Variable Neighborhood Search Research Articles

A lightweight genetic algorithm with variable neighborhood search for multi-depot vehicle routing problem with time windows

A multi-depot green vehicle routing problem with time windows considering customer satisfaction (MDGVRPTW-CS) was constructed. To optimize it, we proposed a lightweight genetic algorithm with variable neighborhood search (LGAVNS), which takes the genetic algorithm as the upper algorithm and the variable neighborhood algorithm as the neighborhood search algorithm. In our constructed algorithm, the neighborhood search operators were applied to the optimal gene instead of all genes. Additionally, an enhanced crossover operator was developed to facilitate the effective transmission of gene information. Finally, we extended and optimized the parameters of the algorithm. Experimental results demonstrated that our approach exhibited significant advantages in terms of optimization effectiveness and convergence speed compared to six state-of-the-art algorithms, particularly when addressing MDGVRPTW-CS in large-scale scenarios. Moreover, the lightweight nature of our algorithm can be utilized for optimizing both the number and location of depots while further exploring the optimization potential of MDGVRPTW-CS.

A mathematical model and solution algorithms for optimising system-level configurations of reconfigurable single part flow lines

This study addresses a system-level configuration selection problem for reconfigurable single part flow lines (R-SPFLs) with parallel identical flexible machines at each stage. The problem is to determine the number of stages, the number of machines of a certain type at each stage and the assignment of operations to each stage in order to satisfy the demand of a part type. Precedence relations among the operations and space limitations are also considered. For the objective of minimising the sum of machine purchase and operation processing costs, a nonlinear integer programming model is developed that gives the optimal solutions. Then, due to the problem's complexity, a basic variable neighbourhood search algorithm is proposed that constructs an initial solution using a greedy-type heuristic and improves it using a shaking and a local search improvement methods. Moreover, the basic algorithm is extended to a general one that uses a variable neighbourhood descent method. Computational results show that the two algorithms outperform the previous one significantly in both solution quality and computation times, and the general algorithm improves the basic one significantly. Finally, the applicability of the variable neighbourhood search algorithms is shown by reporting a brief case study.

Joint optimization of train timetable and passing facility: A capacity allocation strategy

To addreess the challenge of overcrowding in the urban rail transit system, this paper proposes a novel joint optimization strategy that optimizes the timetable and the passing facility’s working status (PFWS) simultaneously according to the passenger demands. To this end, a mixed-integer nonlinear programming (MINLP) model is formulated to jointly minimize overcrowding on trains and platforms, as well as the passenger travel time. The passing facility setting and the passenger flow activities depiction are particularly taken into account by the rigorous constraints. Subsequently, we design a simulation-based hybrid variable neighborhood search (SHVNS) algorithm to efficiently generate near-optimal solution. This algorithm incorporates a variable neighborhood search (VNS) algorithm, a randomly reset strategy, and a simulation-based algorithm. The VNS algorithm includes five neighborhood operators to enhance search efficiency. Finally, various experiments with the real-world data from Chongqing rail transit line 6 in China are tested to prove the applicability and the performance of our proposed model and algorithm. The computational results show that the joint optimization strategy outperforms a current operation strategy in terms of the overcrowded situation on trains and platforms, often by more than 60%, and some management implications and theoretical support can be obtained for the urban rail transit operator.

Variable Neighborhood Search Based Human Learning Optimization Algorithm for Secure Data Analysis and Computing

Variable Neighborhood Search Based Human Learning Optimization Algorithm for Secure Data Analysis and Computing

A Decision Support Framework for Aircraft Arrival Scheduling and Trajectory Optimization in Terminal Maneuvering Areas

This study introduces a decision support framework that integrates aircraft trajectory optimization and arrival scheduling to facilitate efficient management of descent operations for arriving aircraft within terminal maneuvering areas. The framework comprises three modules designed to tackle specific challenges in the descent process. The first module formulates and solves a trajectory optimization problem, generating a range of candidate descent trajectories for each arriving aircraft. The options for descent operations include step-down descent operation, Continuous Descent Operation (CDO), and CDO with a lateral path stretching strategy. The second module addresses the assignment of conflict-free trajectories to aircraft, determining precise arrival times at each waypoint. This is achieved by solving an aircraft arrival scheduling problem. To overcome computational complexities, a novel variable neighborhood search algorithm is proposed as the solution approach. This algorithm utilizes three neighborhood structures within an extended relaxing and solving framework, and incorporates a tabu search algorithm to enhance the efficiency of the search process in the solution space. The third module focuses on comparing the total cost incurred from flight delays and fuel consumption across the three descent operations, enabling the selection of the most suitable operation for the descent process. The decision support framework is evaluated using real air traffic data from Guangzhou Baiyun International Airport. Experimental results demonstrate that the framework effectively supports air traffic controllers by scheduling more cost-efficient descent operations for arrival aircraft.

