturing, the automation of storage scheduling becomes popular in the steel industry. However, the high customization of steel plates makes the storage scheduling too complex to be optimized. To overcome this challenge, we propose to utilize the big data of steel plate orders and warehouse status to optimize the storage scheduling of steel plates. The agglomerative hierarchical clustering is firstly adopted to reduce the complexity of excessive steel plate specifications, then an optimization problem is defined to formulate the storage scheduling of steel plates with safety. A two-stage heuristic (TSH) algorithm is proposed to solve the optimization problem with low complexity. In TSH, steel plates are firstly assigned to multiple stacks, and then the arrangement of each stack is determined. Experiments are executed based on a cloud manufacturing platform for steel plates production and storage, and the results prove the effectiveness of the proposed works.

Two-stage heuristic algorithm for vehicle-drone collaborative delivery and pickup based on medical supplies resource allocation

This paper aims to optimize medical material distribution in closed community logistics networks during sudden outbreaks with a focus on efficient waste collection and reduced consumable distribution time. First, considering the costs of UAV trajectory distribution, impact, threat, and other costs, a forward and reverse scheduling model with time windows for joint multi-distribution center material distribution and waste anti-epidemic materials collection vehicle-UAV is established. Meanwhile, a two-stage metaheuristic algorithm is proposed in this paper. In the first stage of the solution algorithm, we design the multi-strategy guided adaptive differential evolution (MSGA-DE) to plan the multi-UAV cooperative distribution situation in a 3D environment. In the second stage, an improved beluga whale optimization based on hybrid neighborhood search (HNS-IBWO) is combined to solve the vehicle-UAV scheduling and distribution problem. Furthermore, comparing with various cross-validation algorithms, it validates the superiority of MSGA-DE in solving UAV trajectory issues and the convergence speed and accuracy of HNS-IBWO for high-latitude complex optimizations. Finally, a simulation in a closed Shanghai community validates the proposed model. Results demonstrate its effectiveness, especially in terms of convergence, multi-objective search, and global search capabilities when compared to existing algorithms. This offers an efficient solution for vehicle-UAV scheduling in unforeseen epidemic-related closures.

Virtual Network Function Placement Model Considering Both Availability and Probabilistic Protection for Service Delay

This paper proposes a virtual network function (VNF) placement model considering both availability and probabilistic protection for the service delay to minimize the service deployment cost. Both availability and service delay are key requirements of services; a service provider handles the VNF placement problem with the goal of minimizing the service deployment cost while meeting these and other requirements. The previousworks do not consider the delay of each route which the service can take when considering both availability and delay in the VNF placement problem; only the maximum delay was considered. We introduce probabilistic protection for service delay to minimize the service deployment cost with availability. The proposed model considers that the probability that the service delay, which consists of networking delay between hosts and processing delay in each VNF, exceeds its threshold is constrained within a given value; it also considers that the availability is constrained within a given value. We develop a two-stage heuristic algorithm to solve the VNF placement problem; it decides primary VNF placement by solving mixed-integer second-order cone programming in the first stage and backup VNF placement in the second stage. We observe that the proposed model reduces the service deployment cost compared to a baseline that considers the maximum delay by up to 12%, and that it obtains a feasible solution while the baseline does not in some examined situations.

Multivisit Drone-Vehicle Routing Problem with Simultaneous Pickup and Delivery considering No-Fly Zones

The employment of drones for the distribution of goods represents a significant avenue for addressing logistical challenges at the end of the supply chain. The truck-drone cooperative delivery model overcomes drone limitations such as limited capacity and endurance and has emerged as a crucial mode of drone participation in logistics delivery. This delivery model effectively reduces delivery costs and shortens delivery times. Herein, we examine a variant of the truck-drone routing problem, which encompasses the strategic deployment and routing of multiple fleets of trucks, each equipped with an auxiliary drone. The objective is to fulfill all the pickup and delivery demands of a designated customer base while minimizing the overall route cost. Within this problem domain, drones are authorized to serve multiple customers within their capacity and endurance limits, providing both pickup and delivery services during each trip. However, the utilization of drones for servicing all customers is impeded by the existence of no-fly zones that have been implemented in numerous cities worldwide. These prescribed no-fly zones cause significant challenges when attempting to optimize the routing of truck-drone operations. Thus, this study constructs a mixed integer linear programming (MILP) model for the path optimization problem of joint service of trucks and drones considering no-fly zones and simultaneous pickup and delivery. Given the intricacy of the MILP model, we propose a two-stage heuristic algorithm based on a simulated annealing approach, combined with strategies for rectifying infeasible solutions and expediting algorithmic processes. During the phase of computational experimentation, we explore the advantages derived from enabling drones to serve multiple customers and assess the effectiveness of the proposed model and two-stage heuristic algorithm. Finally, sensitivity analysis is conducted on two key parameters.

