General Variable Neighborhood Search Research Articles

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.

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 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.

General VNS for asymmetric vehicle routing problem with time and capacity constraints

We consider a real-life transportation problem from a hypermarket company in Serbia that consists of delivering online ordered and possibly perishable goods from a single depot to multiple customers. It can be modeled as an asymmetric vehicle routing problem that requires visiting and serving all customers using a limited number of homogeneous vehicles and taking into account time and capacity constraints. The objective function to be minimized is the total distance traveled. We provide a mixed-integer programming (MIP) formulation of the problem and develop several Local Search based metaheuristic methods exploring combinatorial formulation of the considered problem: Multistart Local Search (MLS), Greedy Randomized Adaptive Search Procedure (GRASP), and several variants of General Variable Neighborhood Search (GVNS) methods. All methods are compared on real-life instances provided by the hypermarket company and benchmark instances from the relevant literature. The obtained results show the superiority of GVNS-based methods with respect to both solution quality and running time, confirming that systematic search procedures have more success when dealing with hard optimization problems.

A variable neighborhood search approach for solving a real-world hierarchical multi-echelon vehicle routing problem involving HCT vehicles

This paper studies the Hierarchical Multi-Switch Multi-Echelon VRP (HMSME-VRP), a newly introduced VRP variant based on a real-world case involving High Capacity Vehicles (HCV). The problem originates from the policies of a distribution company in the Nordic countries where HCVs of up to 34.5 m and up to 76 tons are allowed. The HMSME-VRP offer a new way to model distribution problems to cover large geographical areas without substantial costs in infrastructure. Furthermore, it adds complexity to the standard VRP and, as such, remains NP-hard and difficult to solve to optimality. Indeed, it has been demonstrated that only very small instances can be solved to optimality by a commercial solver. Thus, in order to handle instances of real-world size, we propose two General Variable Neighborhood Search (GVNS) procedures, the second of which is adaptive, utilizing an intelligent reordering mechanism. In order to evaluate the proposed procedures, 48 benchmark instances of various sizes and characteristics are generated and made publicly available, comprising of clustered, random, and semi-clustered customers. The computational results show that both GVNS procedures outperform the exact solver. Additionally, the adaptive version outperforms the conventional version based on both average and best solutions. Furthermore, we present a statistical analysis to verify the superiority of the adaptive version.

General Variable Neighborhood Search for the optimization of software quality

In the area of Search-Based Software Engineering, software engineering issues are formulated and tackled as optimization problems. Among the problems within this area, the Software Module Clustering Problem (SMCP) consists of finding an organization of a software project that minimizes coupling and maximizes cohesion. Since modular code is easier to understand, the objective of this problem is to increase the quality of software projects, thus increasing their maintainability and reducing the associated costs. In this work we study a recently proposed objective function named Function of Complexity Balance (FCB). Since this problem has been demonstrated to be NP-hard, we propose a new heuristic algorithm based on the General Variable Neighborhood Search (GVNS) schema to tackle the problem. For the GVNS, we propose six different neighborhood structures and categorize them into three different groups. Then, we analyze their contribution to the results obtained by the algorithm. In order to improve the efficiency of the proposed approach, we leverage domain-specific information to perform incremental evaluations of the objective function and to explore only areas of interest in the search space. The proposed algorithm has been tested over a set of real world software repositories, achieving better results than the previous state-of-the-art method, a Hybrid Genetic Algorithm, in terms of both quality and computing times. Furthermore, the relevance of the improvement produced by our proposal has been corroborated by non-parametric statistical tests.

