General Variable Neighborhood Search Algorithm 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.

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.

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.

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.

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.

General variable neighborhood search for the parallel machine scheduling problem with two common servers

We address in this paper the parallel machine scheduling problem with a shared loading server and a shared unloading server. Each job has to be loaded by the loading server before being processed on one of the available machines and unloaded immediately by the unloading server after its processing. The objective function involves the minimization of the overall completion time, known as the makespan. This important problem raises in flexible manufacturing systems, automated material handling, healthcare, and many other industrial fields, and has been little studied up to now. To date, research on it has focused on the case of two machines. The regular case of this problem is considered. A mixed integer programming formulation based on completion time variables is suggested to solve small-sized instances of the problem. Due to its mathcal{NP}mathcal{}-hardness, we propose two greedy heuristics based on the minimization of the loading, respectively unloading, server waiting time, and an efficient General Variable Neighborhood Search (GVNS) algorithm. In the computational experiments, the proposed methods are compared using 120 new and publicly available instances. It turns out that, the proposed GVNS with an initial solution-finding mechanism based on the unloading server waiting time minimization significantly outperforms the other approaches.

A Double-Adaptive General Variable Neighborhood Search algorithm for the solution of the Traveling Salesman Problem

This work addresses a novel General Variable Neighborhood Search (GVNS) solution method, which integrates intelligent adaptive mechanisms to re-order the search operators during the intensification and diversification phases, in an effort to enhance its overall efficiency. To evaluate the performance of the new GVNS scheme, asymmetric and symmetric instances of the classic Traveling Salesman Problem (TSP) from the TSPLib were solved. The obtained results of the Double-Adaptive GVNS were compared with those achieved by two single-adaptive GVNS, which use an adaptive mechanism either for the intensification or the diversification phase and with a conventional GVNS. For a fair comparison, all GVNS schemes were structured using the same local search and shaking operators. Moreover, the novel GVNS algorithm was compared with some recent solution methods for the TSP, found in the open literature. The comparative studies revealed the high efficiency of the novel VNS scheme and underlined the significant impact of intelligent mechanisms on the performance of classic metaheuristic frameworks.

Optimisation of the electric truck route for milk collection problem: a real case study

ABSTRACT This study dwells upon the electric milk collection problem. The problem extends electric vehicle routing problem with time windows, considering multi-depot, multi-product, split deliveries, multi-compartment, fast chargers and fleet composition. The problem aims to create an effective routing decision-making system for electric trucks in transporting milk of different quality from producers (or milk collection points) in different locations to the factories. The objective of the electric milk collection problem is to minimize the sum of the total energy costs of electric trucks. We develop an adaptive general variable neighborhood search algorithm that involves several procedures having been tailored to handle specific features of the problem. We perform extensive computational experiments on real-life data to investigate the performance of the heuristics and offer particular insight. The results indicate that our algorithm successfully solves small- and large-scale instances in terms of solution quality and computational time. Our results also quantify the benefits of using fast charger types and fleet composition on the total energy costs.

A general variable neighborhood search algorithm for a parallel-machine scheduling problem considering machine health conditions and preventive maintenance

In this paper, a parallel-machine scheduling problem considering machine health conditions and preventive maintenance is studied with the objective to minimize total tardiness and quality risk. The problem stems from semiconductor manufacturing where machines can be identified with different health conditions by Advanced Process Control (APC) tools. We develop two mixed integer linear programming models to formulate the problem. A general variable neighborhood search heuristic is proposed in which an efficient branch-and-bound algorithm is embedded as one of the search operators. The algorithm is compared with a classic tabu search heuristic that was proved to be very efficient in parallel-machine scheduling. Computational experiments show that the proposed algorithm outperforms the tabu search heuristic by averagely 2.20% in terms of the solution quality. Managerial insights are also derived that considering health information allows us to achieve a good balance between quality risk and delivery requirement.

ALGORITMA GENERAL VARIABLE NEIGHBORHOOD SEARCH PADA CAPACITATED VEHICLE ROUTING PROBLEM WITH TIME WINDOWS DAN IMPLEMENTASINYA

The Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) is one of the variants of the Vehicle Routing Problem (VRP), which is the problem of determining the optimal route from the depot to the consumer which is located spread out with different requests. In CVRPTW problem solving considers capacity and time constraints. Determining the optimal route can reduce costs and energy spent during the distribution process. The General Variable Neighborhood Search (GVNS) algorithm can be applied to the CVRPTW problem. The GVNS algorithm is an improvement on the VNS algorithm using RVND. The GVNS algorithm starts with finding the initial solution, continues with perturbation, and then the repair procedure is carried out. Perturbation and improvements to the GVNS algorithm are performed repeatedly according to the predetermined IterMax. The GVNS algorithm for CVRPTW will be implemented using the Borland Delphi 7.0 programming language. The product in the form of this application can be used more practically to solve CVRPTW problems using the GVNS algorithm. Keywords: Capacitated Vehicle Routing Problem with Time Windows (CVRPTW), General Variable Neighborhood Search (GVNS) Algorithm, Randomized Variable Neighborhood Descent (RVND)