An integrated approach for optimizing location-inventory and location-inventory-routing problem for perishable products

The grocery market, especially the perishable product market is under amazing developments in China, accounting for half of overall food expenditure. However, the supply chain of perishable products has encountered serious problems, including significant freight losses, high inventory and transportation costs, etc. To solve these problems, the current paper proposes an integrated approach for simultaneously optimizing the decisions involved in the supply chain, typically including location, inventory, and routing strategy. A three-echelon supply chain including suppliers, DCs and retailers is structured in this paper, with the impacts of whether allowing direct shipment from supplier to retailer being considered. Two typical problems are investigated: location-inventory problem (LIP) and location-inventory-routing problem (LIRP). Mixed integer nonlinear programming model for LIP is proposed while Mixed integer linear programming models for LIRP is proposed, with the objective of minimizing the overall costs of supply chain, which are composed of infrastructure construction costs, transportation costs, inventory costs, and freight losses. CPLEX is used for LIP model solution and a two-stage heuristic algorithm based on Simulated Annealing is designed to solve the LIRP model. The proposed mathematical models and solution method are then applied to a real supply chain network for fresh milk. The optimized results suggest that considering the direct shipment from supplier to retailer is beneficial in terms of reducing the overall supply chain costs by 31%, with 43% reductions in transportation costs, 69.4% reductions in freight losses, 99.4% increases in inventory costs. With the developments of e-retailers for perishable products, allowing the direct shipment from supplier to retailer will bring more benefits in the future.

Service Function Chain Scheduling in Heterogeneous Multi-UAV Edge Computing

Supporting Artificial Intelligence (AI)-enhanced intelligent applications on the resource-limited Unmanned Aerial Vehicle (UAV) platform is difficult due to the resource gap between the two. It is promising to partition an AI application into a service function (SF) chain and then dispatch the SFs onto multiple UAVs. However, it is still a challenging task to efficiently schedule the computation and communication resources of multiple UAVs to support a large number of SF chains (SFCs). Under the multi-UAV edge computing paradigm, this paper formulates the SFC scheduling problem as a 0–1 nonlinear integer programming problem. Then, a two-stage heuristic algorithm is put forward to solve this problem. At the first stage, if the resources are surplus, the SFCs are deployed to UAV edge servers in parallel based on our proposed pairing principle between SFCs and UAVs for minimizing the completion time sum of tasks. In contrast, a revenue maximization heuristic method is adopted to deploy the arrived SFCs in a serial service mode when the resource is insufficient. A series of experiments are conducted to evaluate the performance of our proposal. Results show that our algorithm outperforms other benchmark algorithms in the completion time sum of tasks, the overall revenue, and the task execution success ratio

Energy-efficient single-machine scheduling with release dates under time-of-use electricity tariffs