The Vehicle Routing Problem with Cross-Docking and Scheduling at the Docking Station: Compact formulation and a General Variable Neighborhood Search metaheuristic

In this article, we introduce the Vehicle Routing Problem with Cross-Docking and Scheduling at the Docking Station (VRPCDSD), which integrates pickup and delivery routing decisions with the cross-docking scheduling of the unloading and reloading of requests. We present a compact Mixed Integer Programming (MIP) formulation and a General Variable Neighborhood Search (GVNS) metaheuristic for the problem. The proposed GVNS employs several routing and scheduling neighborhoods that require problem-specific adjustments due to the integrated characteristic of the problem. Computational experiments indicate that the MIP formulation can solve instances with up to 31 nodes (15 requests) within the specified time limit when using a standard commercial solver. Furthermore, the GVNS metaheuristic can obtain high-quality solutions that at least match those encountered by the solver for the tested instances, achieving considerably large improvements over the latter especially as the number of requests increases. In fact, GVNS is able to find the optimal solution for all the instances for which the optimal is known. In addition, GVNS is a viable alternative for tackling larger instances of VRPCDSD and is very robust in that it obtains low deviations from the best-encountered solutions when multiple executions are performed. We also present some insights on how the different cross-docking operation costs impact the optimal solutions.

The home health care routing with heterogeneous electric vehicles and synchronization

AbstractThis paper studies the problem of heterogeneous electric vehicles, fast chargers, and synchronized jobs that have time windows in home healthcare routing and scheduling. We consider a problem that aims to establish daily routes and schedules for healthcare nurses to provide a variety of services to patients located in a scattered area. Each nurse should be assigned to an electric vehicle (EV) from a heterogeneous fleet of EVs to perform the assigned jobs within working hours. We consider three different types of EVs in terms of battery capacity and energy consumption. We aim to minimize the total cost of energy consumption, fixed nurse cost, and costs arising from the patients that cannot be served within the working day. We model the problem as a mixed integer programming formulation. We develop a hybrid metaheuristic based on a greedy random adaptive search procedure heuristic, to generate good quality initial solutions quickly, and an adaptive variable neighborhood search algorithm to generate high quality solutions in reasonable time. The hybrid metaheuristic employs a set of new advanced efficient procedures designed to handle the complex structure of the problem. Through extensive computational experiments, the performance of the mathematical model and the hybrid metaheuristic are evaluated. We conduct analyses on the robustness of the metaheuristic and the performance contribution of employing adaptive probabilities. We analyze the impact of problem parameters such as competency requirements, job duration, and synchronized jobs.

Research on vehicle path planning of automated guided vehicle with simultaneous pickup and delivery with mixed time windows

AbstractThe authors investigate new Automated Guided Vehicle (AGV) Routing Problem with Simultaneous Pickup and Delivery with Mixed Time Windows (VRPSPDMTW) in smart workshops, a variation of the classic Vehicle Routing Problem (VRP). A mixed time window vehicle routing model was developed for simultaneous deliveries. This model reduces the cost of AGVs used and distribution cost, along with time window penalties. To address this complex challenge, a Hybrid Adaptive Genetic Algorithm using Variable Neighbourhood Search (AGA‐VNS) is proposed. This algorithm enhances the genetic algorithm's local search capabilities while preserving solution diversity, thereby improving both efficiency and quality of solutions. Comprehensive computational experiments are conducted, which include both VRPSPDTW test benchmark and real‐world smart factory instance studies. The outcomes reveal that the AGA‐VNS algorithm outperforms both professional solver software and advanced heuristic methods significantly. Moreover, the newly developed mixed time window model is more aligned with the requirements of real‐world production processes compared to the traditional time window model. Thus, this research not only presents novel insights into the domain of vehicle routing problems but also demonstrates its significant applicability and potential in the background of intelligent workshops.