A general variable neighborhood search for the traveling salesman problem with time windows under various objectives

The traveling salesman problem with time windows (TSPTW) has wide practical applications in transportation and scheduling operations. We study the TSPTW in the deterministic case as well as under travel time uncertainty. We consider the three classical TSPTW variants with the objectives of minimizing cost, completion time, and tour duration. In addition, a new TSPTW variant that maximizes the minimum slack of a tour, i.e., the smallest time buffer between the arrival time and the end of the time window over all nodes visited on the tour, is introduced. We further address a variant of the TSPTW in which the arc travel times are uncertain. This problem is modeled by means of an uncertainty set, and the goal is to determine a tour that remains feasible in the worst case within a budget stipulating the sum of all travel time deviations from their nominal values. To solve all targeted problem variants, we develop a two-phase general variable neighborhood search (GVNS) that applies an efficient move evaluation approach within the local search. Extensive numerical experiments on benchmark instances from the literature show that our GVNS finds high-quality solutions that are competitive with those obtained by the state-of-the-art heuristics for all problem variants.

Self-adaptive General Variable Neighborhood Search algorithm for parallel machine scheduling with unrelated servers

This paper introduces a machine learning-augmented General Variable Neighborhood Search algorithm, termed Self-adaptive General Variable Neighborhood Search (SGVNS), for solving the two-identical parallel machine scheduling problem with unrelated servers. The studied problem is of high practical relevance in various industries and presents a significant gap in the existing literature. The motivation for this study stems from the healthcare industry, specifically surgery scheduling with limited anesthesiologists’ availability. Two mathematical formulations are presented to solve this scheduling problem. However, these formulations are limited to small-scale problems, prompting the need for an efficient metaheuristic. Therefore, a novel variant of the General Variable Neighborhood Search metaheuristic is developed, incorporating a self-adaption mechanism based on an Extreme Learning Machine (ELM) algorithm. Extensive experiments are conducted to assess the performance of the SGVNS metaheuristic on various classes of instances. The results demonstrate the effectiveness and efficiency of SGVNS in solving previously unsolved small-sized instances, outperforming both formulations while maintaining reasonable computation times.

Hybrid Variable Neighborhood Search for Solving School Bus-Driver Problem with Resource Constraints

The School Bus-Driver Problem with Resource Constraints (SBDP-RC) is an optimization problem with many practical applications. In the problem, the number of vehicles is prepared to pick a number of pupils, in which the total resource of all vehicles is less than a predefined value. The aim is to find a tour minimizing the sum of pupils’ waiting times. The problem is NP-hard in the general case. In many cases, reaching a feasible solution becomes an NP-hard problem. To solve the large-sized problem, a metaheuristic approach is a suitable approach. The first phase creates an initial solution by the construction heuristic based on Insertion Heuristic. After that, the post phase improves the solution by the General Variable Neighborhood Search (GVNS) with Random Neighborhood Search combined with Shaking Technique. The hybridization ensures the balance between exploitation and exploration. Therefore, the proposed algorithm can escape from local optimal solutions. The proposed metaheuristic algorithm is tested on a benchmark to show the efficiency of the algorithm. The results show that the algorithm receives good feasible solutions fast. Additionally, in many cases, better solutions can be found in comparison with the previous metaheuristic algorithms.

The drone-assisted vehicle routing problem with robot stations

Following the widespread interest of both the scientific community and companies in using autonomous vehicles to perform deliveries, we propose the ‘Drone-Assisted Vehicle Routing Problem with Robot Stations’ (VRPD-RS), a problem that combines two concepts studied in the autonomous vehicles literature: truck-drone tandems and robot stations. We model the VRPD-RS as a mixed-integer linear program (MILP) for two different objectives, the makespan and operational costs, and analyze the impact of adding trucks, drones, and robots to the delivery fleet. Given the computational complexity of the problem, we propose a General Variable Neighborhood Search (GVNS) metaheuristic to solve more realistic instances within reasonable computational times. Results show that, for small instances of 10 customers, where the solver obtains optimal solutions for almost all cases, the GVNS presents solutions with gaps of 0.7% to the solver for the makespan objective and gaps of 0.0% for the operational costs variant. For instances of up to 50 customers, the GVNS presents improvements of 21.5% for the makespan objective and 8.0% for the operational costs variant. Furthermore, we compare the GVNS with a Simulated Annealing (SA) metaheuristic, showing that the GVNS outperforms the SA for the whole set of instances and in more efficient computational times. Accordingly, the results highlight that including an additional drone in a truck-drone tandem increases delivery speed alongside a reduction in operational costs. Moreover, robot stations proved to be a useful delivery element as they were activated in almost every studied scenario.