The global trend of increasing resource utilization in industry has drawn great attention from researchers and practitioners. Industrial managers are increasingly optimizing their production strategies based on time-of-use (TOU) electricity tariffs to reduce energy consumption costs. This study investigates a new energy-efficient single-machine scheduling problem with release dates under TOU electricity tariffs. It consists in sequencing a set of jobs with release dates to a machine under TOU pricing to minimize the total energy cost given a bounded maximum completion time. We first formulate the problem using the widely used time-indexed mixed-integer linear programming (T-MILP). Due to its time-consuming disadvantage, a new period-based MILP (P-MILP) model is developed based on the characteristics of the problem. Given the NP-hardness of the problem, a two-stage heuristic (TSH) algorithm is proposed to solve practical-sized problems. Specifically, in the first stage, a constructive heuristic is designed to obtain an initial solution, and in the second one, a tailored tabu search is devised to yield a better satisfactory solution. Numerical experiments are conducted on a real-life case and 1150 randomly generated instances with up to 1000 jobs. Computational results show that (i) the proposed models can save the total electricity cost by about 30% compared with an existing empirical scheduling method when solving small-sized instances; (ii) the efficiency of P-MILP is about 140.94% higher than that of T-MILP; and (iii) the proposed TSH algorithm can efficiently obtain high-quality solutions for practical-sized instances with gaps of less than 7% compared to the lower bounds, which can effectively support production managers to save the energy costs in practical production.

The multi-visit drone routing problem for pickup and delivery services

Unmanned aerial vehicles, commonly known as drones, have gained wide attention in recent years due to their potential of revolutionizing logistics and transportation. In this paper, we consider a variant of the combined truck-drone routing problem, which allows drones to serve multiple customers and provide both pickup and delivery services in each flight. The problem concerns the deployment and routing of a fleet of trucks, each equipped with a supporting drone, to serve all the pickup and delivery demands of a set of customers with minimal total cost. We explicitly model the energy consumption of drones by their travel distance, curb weight and the carrying weight of parcels, develop a mixed-integer linear programming model (MILP) with problem-customized inequalities, and show a sufficient condition for the benefit of the combined truck-drone mode over the truck-only mode. Considering the complexity of the MILP model, we propose a novel two-stage heuristic algorithm in which a maximum payload method is developed to construct the initial solutions, followed by an improved simulated annealing algorithm with problem-specific neighborhood operators and tailored acceleration strategies. Furthermore, two methods are developed to test the feasibility for both trucks and drones in each solution. The proposed algorithm outperforms two benchmark heuristics in our numerical experiments, which also demonstrate the considerable benefit of allowing multiple visits and both pickup and delivery operations in each drone flight.

A mathematical programming–based heuristic for coordinated hydrothermal generator maintenance scheduling and long-term unit commitment

This paper studies the coordinated optimization between generator maintenance scheduling and long-term unit commitment in hydrothermal power systems, which can deal with the increased conflicts between these two tasks brought on by the extensive integration of cascade hydropower, but encounters difficulty in finding solutions when the system scale is large. A coordinated optimization model between hydrothermal generator maintenance scheduling and long-term unit commitment is proposed, in which the network security constraints and coupling characteristics between cascade hydro plants are considered. To accelerate the solution of this complex mixed-integer linear programming problem, an improved two-stage heuristic algorithm based on the objective scaling ensemble approach is proposed. The first stage is a detection process in which a maintenance interval detection strategy is used to probe the maintenance variables to be fixed. The second stage is a fix-and-solve process in which the reduced model is solved after fixing the maintenance variables detected at the first stage. Finally, simulations on a modified IEEE 30-bus and 6-unit hydrothermal power system and a real 1348-bus and 155-unit hydrothermal power system are conducted, focusing on the solution quality and the acceleration effect of the proposed algorithms, as well as the results of the proposed model. The numerical results reveal that the proposed algorithm can speed up the process of finding a near-optimal solution for large-scale systems through a detection strategy with high accuracy and efficiency. The proposed model can plan out feasible and coordinated maintenance scheduling and long-term unit commitment scheme simultaneously.

Two stochastic optimization methods for shift design with uncertain demand

The purpose of this paper is to investigate the shift design problem with a probability constraint on demand satisfaction and to design the corresponding stochastic model so that the staffing for each shift can cope with stochastic demand. To solve this stochastic model, we propose two solution methods: a method involving average sample approximation and a two-stage heuristic algorithm based on statistics with a greedy strategy. Numerical results show that both methods can solve the stochastic model of this paper well, and the sample average approximation method outperforms the two-stage heuristic algorithm in terms of cost optimization. However, as the number of scenarios used to approximate realistic situations increases, the superiority of the two-stage heuristic algorithm in terms of solution speed becomes progressively more significant.

