Neighborhood Search Research Articles

A Lower Bound on Complexity of a Locator Cellular Automaton Solution for the Closest Neighbor Search Problem

A Lower Bound on Complexity of a Locator Cellular Automaton Solution for the Closest Neighbor Search Problem

An improved multi-objective Wild Horse optimization for the dual-resource-constrained flexible job shop scheduling problem: A comparative analysis with NSGA-II and a real case study

The equipment manufacturing industry needs skilled workers to operate a specific set of machines following process specifications. Optimizing machine and worker assignments to achieve maximum efficiency is a critical problem for workshop managers. This paper investigates a multi-objective dual-resource-constrained flexible job shop scheduling problem. An improved wild horse optimization (IWHO) algorithm is developed to simultaneously optimize three objectives: makespan, maximum machine workload, and total machine workload. To evaluate the quality of individuals in multi-objective optimization, the Pareto fast non-dominated sorting method is used, and the crowding distance is calculated. To update the algorithm's solution, the crossover and mutation operations are used. Further, a local neighborhood search strategy is employed to enhance searchability and avoid trapping into the local optima. The benchmark of the flexible job shop scheduling problem is extended to create test instances, and the performance of the suggested IWHO algorithm is evaluated compared with the NSGA-II. The computational results show that the IWHO algorithm provides a non-dominated efficient set within a reasonable running time. Furthermore, a buffers and chain coupler assembly process is designed to analyze the practical value of the IWHO algorithm. The proposed solutions can be used to generate daily schedules for managing machines, workers, and production cycles.

An ALNS-based matheuristic algorithm for a multi-product many-to-many maritime inventory routing problem

In this paper, we propose an adaptive large neighborhood search-based matheuristic algorithm to solve a multi-product many-to-many maritime inventory routing problem. The problem addresses a short sea inventory routing problem that aims to find the best route and distribution plan for multiple products with a heterogeneous fleet of vessels through a network including several producers and customers. Each port can be visited a given number of times during the planning horizon, and the stock level for each product should lie within the predefined bound limits. The problem was introduced by Hemmati et al. (Eur J Oper Res 252:775–788, 2016). They developed a mixed integer programming formulation and proposed a matheuristic algorithm to solve the problem. Although their proposed algorithm worked well in terms of running time, it suffers from disregarding a part of the solution space. In this study, we propose a new matheuristic algorithm to find better solutions by exploring the entire solution space for the same problem. In our solution methodology, we split the variables into routing and non-routing variables. Then in an iterative process, we determine the values of the routing variables with an adaptive large neighborhood search algorithm, and we pass them as input to a penalized model which is a relaxed and modified version of the mathematical model introduced in Hemmati et al. (2016). The information from solving the penalized model, including the values of the non-routing variables, is then passed to the adaptive large neighborhood search algorithm for the next iteration. Several problem-dependent operators are defined. The operators use the information they get from the penalized model and focus on decreasing the penalty values. Computational results show up to 26% improvement in the quality of the solutions for the group of instances with a large feasible solution space. We get the optimal value for the remaining instances matched with the reported results.

Tabu Search with Variable Neighborhood Search Algorithm for Home Healthcare Routing Problem for Multiple Hospitals with Balanced Workload

In this paper, we study home healthcare routing and scheduling problem where multiple hospitals serve patients. In the public hospitals in healthcare system of Türkiye, patients requiring home healthcare are assigned to the hospital that serves their place of residence. This can cause the workload of hospitals to become unbalanced in terms of the time needed for both traveling and operation. The aim of this paper is to generate routes with a balanced workload for hospitals, giving consideration to the time windows of patients and the working hours of health workers. Firstly, we construct a mathematical model which can solve toy and small-scale problems whilst taking into account the importance of a balanced workload. Then, a Tabu Search with a Variable Neighborhood Search (TS-VNS) algorithm is developed to solve large-scale problems. The performance of the TS-VNS algorithm is tested by comparing the results of the mathematical model with the generated test problems at a small scale. Additionally, large-scale test problems from the literature are sourced for the problem and solved by the TS-VNS algorithm. The results demonstrate the efficiency of the TS-VNS algorithm.