STUDI ALGORITMA IGVNS, ALGORITMA GVNS, DAN ALGORITMA ABC PADA MULTIPLE TRIP VEHICLE ROUTING PROBLEM (MTVRP)

The Multiple Trip Vehicle Routing Problem (MTVRP) is one of the VRP variants with vehicle capacity constraints, and the limited number of vehicles allows each vehicle to distribute more than one route so as to minimize the number of vehicles used. The algorithm used in this study is the Improved General Variable Neighborhood Search (IGVNS) algorithm. The IGVNS algorithm is a hybrid between the GVNS algorithm and the VNS algorithm. The calculation results of the IGVNS algorithm will be compared with the GVNS algorithm and the ABC algorithm. The main stages of the IGVNS and GVNS algorithms are initial solution formation, perturbation, and solution improvement. The main stages of the ABC algorithm are initialization, solution improvement and optimization. Based on manual calculations using 8 points, the ABC algorithm produces a distance of 86 km and a service time of 1.47 hours, the GVNS algorithm produces a distance of 80 km and a service time of 1.37 hours, the IGVNS algorithm produces a distance of 79 km and service time is 1.35 hours. Based on one example of the ABC algorithm, the calculation solution using the IGVNS algorithm shows more optimal results. Based on the results of parameter testing, the v max parameter affects the calculation results, that is the greater the v max value, the more optimal the resulting solution. While the a max parameter does not affect the calculation results because it shows constant results in two successive iterations carried out.

Backtracking Algorithms for Constructing the Hamiltonian Decomposition of a 4-regular Multigraph

We consider a Hamiltonian decomposition problem of partitioning a regular graph into edge-disjoint Hamiltonian cycles. It is known that verifying vertex non-adjacency in the 1-skeleton of the symmetric and asymmetric traveling salesperson polytopes is an NP-complete problem. On the other hand, a suffcient condition for two vertices to be non-adjacent can be formulated as a combinatorial problem of finding a Hamiltonian decomposition of a 4-regular multigraph. We present two backtracking algorithms for verifying vertex non-adjacency in the 1-skeleton of the traveling salesperson polytope and constructing a Hamiltonian decomposition: an algorithm based on a simple path extension and an algorithm based on the chain edge fixing procedure. Based on the results of the computational experiments for undirected multigraphs, both backtracking algorithms lost to the known heuristic general variable neighborhood search algorithm. However, for directed multigraphs, the algorithm based on chain fixing of edges showed comparable results with heuristics on instances with existing solutions, and better results on instances of the problem where the Hamiltonian decomposition does not exist.

A modified optimization method for optimal control problems of continuous stirred tank reactor

‎Continuous stirred tank reactor (CSTR) is an important and constructive part in various chemical and process industries and therefore it is necessary to control the process in optimal temperature and concentration conditions. Because of the nonlinear nature and limits of the control input‎, ‎solving this problem is very difficult. To achieve a sub-optimal control policy for chemical processes‎, ‎we focused on a new construction model‎. Then‎, ‎a two-phase algorithm‎, ‎denoted as modified sequential general variable neighborhood search (MSGVNS) algorithm based on three local searches that use efficient neighborhood interchange has been employed to solve CSTR problems numerically. The results of the proposed method show that its convergence to the exact solution is achieved by the accuracy comparable to other numerical algorithms in few times‎.

Optimizing a Disassembly Sequence Planning With Success Rates of Disassembly Operations via a Variable Neighborhood Search Algorithm

Disassembly planning is an effective way to recycle valuable parts or materials from end-of-life products. Due to the parts are easily affected by some unpredictable factors in the real disassembly process (such as defective parts and human factors), there may be failure operations that cannot successfully disassemble the corresponding parts in the real world. Therefore, a partial disassembly sequence planning with uncertainty is proposed in the paper, where the success rates of disassembly operations are formulated to model an expected profit-based disassembly sequence planning. Also, a general variable neighborhood search algorithm is developed to optimize the mathematical model. Meanwhile, in the approach, a heuristic procedure is utilized to obtain a high-quality initial solution, and four different neighborhood structures are introduced to improve the disassembly solution. Its superiority and effectiveness are well illustrated by two case studies and comparison with two existing metaheuristics, i.e., artificial bee colony algorithm and genetic algorithm.