Location Optimization of Fresh Agricultural Products Cold Chain Distribution Center under Carbon Emission Constraints

This paper seeks to effectively realize energy saving and emission reduction in the process of location for fresh agricultural cold chain logistics. It is based on the traditional location for distribution center optimized for both freshness and carbon emissions. A bi-objective function location model was constructed to minimize the total cost and carbon emission and a two-stage heuristic algorithm was designed to solve the model. According to analyzing the location case of Y enterprise in Zhejiang Province, the THA had an average total cost optimization rate of 7.70% and an average carbon emission optimization rate of 10.23% compared to the WOA, while it had a rate of 12.77% and 14.12%, respectively, compared to the PSO. When the unit carbon emission cost increased from 0.02 dollar/kg to 0.06 dollar/kg, the comprehensive carbon emission cost increased by 42.07% and the total cost increased by 3.05%. Therefore, logistics enterprises can achieve the reduction of logistics costs and sustainable development through reasonable location for fresh agricultural products cold chain distribution centers.

Wavelength Allotment for All-to-All Broadcast in WDM Optical Bidirectional ring with 3-Length Extension

All-to-all broadcast communication, distributing messages from each node to every other node, is a dense communication pattern and finds numerous applications in advanced computing and communication networks from the control plane to datacenters. A ring network topology is one of the important regular network topologies due to its simple structure, high speed, easy to extend and tolerant to link and node failures. Few researchers recommended connecting the alternate nodes of the ring with additional fibers in the ring network, to support increased call connection probability, higher tolerable to multiple link and node failures, enormous traffic handling capability and improved survivability. To reduce the complicatedness and cost of the network, it is essential to reduce the wavelength-number required to establish all-to-all broadcast in wavelength-division multiplexed ring network. In this paper, a ring network is extended by directly linking all nodes which are separated by two intermediate nodes with additional fibers and this network is referred as ring with 3-length extension. The wavelength allotment methods are proposed for realizing all-to-all broadcast over a WDM optical bi-directional ring with 3-length extension under multiple unicast routing model using a two-stage heuristic algorithm. The heuristic algorithm is developed to identify non-overlapping connections and an explicit wavelength allotment method based on the output of the heuristic technique is given. The result obtained shows that wavelength-number required atmost to establish all-to-all broadcast in a bi-directional ring with 3-length extension is reduced by a minimum of 57% and a maximum of 66% when compared to bi-directional primary ring. Similarly, the wavelength-number required atmost to establish all-to-all broadcast in a bi-directional ring with 3-length extension is reduced by a minimum of 20% and a maximum of 33% when compared to a bi-directional ring with 2-length extension.

Joint Task Offloading and Resource Allocation for Multi-Access Edge Computing Assisted by Parked and Moving Vehicles

In the Internet of Vehicles (IoV) scenarios, vehicles are equipped with computing resources to support vehicle-oriented IoV applications. Meanwhile, these computing resources can be also leveraged to enhance the task processing performance for the devices in Multi-access Edge Computing (MEC) scenarios, and alleviate the load of edge servers. Existing research works rarely consider the resource utilization of moving vehicles, which can be an important complement to the MEC schemes with the assistance of parked vehicles. In this paper, a joint task offloading and resource allocation scheme is proposed for a parked-and-moving-vehicles-assisted MEC scenario consisting of multiple devices, parked vehicles, and moving vehicles covered by a Base Station (BS) equipped with an edge server. The tasks of the devices can be either offloaded to the BS or further offloaded from the BS to the vehicles. The service time that a moving vehicle can provide its task offloading service before it moves out of the coverage of the BS, are taken into account of our system model. The aim of our scheme it to minimize the total priority-weighted task processing delay for all the devices through offloading the tasks to the edge server or to the vehicles, allocating the wireless channels of the BS, and allocating the computing resource of the edge server and the vehicles. A generalized benders decomposition and reformulation linearization-based iterative algorithm is designed to obtain the optimal solution to the optimization problem, and a two-stage heuristic algorithm is also given to provide near-optimal solutions with low computational complexity. The simulation results demonstrate the superiority of our scheme in seven different scenarios by comparing it with three other schemes.