Two-layer intelligent deployment of capsule airports and unmanned aerial vehicles for providing emergency communication services

The utilization of Unmanned Aerial Vehicles (UAVs) as base stations for emergency communication services has garnered significant attention due to their lightness and agility. To increase the capacity and coverage of UAVs, the Capsule Airport (CA) is developed, which serves as a recharging and retrieval station for UAVs. Meanwhile, deploying CAs and UAVs in appropriate positions is crucial for ensuring high-quality and efficient service provision. To address this challenge, we propose the Two-Layer Maximum Deployment Problem for Capsule Airports and Unmanned Aerial Vehicles (2L-MCDP-C&U). The objective of the 2L-MCDP-C&U is to maximize the number of served users by determining the ground locations for opening a given number of CAs and deploying their UAVs in 3D space, while considering the connectivity of UAV-to-UAV, UAV-to-CA, and UAV-to-user. An improved variable neighborhood search algorithm is designed based on the k-means (VNS-K) to solve the 2L-MCDP-C&U. To further validate its efficacy, we conduct experiments on random instances of various sizes and a practical case study of Zhulin town in China. Our work paves the way for more efficient and effective emergency communication services using CAs and UAVs.

An adaptive large neighborhood search metaheuristic for the Generalized Bin Packing problem with incompatible categories

This paper addresses the Generalized Bin Packing Problem with Incompatible Categories (GBPPIC), a challenging optimization problem related to last-mile distribution in large cities. We aim to determine the best assignment of deliveries of distinct products to a homogeneous fleet of capacitated vehicles to minimize the number of required vehicles (bins), considering the concept of incompatible categories (i.e., types of items that cannot be transported together). Unlike the Bin Packing Problem with Compatible Categories (BPCC), deliveries to be assigned to the vehicles can be of two types: to regular or sporadic customers; the former must be serviced while the latter does not necessarily need to be serviced but may bring additional revenue that does not offset the cost of an additional vehicle. Due to the difficulty in solving to optimality large instances found in practice, an Adaptive Large Neighborhood Search (ALNS) metaheuristic is proposed. It is applied to new benchmark instances derived from the BPCC, and the results are compared to exact solutions. The computational experiments indicate that our ALNS algorithm can effectively solve the GBPPIC in very short running times, even for larger instances that require significantly longer times for the exact approach. The ALNS also outperforms a previous VNS heuristic for the BPCC.

Differential evolution with stage stratification method and dual balanced mutation strategy for real-parameter numerical optimization

Traditional differential evolution (DE) algorithms have functional limitations in effectively addressing increasingly intricate numerical optimization problems. The key to responding to this challenge is to strike a suitable balance between exploration and exploitation. Exploration is used to find the global optimal solution, and exploitation is used to improve the accuracy of the global optimal solution. Therefore, this study introduces a novel differential evolution algorithm with a stage stratification method and a dual balanced mutation strategy framework, named SbmDE. To enhance the balance between convergence and diversity, the population is stratified into exploration and exploitation layers based on the size of the fitness value and evolutionary period. In the exploitation layer, a hybridization mutation is applied as the first mutation. A novel dual improved mutation operation is proposed and applied to the exploration layer. For the first mutation, the hybridization mutation is used in the same manner as for the exploitation layer. For the secondary mutation, two improved mutation strategies are proposed to alleviate premature convergence at the early stage of evolution and to enhance the local neighborhood search at a later stage, named DE/ranking-to-rand/1 and DE/best-current-dev/1. Experiments were conducted on the CEC2017 benchmark suite, which contains 29 single-objective real-parameter numerical optimization problems, to evaluate the performance of the proposed algorithm. Compared with 11 state-of-the-art algorithms, the results demonstrate the superiority of the proposed algorithm, which does not increase the time complexity. Additionally, based on the four engineering design problems, the proposed algorithm is fully competent in solving practical constrained optimization problems.

The vehicle routing problem with underground logistics: Formulation and algorithm

Recognizing the pressure on urban logistics and the overcapacity of urban public transportation systems during off-peak hours, this study investigates a subway-assisted delivery model. This is a system in which part of the goods to be delivered into a city can be transferred to specific subway stations in advance (e.g., during the night) using underground logistics. During the day, vehicles can then be replenished at these subway stations. In our study, we investigate how a system of this kind affects the decisions to be made by a logistics service provider. We introduce the vehicle routing problem with underground logistics to model how to find the best vehicle routes and goods transfer plan in this system. First, we formulate this problem as a mixed integer linear model. Then, we propose a problem-customized adaptive large neighborhood search heuristic algorithm to solve it. Numerical experiments demonstrate that our methodology performs well in terms of effectiveness and efficiency. Additionally, we discuss the resulting schedules and include a sensitivity analysis of the transfer prices to provide information that can be used in strategic and tactical decision making in a subway-assisted delivery system.

