Variable Neighborhood Search Algorithm Research Articles

Heuristics for Multi-Vehicle Routing Problem Considering Human-Robot Interactions

Autonomous mobile robots (AMRs) are being used extensively in civilian and military applications for applications such as underground mining, nuclear plant operations, planetary exploration, intelligence, surveillance and reconnaissance (ISR) missions and manned-unmanned teaming. We consider a multi-objective, multiple-vehicle routing problem in which teams of manned ground vehicles (MGVs) and AMRs are deployed respectively in a leader-follower framework to execute missions with differing requirements for MGVs and AMRs while considering human-robot interactions (HRI). HRI studies highlight the costs of managing a team of follower AMRs by a leader MGV. This paper aims to compute feasible visit sequences, replenishments, team compositions and number of MGV-AMR teams deployed such that the requirements for MGVs and AMRs for the missions are met and the routing, replenishment, HRI and team deployment costs are at minimum. The problem is first modeled as a a mixed-integer linear program (MILP) that can be solved to optimality by off-the-shelf commercial solvers for small-sized instances. For larger instances, a variable neighborhood search algorithm is offered to compute near optimal solutions and address the challenges that arise when solving the combinatorial multi-objective routing optimization problem. Finally, computational experiments that corroborate the effectiveness of the proposed algorithms are presented.

Joint scheduling of barges and tugboats for river–sea intermodal transport

In this paper, we study a barge and tugboat joint scheduling problem arising from a river–sea intermodal transport system, where non-self-propelled barges travel with the help of tugboats between an inland river bulk port and sea transshipment platforms to transport cargo. Due to limited channels and the sequential scheduling among ships, transit inefficiency and resource under-utilization often occur, thus it is essential to design barge timetables and tugboat paths. This paper jointly schedules barges and tugboats in a river–sea transshipment port with a tidally influenced channel, and focuses on barge round trips with multiple legs. We construct a state-space–time network from the perspective of tugboats, in which the state implies whether a barge is served by a tugboat. The problem is formulated as an integer programming model based on the network to minimize time taken for bulk cargo transshipment. A tailored variable neighborhood search algorithm is designed and its efficiency, effectiveness, and stability are demonstrated by numerical experiments, which are based on real data from the Boffa port. It is demonstrated that, by joint scheduling barges and tugboats, transfer efficiency can be significantly improved under limited tugboat resources and shorter tidal windows. The results also provide managerial insights on schedule and valuable conclusions about the resource allocation in the port.

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.

Combining variable neighborhood with gradient ascent for learning to rank problem

Metaheuristic applications for information retrieval research are limited in spite of the importance of this problem domain. Ranking the retrieved documents based on their importance is a vital issue for the scientific and industrial communities. This paper proposes a novel variable neighborhood search (VNS) algorithm with adaptation based on an objective function for the learning to rank (LTR) problem. VNS is a global optimum metaheuristic algorithm that has been engaged to evolve the optimal solutions for heuristic problems based on exploring better neighbor solutions from the current one. The changes from the current to the next optimal solution are made during the perturbation stage to identify the global optimal solutions. The exploration procedure has been made through various mutation step sizes, whereas the exploitation process has been done by checking the quality of the evolved solutions using the fitness function. This research proposes a novel version of VNS based on four random probability distributions with gradient ascent. In addition to using the traditional random generator with gradient ascent for modifying the mutated genes of the neighborhood candidate solution in the following evolving iteration. This novel method in LTR is called gradient variable neighborhood (GVN). In the experiments, we utilized Microsoft Bing search (MSLR-WEB30K), Yahoo, and TREC Million Queries Competitions in 2008 and 2007 (LETOR 4) datasets. From the findings of the results, we can deduce that the GVN method outperformed recent studies on LTR methods.

Dual-Sourcing Inventory Routing Problem with Route-Dependent Lead Times in Rolling Horizon Framework

Traditional inventory routing problems ignore the time consumption in transportation. In this paper, an inventory routing problem with air–land transportation and route-dependent lead times is studied. The model is based on the rolling horizon framework which can serve as a “here-and-now” approximation for multi-period inventory routing problems. A planning horizon crossing strategy is proposed to consider the effect of the single-period decision on long-term planning. The box uncertainty set is used to depict demands. A tractable closed-form robust solution for optimal replenishment quantity is derived. An adaptive variable neighborhood search algorithm is developed for this problem. A novel shaking phase is proposed, and the performance of shaking operators is evaluated in numerical experiments. Results also validate the effectiveness of the robust solution and the planning horizon crossing strategy.