A double-adaptive general variable neighborhood search for an unmanned electric vehicle routing and scheduling problem in green manufacturing systems

In recent years, more and more manufacturing factories have employed unmanned electric vehicles (UEVs) to perform the materials delivery, and efficient routing and scheduling approaches are required to improve the delivery efficiency. However, most of existing papers studied the routing problem of fuel vehicles or the drones. This paper investigates the optimization of UEVs delivery routes and charging strategies. Due to the limited payload capacity and battery capacity, the UEV must return to the depot multiple times to load the materials and go to the recharging station during the route to charge, and thus the problem is modeled as a multi-trip UEV routing and scheduling problem, which assigns the recharging station to the UEV’s route and optimizes a set of UEV’s trips. The investigated problem is firstly formulated as a mixed integer programming model. Then, considering the routing and scheduling challenges, we develop an efficient double-adaptive variable neighborhood search (DA-GVNS), which incorporates the general variable neighborhood search with a new adaptive mechanism, for this problem. The experimental results on the test and benchmark instances highlight that the DA-GVNS outperforms other existing algorithms. Furthermore, sensitivity analyses are conducted to study the impact of model’s characteristics on the optimality and complexity of solutions. Finally, a case study is proposed to present how the developed approach works for a manufacturing factory. This paper can offer decision-makers a valuable approach to construct a high-quality routing and scheduling scheme for the UEV delivery while providing potential managerial insights for implementing efficient green manufacturing systems.

Variable Neighborhood Search for precedence-constrained tasks optimization on heterogeneous systems

Supercomputing power is one of the fundamental pillars of the digital society, which depends on the accurate scheduling of parallel applications in High-Performance Computing (HPC) centers to minimize computing times. However, precedence-constraint task scheduling is a well-known NP-Hard optimization problem, and no optimal polynomial-time algorithm exists to solve it. Therefore, as accurate as possible to the optimal values, heuristic algorithms are of relevant interest. Our new scheduling proposal name is EFT-GVNS, which stands for Earliest Finish Time - General Variable Neighborhood Search. EFT-GVNS uses a Composite Local Search (CLS), making our proposal more efficient than traditional GVNS. EFT-GVNS accuracy against four high-performance algorithms from the state-of-the-art (EDA, EFT-ILS, GRASP-CPA, MPQGA) and one reference algorithm in the literature (HEFT) is studied. Experimental results over four real-world applications (Fpppp, LIGO, Robot, Sparse) and 14 synthetic instances from the literature show that EFT-GVNS outperforms in terms of the median achieved results, with a global improvement of 37.6%, 27.4%, 17.8%, 6.1%, 2.2% to HEFT, EDA, EFT-ILS, GRASP-CPA, and MPQGA, respectively. EFT-GVNS achieves all the 14 optimal values of the synthetic benchmark.

Multiple traveling salesperson problem with drones: General variable neighborhood search approach

A key factor to consider in the development of new technologies in a number of fields is the use of unmanned aerial vehicles. This rapidly developing technology is used in military, communication, health, mapping, agriculture and transportation fields. The importance of cargo transportation has grown due to the growth of e-commerce. Currently, with advancing technology, and the effect of the pandemic, purchases are increasingly made over the internet. For cargo transporters, this situation leads to an increase in the number of destination points, in distances traveled, and in the delivery frequency, and a decrease in the package sizes. As a result, the planning of transportation has become increasingly complex. One solution is to make greater use of unmanned aerial vehicles in this sector, and to reduce reliance on trucks through appropriate planning. This involves two aspects: the unmanned aerial vehicle delivering to a point, while the cargo truck delivers to a separate point. In this study, we consider a multiple traveling salesperson problem simultaneously using multiple trucks and unmanned aerial vehicles for package delivery. We develop a general variable neighborhood search algorithm, and compare the results with the existing studies in the literature. Computational experiments show that our approach is able to find highly satisfactory solutions in reasonable time, and outperforms the existing methods in terms of best solution, average solution and solution time in majority of the instances.