Multi-day fair collaboration in demand-responsive transportation

In this paper, we consider the case of companies that offer a demand-responsive transportation service, such as a shared-taxi service, and are engaged in a horizontal collaboration initiative. The goal of the coalition is to optimize the transportation operations in such a way that no company is penalized, in terms of customers served and/or working time. We present an optimization model for a multi-day planning horizon that includes constraints aimed at guaranteeing a level of fairness to all companies that can be controlled over the planning horizon and day-by-day, if beneficial. An adaptive large neighborhood search heuristic is then presented for its solution. The computational experiments show that, although the model constraints the optimization space, it still guarantees substantial savings. Moreover, they show that the model is flexible and can guarantee the sustainability in the long term of the collaboration initiative.

RETRACTED ARTICLE: Effectiveness of Mixed Fuzzy Time Window Multi-objective Allocation in E-Commerce Logistics Distribution Path

The study of logistics distribution network under e-commerce environment is conducive to the establishment of efficient logistics distribution system, but also to promote the further development of e-commerce and improve social benefits of great significance. This study considers multiple fuzzy factors and introduces a customer fuzzy time window with variable coefficients, establishes a multi-objective set allocation integrated multi-level location path planning model, and proposes an archive type multi-objective simulated annealing improvement algorithm based on master–slave parallel framework embedded taboo search to solve the model. Tabu search and large-scale neighborhood algorithm are used to solve the initial solutions of the first level network and the second level network respectively, and archival reception criterion is introduced to deal with the multi-objective problem. The results of the proposed algorithm for the two-level site-routing problem are less than 6% different from the internationally known optimal solution. The master–slave parallel computing framework improves the efficiency of the algorithm by about 6.38%. The experimental results prove the effectiveness and necessity of the improved optimization. In addition, this study simulates the site-routing problem model constructed by the study by extending the data of standard examples. The experimental results prove the correctness and reference significance of the multilevel site-routing problem model with multiple fuzzy factors.

Integrated optimization of train timetable and train unit circulation for a Y-type urban rail transit system with flexible train composition mode

With the increasing complexity of urban rail transit (URT) networks and the revolution of train control technology, a large number of diverse operation and organization modes have emerged. This paper studies the train operation plan problem for a Y-type URT system with flexible train composition mode. The studied problem can be defined as an integrated optimization of the train timetable problem (TTP) and train unit circulation problem (TUCP) under time-dependent passengers, where the train compositions can be coupled or decoupled during the trip. By considering train operation constraints, train composition constraints, train unit circulation constraints, and passenger demand constraints with limited train capacity, our problem is formulated as an integer programming (IP) model, where the objective is to minimize the passengers’ total waiting time and the number of train units used. To solve large-scale real-world instances, we design a heuristic algorithm by improving the classical framework of the adaptive large neighborhood search (ALNS) algorithm. Several groups of experiments, including small-case instances and real-world instances of Guangzhou Metro Line 14, are investigated to verify the effectiveness of the proposed model and algorithm. Compared with the traditional fixed train composition mode, both the passengers’ total waiting time and the number of train units used under the condition of flexible train composition mode are reduced. This will effectively improve the quality of the passenger service and reduce the costs of URT departments.

A mixing algorithm of ACO and ABC for solving path planning of mobile robot

Path planning is involved in many applications such as trajectory planning, mobile robotics, pipeline layout, etc. Researchers use artificial intelligence algorithms to solve path planning efficiently, among which the ant colony algorithm (ACO) is one of the common intelligent algorithms to solve path planning problems. However, the traditional ACO has defects such as low early search efficiency and easy to fall into local optimum, while the artificial bee colony algorithm (ABC) has high search efficiency. Therefore, an improved ant colony optimization-artificial bee colony algorithm (IACO-IABC) is proposed in this study. IACO-IABC contains three mechanisms. First, the heuristic mechanism with directional information for the ACO is improved to enhance the efficiency of steering towards the target direction. Secondly, the novel neighborhood search mechanism of the employed bee and the onlooker bee in the ABC is presented to enhance the exploitation of optimal solutions. Then, the path optimization mechanism is introduced further to reduce the number of turn times in the planned path. To verify the performance of the IACO-IABC, a series of experiments are conducted with 10 different maps. The experiments compare nine variants of ACO and eight commonly used intelligent search algorithms, and the results show the advantages of the IACO-IABC in reducing the number of turn times and path lengths and enhancing the convergence speed of the algorithm. Compared to the best results of other algorithms, the average improvement percentages of the proposed algorithm in terms of the path turn times are 375%, 258.33%, 483.33%, 186.67%, 166.77% and 255.33%, further demonstrating the ability of IACO-IABC to obtain high-quality path planning result.