Unrelated Parallel Machine Photolithography Scheduling Problem With Dual Resource Constraints

This paper studies an unrelated parallel machine photolithography scheduling problem with dual resource constraints (DRC). This is an emerging problem in the semiconductor industry, where the masks can be transferred from one working station to another, increasing the flexibility of production through sharing the auxiliary resource. It gives rise to a complex DRC scheduling problem involving jobs, machines, and masks, restricted by sequence-dependent setup time and station-dependent mask transfer time. This study proposes two mixed-integer programming (MIP) models (Model 1 and Model 2) and an improved naked mole-rat algorithm that hybrids with a genetic algorithm (GA) and variable neighborhood search algorithm (VNS). Numerical experiments show that Model 2 performs better compared with Model 1, and the improved naked mole-rat algorithm brings a significant improvement over GA and VNS.

Application of an improved whale optimization algorithm in time-optimal trajectory planning for manipulators.

To address the issues of unstable, non-uniform and inefficient motion trajectories in traditional manipulator systems, this paper proposes an improved whale optimization algorithm for time-optimal trajectory planning. First, an inertia weight factor is introduced into the surrounding prey and bubble-net attack formulas of the whale optimization algorithm. The value is controlled using reinforcement learning techniques to enhance the global search capability of the algorithm. Additionally, the variable neighborhood search algorithm is incorporated to improve the local optimization capability. The proposed whale optimization algorithm is compared with several commonly used optimization algorithms, demonstrating its superior performance. Finally, the proposed whale optimization algorithm is employed for trajectory planning and is shown to be able to produce smooth and continuous manipulation trajectories and achieve higher work efficiency.

Two‐Stage Hybrid Optimization Algorithm for Silicon Single Crystal Batch Scheduling Problem under Fuzzy Processing Time

Considering the widely existing processing time uncertainty in the real‐world production process, this paper constructs a fuzzy mathematical model for the silicon single crystal production batch scheduling problem to minimize the maximum completion time. In this paper, a two‐stage hybrid optimization algorithm (TSHOA) is proposed for solving the scheduling model. Firstly, the improved differential evolution algorithm (IDE) is used to solve the order quantity allocation problem of silicon single crystal with different sizes to obtain the quantity of silicon single crystal rods with different sizes produced by different types of single crystal furnaces. Secondly, the variable neighborhood search (VNS) algorithm is adopted to optimize the order quantity sequencingof batch production processes. Finally, simulations and comparisons demonstrate the feasibility of the model and the effectiveness of TSHOA.

Robust Optimization for Perishable Product Distribution under Uncertainty of Multimodal Transportation Services

Unusual logistics service uncertainties resulting from recent mega-disruptions, such as COVID-19 outbreak or the Russia-Ukraine conflict, are placing increasing pressure on practitioners and researchers to develop robust solutions to mitigate these uncertainties. Perishable products, such as fresh produce, medicine, and vaccines, which deteriorate quickly and have short shelf-lives, are particularly vulnerable to the lead-time uncertainty from the global logistics services, which causes huge waste or even fatal outcomes. Moreover, modeling such time uncertainties using probability distributions is challenging due to the lack of historical data on unprecedented and complex disruptions. The literature on distribution and transportation service planning for perishable products under unknown probability distributions is also scarce. This paper aims to provide shippers with robust solutions for distribution planning of perishable products considering available transportation services within a multimodal transportation network under uncertainty of transit time including waiting time at sites and transportation time between sites. A robust model is proposed to minimize the total distribution costs composed of transportation, transshipment, and deterioration costs. Our model applies the budget of uncertainty to adjust the degree of conservatism in the solutions. A variable neighborhood search (VNS) algorithm is devised to solve the robust model. Finally, computational experiments are carried out to evaluate the performance and applicability of the proposed model and algorithm.

A variable neighborhood search for Open Vehicle Routing Problem

AbstractIn this study, the Open Vehicle Routing Problem, which the companies widely employ in practice using third‐party logistics services, is discussed. This problem is in the class of high‐dimensional and complex optimization problems. A three‐phase Variable Neighborhood Search Algorithm was proposed to solve large‐scale problems efficiently. In this proposed method, eight different neighborhoods are used, four within the route and four between the routes. In addition to this, wise shaking strategies are designed to escape local optimal solutions. The method's performance was tested on literature test instances and comparatively reported its competitiveness.

Optimizing minimum spanning tree using stochastic–Variable neighborhood search for efficient clustering of cancer gene data

SummaryWith the rapid advancement of DNA microarray technologies, researchers in biology can now monitor several gene expression levels in one single experiment that is very useful in detecting or classifying specific types of tumors. The microarray data and its high‐dimensional nature, along with a small set of samples, have presented a new but well‐known phenomenon called the curse of dimensionality. The process of organizing all objects into various groups based on their traits that are either similar or dissimilar is known as clustering. The framework has the foundation of a minimum spanning tree (MST), which is the representation of one set of gene expression data that is multidimensional. The main property of such representations is that every cluster of this expression data will correspond to a subtree in the MST that can convert the problem of multidimensional Clustering to the problem of tree partitioning. A stochastic diffusion search (SDS) has been deployed for clustering. The algorithm was used to be a multi‐agent technique of search and optimization. A variable neighborhood search (VNS) algorithm has been proposed to be a metaheuristic that solves problems of global and combinatorial optimization. The goal of this method was proceeded to get a systematic change to the neighborhood in a local search algorithm. The algorithm will continue to remain the same as an optimal solution that explores the far neighborhoods until better solutions are identified.