Scheduling multi-staged jobs on parallel identical machines and a central server with sequence-dependent setup times: An application to an automated kitchen

We address the problem of scheduling multi-staged jobs in a production environment with parallel identical machines and a central server with sequence-dependent setup times motivated by a real-life application in a robotic automated kitchen. The proposed model addresses a makespan minimization offline optimization problem that arises in the context of mise-en-place preparation. We present two mathematical formulations, one with a machine index and one without, as well as lower bounds. We also propose an effective general variable neighborhood search algorithm based on heuristics which aims to improve the incumbent by eliminating idle times. Through a series of experiments on random instances, we demonstrate the effectiveness of the proposed method under various combinations of instance parameters. On instances with known optimal solutions, the metaheuristic produces solutions with an average gap of 0.31% in very short computation times. On large-size instances, the metaheuristic produces solutions with an average gap of 6.04% when measured against a known lower bound. We also present a real-life case study provided by our industrial partner and we investigate how to maximise the output of the studied automated production system.

Multi-objective energy-efficient hybrid flow shop scheduling using Q-learning and GVNS driven NSGA-II

The urgent mission for carbon peak and carbon neutrality is demanding greater industrial sustainability. Energy-efficient hybrid flow shop scheduling problem (EEHFSP) has been raising increasing attention in recent years. This paper studies a new EEHFSP with uniform machines to minimize total tardiness, total energy cost, and carbon trading cost. Time-of-use tariffs and power down strategies are simultaneously adopted. A novel multi-objective mixed-integer nonlinear programming model for the problem is proposed. To solve the model, we propose a Q-learning and general variable neighborhood search (GVNS) driven non-dominated sorting genetic algorithm II (QVNS-NSGA-II). The novelty of the algorithm is that we incorporate Q-learning into GVNS to guide premium adaptive operator selection throughout the shaking and local search processes. A distinguishing feature is that the states and actions of Q-learning are set as neighborhood structures and local search operators. The Q-learning-driven GVNS is embedded into NSGA-II to promote the exploration and exploitation capability. Experimental results show that the proposed QVNS-NSGA-II outperforms NSGA-II, improved Jaya, and modified MOEA/D in terms of the quantity, quality of Pareto solutions, and computational efficiency. Sensitivity analysis also derives several managerial implications. The proposed approach can be applied to improve sustainability and productivity for hybrid flow shop manufacturers.

A GVNS algorithm applied to the single allocation hub location problem with heterogeneous economies of scale

This paper addresses the single allocation hub location problem with heterogeneous economies of scale. This problem consists of selecting the nodes to establish the hubs in order to minimize the total cost of installing the hubs and routing demand flows, assuming that there is an economy of scale that depends on the amount of flow routed in each arc. We proposed a formulation to model the problem and an algorithm based on the General Variable Neighborhood Search (GVNS) meta-heuristic to handle the problem. Computational experiments were performed using instances from the literature with up to 500 nodes. The results show that the GVNS algorithm is effective for solving the instances in terms of runtime and solution quality. The results also show that the proposed formulation outperforms the literature formulation when activating the Benders decomposition method available in the CPLEX solver.