Collaborative orchard pesticide spraying routing problem with multi-vehicles supported multi-UAVs

The application of UAVs in orchard management presents a substantial opportunity to enhance efficiency and promote environmentally friendly agricultural production. While individual UAVs encounter limitations, such as endurance constraints, these challenges can be mitigated through collaborative efforts involving multiple vehicles and UAVs. This study addresses the issue of multi-UAV cooperative orchard path planning with multiple vehicles by formulating a mathematical optimization model aimed at minimizing the maximum UAV operation time. In the proposed model, the vehicle solely provides batteries and supplies to the UAV. To efficiently solve this model, we propose an improved Simulated Annealing-Lin Kernighan Helsgaun (SA-LKH) algorithm. The proposed algorithm utilizes the K-means and convex hull algorithm to generate the initial solution. Subsequently, the paths of each group of UAVs and vehicles are optimized based on the LKH algorithm. Additionally, we construct a directed perturbation operator that perturbs the maximum and minimum time-consuming paths to achieve fast convergence of the algorithm. The results from four different cases demonstrate that, compared to the general variable neighborhood search algorithm, the improved Ant Colony Algorithm and Improved Genetic Algorithm, the proposed algorithm has demonstrated an average improvement in solution quality of 3.41%, 5.72% and 9.67%, respectively. The proposed method effectively enhances the solution quality, which can provide valuable insights into green cleaning management of orchards.

Multi-objective Evolutionary Algorithm with Variable Neighborhood Search for Optimizing Green Scheduling in a Re-Entrant Hybrid Flow Shop with Dynamic Events

In previous studies on re-entrant hybrid flow shops, the impact of dynamic events was often ignored despite being a common occurrence in practical production. To address this issue and simultaneously reduce energy consumption, a multi-objective evolutionary algorithm with variable neighborhood search (MOEA-VNS) has been proposed to optimize the green scheduling problem in a re-entrant hybrid flow shop with dynamic events (RHFS-GDS).The approach involves creating a green dynamic scheduling optimization model, which aims to minimize the makespan, total energy consumption, and stability of rescheduling solutions. A hybrid green scheduling decoding method is then employed to select machines for each operation and calculate fitness. Additionally, three neighborhood structures are designed to improve the population diversity and optimality of the MOEA-VNS algorithm. Two rescheduling strategies are also adopted to handle dynamic events that may occur during production. Experimental results demonstrate that these approaches are effective in solving the RHFS-GDS problem and can guide actual production. By incorporating dynamic events and rescheduling strategies into the optimization process, the proposed MOEA-VNS algorithm provides a comprehensive solution to the complex challenges faced by re-entrant hybrid flow shops in practical production environments.

A hybrid estimation of distribution algorithm for solving assembly flexible job shop scheduling in a distributed environment

This paper proposes a novel distributed assembly flexible job shop scheduling problem (DAFJSP), which involves three stages: production stage, assembly stage, and delivery stage. The production stage is accomplished in a few flexible job shops, the assembly stage is accomplished in a few single-machine factories, and the delivery stage is to deliver the obtained products to the corresponding customers. To address the problem, a hybrid estimation of distribution algorithm based on differential evolution operator and variable neighborhood search (HEDA-DEV) is proposed with the goal of minimizing the total cost and tardiness. Firstly, a new multidimensional coding method is designed based on the features of the DAFJSP. Secondly, two mutation operators and the similarity coefficient based on the probability matrix are put forward to implement the dynamic mutation. Thirdly, five types of neighborhood structures satisfying cooperative search strategies are employed to adequately improve the local exploitation ability. Finally, the comparison experiment results suggest that the proposed HEDA-DEV has competitive performance compared to the selected efficient algorithms. Moreover, a real case study is used to demonstrate that HEDA-DEV is an effective method for solving DAFJSP.

A variable neighborhood search for the median location problem with interconnected facilities

AbstractThe ‐median problem has been widely studied in the literature. However, there are several variants that include new constraints to the classical problem that make it more realistic. In this work, we study the variant that considers interconnected facilities, that is, the distances between each pair of facilities are less than or equal to a certain threshold . This optimization problem, usually known as the median location problem with interconnected facilities, consists of locating a set of interconnected facilities to minimize the distance between those interconnected facilities and the demand points. The large variety of real‐world applications that fit into this model makes it attractive to design an algorithm able to solve the problem efficiently. To this end, a procedure based on the variable neighborhood search methodology is designed and implemented by using problem‐dependent neighborhoods. Experimental results show that our proposal is able to reach most of the optimal solutions when they are known. Additionally, it outperforms previous state‐of‐the‐art methods in those instances where the optima are unknown. These results are further confirmed by conducting nonparametrical statistical tests.