A simulation-based metro train scheduling optimization incorporating multimodal coordination and flexible routing plans

The promotion of multimodal coordination is of great significance to the joint development of diversified urban transportation systems. Focusing on an urban comprehensive passenger transport hub (UCPTH) that converges both inter-city modes and multiple inner-city modes, this study aims to customize a bridging metro train operation plan with the utilization of multimodal passenger simulation. A bi-objective integer nonlinear programming model (INLP) incorporating train schedule and flexible routing plan is proposed to minimize passenger waiting time and operating costs simultaneously. Notably, a real-time flow prediction method based on Monte Carlo simulation and queuing network system is proposed and embedded in the optimization model framework to reflect the difference of individual passengers’ transfer walking time and thereby provide detailed passenger distribution on the platform for metro hub stations connecting UCPTH. Compared with the estimation using historical data, this method can particularly support the scheduling coordination of metro and other modes during an abrupt change of arrival flows. Moreover, to solve the collaborative optimization model tractably, the ε-constraint method based on a tailored variable neighborhood search algorithm is developed to generate approximate Pareto optimal solutions, including the number of effective trains, demand-sensitive headway, the route pattern of each effective train, and train dwell time. Finally, two sets of numerical experiments, including a small-scale case and a real-world hub-metro network instance are conducted to demonstrate the effectiveness of the proposed approaches. The study associated with the findings can benefit both metro providers and users especially those who need to transfer to the metro system at hubs by achieving the best match between passenger and train flows in temporal and spatial domains.

An adaptive hybrid variable-large neighborhood search algorithm for profit maximization problem in designing production lines

Designing production lines is an important research issue for both academy as well as industry since it should consider both system efficiency and production costs. In this study, the buffer allocation problem (BAP) is solved to maximize the profit of unreliable lines. The profit of a production line is a function of the throughput and various costs, such as WIP, holding and buffer space costs. In this respect, a crucial decision-making problem, i.e., BAP, is how to allocate the finite buffers to deal with the trade-off between maximizing the throughput of the line and production costs. In this study, profit maximization problem is formulated considering two different objective functions and solved under different constraint sets. An adaptive hybrid variable neighborhood search algorithm that incorporates large neighborhood search as a part of the diversification strategy is proposed to solve the problem. Moreover, a new initialization procedure based on the buffer location providing more profit is proposed to reduce the search effort. The efficiency of the proposed algorithm is tested on existing benchmark problems as well as the newly introduced large-sized data sets. In addition to these experiments, a comprehensive experimental design is conducted to determine the influencing factors on the problem at hand. The experimental study reveals that the proposed solution algorithm is capable to solve the profit maximization problem for large production lines, and the number of machines and the reliability parameters are the most influential factors in solving the BAP for profit maximization. Moreover, it has been observed that the proposed initialization procedure significantly reduces the search effort.

Modified variable neighborhood search algorithm for maximum power point tracking in PV systems under partial shading conditions

Photovoltaic (PV) systems are being increasingly popular for power generation from solar radiation as the usage of renewable energy grows. To improve the efficiency, the system should operate at its the maximum power point. Hence, several algorithms have been developed for this purpose. Continuous tracking for the maximum power point often leads to heavy energy loss. Furthermore, partial shading can dramatically lower the performance of the system. A modified variable neighborhood search algorithm is proposed resulting zero oscillations around the operating point. A set of variables are used to improve the system’s configurability in various atmospheric and geographical conditions. Simulation result proves the operation of the proposed algorithm, its accuracy, and its fast response time.

Research on Optimizing the Location and Layout of National Emergency Material Reserve

Scientific planning, and the layout of the national level reserve base of emergency materials, will help improve the effectiveness of a country’s overall emergency disaster reduction system. Based on the P-center location theory, this paper analyzes the factors affecting site selection at the national and state levels, determines the reasonable number of emergency material reserve bases at national and state levels, and then develops a national macro-level emergency supply reserve location planning model. In this study, the city of 28 states in a country were selected as alternative reserve cities and emergency demand city matrix, to conduct the research. The model is solved using a variable neighborhood search algorithm (VNS). The calculation results obtain the reasonable number of emergency material reserve bases set at the national level in this studied country, and the optimal solution of the base layout can be obtained if the number of emergency reserve bases set at the national level remains unchanged. The experimental results shows that the selected algorithm is reasonable.