Synchromodal freight transport re-planning under service time uncertainty: An online model-assisted reinforcement learning

The objective of this study is to address the issue of service time uncertainty in synchromodal freight transport, which can cause delays, inefficiencies, and reduced satisfaction for shippers. The proposed solution is an online deep Reinforcement Learning (RL) approach that takes into account the service time uncertainty, assisted by an Adaptive Large Neighborhood Search (ALNS) heuristic that provides state and reward information based on the routing and scheduling. The proposed planning approach re-plans in response to unexpected events and learns from real-time information from various transport modes, including road, railway, and inland waterways. The performance of the proposed planning approach is evaluated in the European Rhine-Alpine corridor under various scenarios with different types and severities of unexpected events. The results demonstrate that the RL approach consistently outperforms other strategies by effectively handling service time uncertainty, leading to reduced costs, emissions, and waiting time, as well as decreased transport delays and improved rewards through accurate decision-making and agile transport re-planning. This study also finds that incorporating event severity information improves the average reward obtained by the RL approach in scenarios involving multiple types of events.

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.

Analyzing the benefits of a city hub: An inventory and routing perspective

Collaboration is one of the crucial elements in city logistics and it is often pursued by the introduction of two- or multi-echelon systems using one or more intermediate consolidation points, such as Urban Consolidation Centers (UCCs), city depots, city hubs, etc. Our literature review shows that the study of inventory aspects in such a context is relatively unexplored. Therefore, this paper studies the effect of using a UCC or city hub in a B2B city logistics system in terms of both inventory and routing aspects. A multi-period optimization model is proposed to support the operational decisions in urban B2B distribution when using a city hub. We study the effect of introducing a city hub by comparing our model with a baseline model in which urban retailers operate without a city hub. The model accounts for the complexity of urban logistics by considering a heterogeneous vehicle fleet, the option to perform multiple trips per day, and strict customer time windows. A metaheuristic algorithm based on Large Neighborhood Search (LNS) is used to solve the route optimization problem for realistic problem instances. Extensive numerical experiments are conducted according to an experimental design and a statistical analysis. Results indicate that the introduction of a city hub leads to significant reductions in operational costs and societal impacts (e.g., loading degree, number of urban trips, traveled distances). Our analysis shows that these savings are significantly impacted by the problem context (e.g., replenishment policy, number of retailers, number of suppliers, and holding cost). For example, how retailers make replenishment decisions significantly impacts the costs of the overall system and the potential savings. The most cost-efficient replenishment method is often not the most interesting one from a societal perspective. Finally, from a city’s perspective, a sufficient number of retailers and suppliers should participate in the system to maximize consolidation opportunities. However, in relative terms, the largest potential savings by introducing a city hub are reached when not too many suppliers are included and suppliers have a relatively limited number of customers to serve.

The drone-assisted pickup and delivery problem: An adaptive large neighborhood search metaheuristic

The use of unmanned aerial vehicles (UAVs), also known as drones, for last-mile delivery has grown in popularity in research and industry over the last decade. We propose a mathematical model formulation for the coordination of parcel pickups and deliveries between trucks and drones in this paper, which we call the drone-assisted pickup and delivery problem (DAPDP). In the DAPDP, multiple trucks depart a depot with a UAV on board. As the trucks pick up packages and make deliveries, the corresponding UAV can also be used to make deliveries to customers near the truck’s position. While the UAVs are making deliveries, the trucks continue on their route, making additional deliveries along the way, and retrieving the UAVs at customer locations other than the launch points. We formulate the DAPDP model as a mixed integer linear program (MILP) and propose an adaptive large neighborhood search (ALNS) metaheuristic to solve it for instances of practical size. Additionally, we propose a novel method for benchmarking the performance of the proposed metaheuristic, which concretely certifies the quality of the solution, with all optimality gaps under 3%.

Special issue dedicated to the 8th International Conference on Variable Neighborhood Search (ICVNS 2021)

This special issue contains 15 papers submitted by the participants of the 8th International Conference on Variable Neighborhood Search (ICVNS 2021), which was held in Abu Dhabi, U.A.E., online due to COVID-19 restrictions, on March 22–24, 2021.