Variable Neighborhood Search for Multi-Port Berth Allocation with Vessel Speed Optimization

This paper delves into the multi-port berth allocation problem (MBAP), enriching the traditional berth allocation problem (BAP) with vessel speed optimization (VSO). In the MBAP, it is assumed that there is cooperation between the port and the shipping companies, and the operation of the vessels and the ports is planned to maximize the overall benefits. Exploring this potential collaboration between ports and shipping entities has the potential to mitigate, or even resolve, the challenges plaguing maritime transportation, e.g., port congestion and suboptimal vessel schedules, to ultimately enhance the efficiency of maritime trade. In this paper, a new mixed-integer linear programming (MILP) model for the MBAP is formulated, which attempts to minimize the total cost incurred during operations, with various constraints such as vessel sailing, the vessel space–time relationship in ports, and the planning period. Meanwhile, an innovative variable neighborhood search (VNS) algorithm is presented, in which the initial solution generation method and neighborhood structures are proposed according to the MBAP characteristics. Furthermore, two sets of MBAP instances are generated to test the proposed MILP and VNS, of which the first set is based on real-world port data and the second on existing studies. The numerical experiments verify that the VNS can efficiently and reliably solve instances of all scales, with each neighborhood structure contributing uniquely to the iterative process. In addition, by analyzing the impact of varying oil prices on the MBAP, the study offers valuable management insights. Finally, a case study based on real data from a port group in the Yangtze River Basin is presented to further demonstrate the necessity of considering vessel service time window and planning period in the MBAP as well as the important role of the VSO in scheduling.

A multi-level capacitated arc routing problem with intermediate facilities in waste collection

This study investigates a multi-level capacitated arc routing problem for waste collection with two levels of intermediate facilities: huts and transfer stations. The problem aims to implement integrated optimisation of the intermediate facilities and find optimal routes for a fleet consisting of manually operated vehicles and vehicles with compressors. We first build an integer linear programming model to address this problem. Then, we propose an extended adaptive large neighbourhood search (E-ALNS) approach, including a tailored Shake procedure inspired by variable neighbourhood search to effectively solve this problem. Computational experiments were conducted on 264 instances generated using existing benchmarks. Compared to commercial optimisation software and other algorithms, our extended algorithm exhibits superior performance for this problem. The results also demonstrate that the integrated optimisation of intermediate facilities significantly decreases the total cost compared to separate optimisations.

A three-phase algorithm for the pollution traveling Salesman problem

This paper studies a variant of the Pollution Traveling Salesman Problem (PTSP) focused on fuel consumption and pollution emissions (PTSPC). The PTSPC generalizes the well-known Traveling Salesman Problem (TSP), classified as NP-Hard. In the PTSPC, a vehicle must deliver a load to each customer through a Hamiltonian cycle, minimizing an objective function that considers the speed of each edge, the mass of the truck, the mass of the load pending delivery, and the distance traveled. We have proposed a three-phase algorithm for the PTSPC. The first phase solves the Traveling Salesman Problem (TSP) exactly with a time limit and heuristically using a Nearest Neighborhood Search approach. This phase considers the constraints associated with the PTSPC by using commercial software. In the second phase, both the obtained solutions and their inverse sequences from the initial phase undergo enhancement utilizing metaheuristic algorithms tailored for the PTSPC. These algorithms include Variable Neighborhood Search (VNS), Tabu Search (TS), and Simulated Annealing (SA). Subsequently, for the third phase, the best solution identified in the second phase—determined by having the minimum value by the PTSPC objective function—is subjected to resolution by a mathematical model designed for the PTSPC, considering the heuristic emphasis of commercial software. The efficiency of the former algorithm has been validated through experimentation involving the adaptation of instances from the Pollution Routing Problem (PRP) to the PTSPC. This approach demonstrates the capacity to yield high-quality solutions within acceptable computing times.

Hybrid Artificial Bee Colony Algorithm with Variable Neighborhood Search for Capacitated Vehicle Routing Problem

Aiming at the capacitated vehicle routing problem, a hybrid integer programming model with goal of lowest path cost is constructed, and a hybrid artificial bee colony algorithm with variable neighborhood search based on the model and the characteristics of the CVRP problem is proposed to solve the problem. The hybrid algorithm integrates the artificial bee colony algorithm and the variable neighborhood search algorithm, embeds a multi-variable neighborhood operator in the local search link of the artificial bee colony to carry out iteration. And the operator contains targeted transformation operations on path nodes, strings, and sub paths to ensure the diversity of the bee population. In addition, a variable neighborhood perturbation strategy is used to strengthen the algorithm's ability to escape from local optima. The comparative analysis of the literature study set and its algorithm solution shows that the designed hybrid variable neighborhood artificial bee colony algorithm has strong global search ability and high solution accuracy, especially in solution stability. HABC-VNS can obtain 47 optimal solutions in 74 examples. The average minimum deviation of the optimal solution is 0.34%, and the average deviation of the average CVRP set is 0.57%. The overall performance is better than the algorithm in the comparative literature.