A VNS-Based Matheuristic to Solve the Districting Problem in Bicycle-Sharing Systems

A matheuristic approach that combines a reduced variable neighbourhood search (rVNS) algorithm and a mathematical programming (MP) solver to solve a novel model for the districting problem in a public bicycle-sharing system is presented. The problem is modelled as an integer programming problem. While the rVNS algorithm aims to find a high-quality set of centres for the repositioning zones, the MP solver computes the optimal allocation network of the stations to the centres of the repositioning zones. We use a predefined grid to reduce the search space the rVNS needs to explore. The proposed approach obtains promising results for small and medium-sized instances, and is also able to handle large-sized models.

Tactical level operating theatre scheduling of elective surgeries for maximizing hospital performance

Tactically, surgical operations are an important frontier of health care systems that involves treatment of injuries, diseases, and other disorders by manual and instrumental means. Further, this frontier constitutes a significant portion of budget in health care systems to provide quality services. Efficient management of operating theatre can reduce costs and increase patients’ satisfaction to enhance hospital performance. Elective surgery within this segment can be scheduled in advance, and can thus yield significant efficiency through efficient management and planning. This paper considers an elective surgery scheduling problem at the tactical level. The problem mainly determines the number of sessions for each department, and the number of treated patients for each surgery type. The problem considers multiple objectives, including maximizing the hospital performance and revenue, and minimizing the number of overdue patients, number of patients on the waiting list, and weighted overdue patients. Variable neighborhood search (VNS) algorithm is used in this research to solve the operating scheduling problem. A numerical experiment is performed in the randomly generated data set to evaluate the effectiveness of the proposed algorithm. Sensitivity analysis is performed to understand the ways to improve the hospital performance. By using the VNS algorithm in elective surgery operating room scheduling, we hope to increase patients’ satisfaction and reduce the cost of hospitals at the same time.

Scheduling algorithms for multi-stage flow shops with reworks under overlapped queue time limits

This study addresses a multi-stage flow shop scheduling problem in which a job is reworked when its queue time between two arbitrary stages exceeds an upper limit. The problem is to determine the start times of jobs and rework setups/operations if incurred for the objective of minimising makespan. As an extension of the previous studies, multiple overlapped queue time limits are considered, i.e. some in-between stages of queue time limits for a job are overlapped. A mixed integer programming model is developed and its performance is reported for small-sized test instances. Then, due to the limited applications of optimal solution approaches, a variable neighbourhood search (VNS) algorithm is proposed that generates an initial solution and improves it using a shaking and a local search improvement methods. In addition, it is extended to the general variable neighbourhood search (GVNS) algorithms with variable neighbourhood descent (VND) methods. Computational results show that the GVNS algorithms outperform the VNS algorithm significantly and also give near optimal solutions for small-sized test instances within a reasonable amount of computation times.

An Improved Arc Flow Model with Enhanced Bounds for Minimizing the Makespan in Identical Parallel Machine Scheduling

In this paper, an identical parallel machine problem was considered with the objective of minimizing the makespan. This problem is NP-hard in the strong sense. A mathematical formulation based on an improved arc flow model with enhanced bounds was proposed. A variable neighborhood search algorithm was proposed to obtain an upper bound. Three lower bounds from the literature were utilized in the improved arc flow model to improve the efficiency of the mathematical formulation. In addition, a graph compression technique was proposed to reduce the size of the graph. As a consequence, the improved arc flow model was compared with an arc flow model from the literature. The computational results on benchmark instances showed that the improved arc flow model outperformed the literature arc flow model at finding optimal solutions for 99.97% of the benchmark instances, with the overall percentage of the reduction in time reaching 87%.

Optimal plan for ordered step-stress stage life testing

ABSTRACT In a progressively censored life testing experiment, the censored units can be used for some other life testing experiments. In a step-stress stage life testing experiment, we run parallel experiments while placing the progressively censored units at the higher stress level along with the main experiment. In this work, multiple step-stress stage life testing experiments are performed under the assumption that the experimental units at different stress levels follow Weibull distributions with the same shape parameter, but different scale parameters. The main objectives of this paper are to provide an order-restricted classical inference of the model parameters and also to find out the optimal life testing scheme. We provide the order-restricted maximum likelihood estimators of the unknown parameters and the associated confidence intervals based on the observed Fisher information matrix. An extensive simulation study and a data analysis are provided for illustrative purposes. In search of the optimal life testing plan under this set ups, a meta-heuristic approach based on a variable neighbourhood search algorithm is employed using D-optimality criterion. Finally, we have indicated how the method can be extended when the shape parameter of the Weibull distributions are also different at different stress levels.