Value of Cargo Pooling in On-Demand Intra-City Freight Logistics

On-demand intra-city freight logistics (ICFL) has recently emerged as a new freight service, where shippers can submit their shipping requests using smartphones and be matched to drivers in real time based on their locations and drivers’ availability. A major challenge faced by on-demand ICFL platforms is the shortage of vehicles during peak demand periods. Cargo pooling, the cargo version of carpooling, offers as a promising way to increase supply: cargoes heading in the same direction would share the cargo compartment of the same vehicle and be serviced simultaneously, which is achieved by careful sequencing of the pickup and delivery locations of the cargoes. We investigate models for cargo pooling for on-demand ICFL and quantify its benefit, which is new to the literature. The major difference between existing studies on ICFL and ours is that we no longer assume that demands are known beforehand. Instead, the demands arrive gradually throughout the day and we need to periodically match requests to drivers and re-optimize vehicle routes. We formulate the matching problem as a dynamic pickup and delivery problem with three-dimensional loading and time window constraints. To solve this model, we develop an algorithm based on large neighborhood search and tree search. The algorithm is tested with real freight data in a city in the Yangtze River Delta. Results show that the algorithm can reduce the total cost by 21.4% and reduce the total vehicle miles traveled by 36.0%.

A tri-individual iterated greedy algorithm for the distributed hybrid flow shop with blocking

Scheduling problem with blocking is an attractive research direction due to its wide practical applications. However, in the distributed hybrid flow shop problem (DHFSP), there are few studies on blocking constraints. In this article, we study a distributed hybrid flow shop scheduling problem with blocking constraints (DBHFSP), where the goal is to minimize the maximum completion time, and propose a tri-individual iterated greedy (TIG) algorithm based on the characteristics of the DBHFSP. First, an active decoding strategy is designed to reduce the idle time of machines. Afterward, a framework of multiple iterative solutions is designed to enhance the diversity of the solutions, in which the multiple solutions are generated through a neighborhood search. Then, a heuristic rule based on blocking constraint is proposed to generate promising initial solutions. In addition, an insertion-based search strategy based on rotating critical factories is designed to accelerate the convergence speed of the TIG algorithm. Finally, the proposed algorithm is compared with state-of-the-art algorithms and classical intelligent optimization algorithms. The experimental results show that the TIG algorithm is superior to the comparison algorithm in solving the DBHFSP.

Automated Georectification, Mosaicking and 3D Point Cloud Generation Using UAV-Based Hyperspectral Imagery Observed by Line Scanner Imaging Sensors

Hyperspectral sensors mounted on unmanned aerial vehicles (UAV) offer the prospect of high-resolution multi-temporal spectral analysis for a range of remote-sensing applications. However, although accurate onboard navigation sensors track the moment-to-moment pose of the UAV in flight, geometric distortions are introduced into the scanned data sets. Consequently, considerable time-consuming (user/manual) post-processing rectification effort is generally required to retrieve geometrically accurate mosaics of the hyperspectral data cubes. Moreover, due to the line-scan nature of many hyperspectral sensors and their intrinsic inability to exploit structure from motion (SfM), only 2D mosaics are generally created. To address this, we propose a fast, automated and computationally robust georectification and mosaicking technique that generates 3D hyperspectral point clouds. The technique first morphologically and geometrically examines (and, if possible, repairs) poorly constructed individual hyperspectral cubes before aligning these cubes into swaths. The luminance of each individual cube is estimated and normalised, prior to being integrated into a swath of images. The hyperspectral swaths are co-registered to a targeted element of a luminance-normalised orthomosaic obtained using a standard red–green–blue (RGB) camera and SfM. To avoid computationally intensive image processing operations such as 2D convolutions, key elements of the orthomosaic are identified using pixel masks, pixel index manipulation and nearest neighbour searches. Maximally stable extremal regions (MSER) and speeded-up robust feature (SURF) extraction are then combined with maximum likelihood sample consensus (MLESAC) feature matching to generate the best geometric transformation model for each swath. This geometrically transforms and merges individual pushbroom scanlines into a single spatially continuous hyperspectral mosaic; and this georectified 2D hyperspectral mosaic is then converted into a 3D hyperspectral point cloud by aligning the hyperspectral mosaic with the RGB point cloud used to create the orthomosaic obtained using SfM. A high spatial accuracy is demonstrated. Hyperspectral mosaics with a 5 cm spatial resolution were mosaicked with root mean square positional accuracies of 0.42 m. The technique was tested on five scenes comprising two types of landscape. The entire process, which is coded in MATLAB, takes around twenty minutes to process data sets covering around 30 Ha at a 5 cm resolution on a laptop with 32 GB RAM and an Intel® Core i7-8850H CPU running at 2.60 GHz.