Machine learning augmented approaches for hub location problems

Hub location problems are widely analyzed in fields of logistic and transportation industry for cost reduction. In this paper, a novel algorithm framework based on machine learning is proposed to improve solution quality of hub location problems for large-scale instances. First, a deep-learning based probabilistic hub-ranker (DLHr) is developed to determine the priority of nodes to be selected as hubs. Next, two node-ranking based approaches DL-CBS and DL-GVNS are developed to augment the DLHr for single allocation hub location problems. DL-CBS is an augment algorithm embedding DLHr-ranking into clustering-based potential hub sets algorithm (CBS) while DL-GVNS embeds DLHr-ranking into general variable neighborhood search (GVNS). The numerical results evidence that DLHr outperforms baselines on the node-ranking task and helps to identify potential hubs. Evaluation on a wide range of experiments shows that DL-CBS and DL-GVNS improve solution quality of single allocation hub location problems compared with vanilla CBS and GVNS, revealing DLHr ranking helps to boost the performance of traditional heuristics.

Coordinated production and delivery scheduling for service-oriented manufacturing systems with deterioration effect

Service-oriented manufacturing (SOM) is a new industrial model that combines manufacturing with service. To enhance the competitiveness of manufacturers in SOM systems, we investigate a coordinated production and delivery scheduling problem considering a third-party logistics (3PL) provider. The considered problem can be divided into two phases, including production phase and delivery phase. In the production phase, jobs are processed by multiple manufacturers located in different geographical zones. Jobs are with deteriorating processing time and set-up time. Several structural properties of the problem in the production phase are proposed, based on which a heuristic algorithm is designed to make decisions on job batching and batch sequencing. After being processed, the finished jobs are immediately delivered to a customer by manufacturers’ own vehicles or the 3PL provider. A dynamic programming algorithm is developed to solve the problem in the delivery phase. The integrated scheduling problem is proved to be NP-hard. Hence, we develop a general variable neighbourhood search (GVNS) to solve the problem in a reasonable time. The basic variable neighbourhood descent (BVND) is used as a local search method in the GVNS. Finally, the computational experiments are conducted and the results verify the effectiveness and stability of the proposed approach.

Optimal distribution of perishable foods with storage temperature control and quality requirements: An integrated vehicle routing problem

The quality of food products deteriorates continuously over time at a speed depending on the storage temperature. Therefore, they must be stored at low temperatures to prolong their shelf life, which increases storage costs significantly. In this paper, we study a distribution problem in which a temperature-controlled warehouse is responsible for supplying a perishable food product, using a homogenous fleet of capacitated vehicles, to multiple customers with minimum quality requirements and delivery time windows. The objective is to minimize the sum of the energy cost at the warehouse and the transportation cost to deliver the customer demand. Decisions include the storage temperature at the warehouse and delivery routes. The distribution problem is formulated as a Mixed-Integer Linear Programming (MILP) model. After presenting an analytical study of the problem, a heuristic based on General Variable Neighborhood Search (GVNS) is designed to solve the large-size problem instances. Using the case of a dairy product, the model is solved under various scenarios. It is observed that the distribution and temperature decisions are dependent. Moreover, the optimal distribution plan and storage temperature are significantly impacted by changes in factors related to food quality, such as truck and environmental temperatures and energy price.

Minimizing total weighted latency in home healthcare routing and scheduling with patient prioritization.

We study a home healthcare routing and scheduling problem, where multiple healthcare service provider teams should visit a given set of patients at their homes. The problem involves assigning each patient to a team and generating the routes of the teams such that each patient is visited once. When patients are prioritized according to the severity of their condition or their service urgency, the problem minimizes the total weighted waiting time of the patients, where the weights represent the triage levels. In this form, the problem generalizes the multiple traveling repairman problem. To obtain optimal solutions for small to moderate-size instances, we propose a level-based integer programming (IP) model on a transformed input network. To solve larger instances, we develop a metaheuristic algorithm that relies on a customized saving procedure and a general variable neighborhood search algorithm. We evaluate the IP model and the metaheuristic on various small-, medium- and large-sized instances coming from the vehicle routing literature. While the IP model finds the optimal solutions to all the small- and medium-sized instances within three hours of run time, the metaheuristic algorithm achieves the optimal solutions to all instances within merely a few seconds. We also provide a case study involving Covid-19 patients in a district of Istanbul and derive insights for the planners by means of several analyses.