A General Variable Neighborhood Search approach based on a p-median model for cellular manufacturing problems

One of the practical application in cellular manufacturing systems is the cell formation problem (CFP). Its main idea is to group machines into cells and parts into part families in a way that the number of exceptional elements and the number of voids are minimized. In literature, it is proved that p-median is an efficient mathematical programming model for solving CF problems. In the present work, we develop a modified p-median based model dedicated to solve CFP respecting the objective of minimizing the sum of dissimilarities of machines. For this aim, we applied a General Variable Neighborhood Search algorithm and we collaborated it with an Estimation of Distribution Algorithm maximizing the group capability index and the grouping efficacy evaluation criteria. Thirty CF problems are taken from the literature and tested by our proposed algorithm and the experimental study demonstrated that the proposed method guided by p-median model provides high quality cells in speed running times and beats other state-of-the-art algorithms particularly for CF instances with large sizes.

Hamiltonian decomposition and verifying vertex adjacency in 1-skeleton of the traveling salesperson polytope by variable neighborhood search

We consider a Hamiltonian decomposition problem of partitioning a regular graph into edge-disjoint Hamiltonian cycles. A sufficient condition for vertex adjacency in the 1-skeleton of the traveling salesperson polytope can be formulated as the Hamiltonian decomposition problem in a 4-regular multigraph. We introduce a heuristic general variable neighborhood search algorithm for this problem based on finding a vertex-disjoint cycle cover of the multigraph through reduction to perfect matching and several cycle merging operations. The algorithm has a one-sided error: the answer "not adjacent" is always correct, and was tested on random directed and undirected Hamiltonian cycles and on pyramidal tours.

On solving the order processing in picking workstations

The Order Processing in Picking Workstations is a real problem derived from the industry in the context of supply chain management. It looks for an efficient way to process orders arriving to a warehouse by minimizing the number of movements of goods, stored in containers in the warehouse, from their storage location to the processing zone. In this paper, we tackle this real optimization problem by providing a new Integer Linear Programming (ILP) formulation for the problem. Due to the $$\mathcal {NP}$$ -Hardness of the problem we have also designed several heuristic procedures, to find high-quality solutions in a reasonable amount of time, which is mandatory for handling real instances. Particularly, the heuristics proposed were combined into a General Variable Neighborhood Search algorithm. Finally, we have performed an extensive experimentation indicating an increased performance of our proposals (ILP and heuristic) over previous approaches in the state of the art, using both synthetic and real datasets of instances.

An improved general variable neighborhood search for a static bike-sharing rebalancing problem considering the depot inventory

Smart shared mobility is an emerging transportation strategy that promotes sustainable and intelligent transportation. As one mode of smart shared mobility bike sharing is gaining popularity in recent years. A daily rebalancing operation is commonly carried out to keep high level service of bike-sharing systems (BSSs). The static bike-sharing rebalancing problems (SBRPs) studied in existing papers focus on determining the vehicle routes with minimal traveling cost. However, the depot inventory is rarely considered during the relocation. Thus, this paper researches the integration of the depot inventory and vehicle routing problems, with the aim of minimizing the daily operational cost including the depot inventory cost (DIC) and the traveling cost. First, two mixed integer programming (MIP) formulations are proposed to find the daily optimal decision on the vehicle routes and the numbers of bikes and vehicles employed from the depot. Based on the models, an improved general variable neighborhood search (IGVNS) algorithm is developed with a variety of neighborhood structures and a hybrid strategy. Finally, we apply a set of benchmark instances to test our proposed model and approach, and the computational results demonstrate that IGVNS can efficiently compute the SBRP and achieve lower operational cost than the existing solutions.

Two multi-start heuristics for the k-traveling salesman problem

This paper is concerned with the k-traveling salesman problem (k-TSP), which is a variation of widely studied traveling salesman problem (TSP). Given a set of n cities including a home city and a fixed value k such that $$1 < k \le n$$ , this problem seeks a tour of minimum length which starts and ends at the home city and visits k cities (including the home city) exactly out of these n cities. Finding a feasible solution to k-TSP involves finding a subset of k cities including the home city first, and then a circular permutation representing a tour of these k cities. In this paper, we have proposed two multi-start heuristic approaches for the k-TSP. The first approach is based on general variable neighborhood search algorithm (GVNS), whereas the latter approach is a hyper-heuristic (HH) approach. A variable neighborhood descent strategy operating over two neighborhood structures is utilized for doing the local search in the GVNS. As part of the hyper-heuristic, two low level heuristics are considered. To the best of our knowledge, these are the first metaheuristic and hyper-heuristic approaches for the k-TSP. To evaluate the performance of our approaches, a set of benchmark instances is created utilizing instances from TSPLIB. Computational results on these benchmark instances show HH approach to be better than GVNS approach.