Solving multi-objective green flexible job shop scheduling problem by an improved chimp optimization algorithm

As environmental contamination becomes more and more severe, enterprises need to consider optimizing environmental criteria while optimizing production criteria. In this study, a multi-objective green flexible job shop scheduling problem (MO_GFJSP) is established with two objective functions: the makespan and the carbon emission. To effectively solve the MO_GFJSP, an improved chimp optimization algorithm (IChOA) is designed. The proposed IChOA has four main innovative aspects: 1) the fast non-dominated sorting (FDS) method is introduced to compare the individuals with multiple objectives and strengthen the solution accuracy. 2) a dynamic convergence factor (DCF) is introduced to strengthen the capabilities of exploration and exploitation. 3) the position weight (PW) is used in the individual position updating to enhance the search efficiency. 4) the variable neighborhood search (VNS) is developed to strengthen the capacity to escape the local optimum. By executing abundant experiments using 20 benchmark instances, it was demonstrated that the developed IChOA is efficient to solve the MO_GFJSP and effective for reducing carbon emission in the flexible job shop.

A Bibliometric Analysis of a Genetic Algorithm for Supply Chain Agility

As a famous population-based metaheuristic algorithm, a genetic algorithm can be used to overcome optimization complexities. A genetic algorithm adopts probabilistic transition rules and is suitable for parallelism, which makes this algorithm attractive in many areas, including the logistics and supply chain sector. To obtain a comprehensive understanding of the development in this area, this paper presents a bibliometric analysis on the application of a genetic algorithm in logistics and supply chains using data from 1991 to 2024 from the Web of Science database. The authors found a growing trend in the number of publications and citations over the years. This paper serves as an important reference to researchers by highlighting important research areas, such as multi-objective optimization, metaheuristics, sustainability issues in logistics, and machine learning integration. This bibliometric analysis also underlines the importance of Non-Dominated Sorting Genetic Algorithm II (NSGA-II), sustainability, machine learning, and variable neighborhood search in the application of a genetic algorithm in logistics and supply chains in the near future. The integration of a genetic algorithm with machine learning is also a potential research gap to be filled to overcome the limitations of genetic algorithms, such as the long computational time, difficulties in obtaining optimal solutions, and convergence issues for application in logistics and supply chains.

The pollution traveling salesman problem with refueling

This study presents the Pollution Traveling Salesman Problem with Refueling, a novel optimization problem which integrates two recently proposed variants of the Traveling Salesman Problem: the Pollution Traveling Salesman Problem and the Traveling Salesman Problem with Refueling. The proposed problem captures the operational dynamics of a real-world routing scenario involving a single vehicle originating from a central depot and delivering products to end customers. When considering the vehicle’s fuel tank capacity and fuel consumption during the routing process, the need to visit fuel stations for refueling arises. To address this complex problem, a new mixed integer linear programming model was developed, and the Gurobi solver was employed to solve smaller instances. For the effective resolution of larger practical problem cases, a two-stage double adaptive general variable neighborhood search method was proposed. The proposed methodology exhibits comparable efficiency to a commercial solver, demonstrating notably low execution time requirements. To further assess its performance, a comparative study was conducted on TSPLib instances. In comparison to various solution approaches documented in the open literature, encompassing both Variable Neighborhood Search-based and alternative methods, our proposed approach consistently yields highly competitive results within low execution times.

Iterated variable neighborhood search for integrated scheduling of additive manufacturing and multi-trip vehicle routing problem

This study addresses a novel problem structure for integrated scheduling of additive manufacturing and delivery processes. In the manufacturing process, we consider batch production of parts, simulating Selective Laser Melting technology in parallel additive manufacturing machines with heterogeneous specifications. A batch production, referred to as a build, must consist of parts with homogenous material. During the production run, sequence-dependent material setup times occur in between builds. In the delivery process, parts are delivered in batches using a limited number of homogenous capacitated vehicles. Each vehicle might perform multi-trips. Thus, the route for each trip and departure schedule among trips must be decided. In this regard, batch delivery is independent to batch production. The problem objective function is to minimize the total completion time of all parts. For optimally solving the problem, a mixed-integer linear programming model is devised. To solve larger problems sizes under a lower computation time, an iterated variable neighborhood search algorithm with embedded rule-based heuristics is proposed. The computational experiment denotes that the proposed algorithm with route minimization rule effectively solves small-scale problems, while capacity usage maximization rule performs the best in large-scale problems and outperforms other existing metaheuristics. Further result analysis is also performed to provide managerial insights.