Variable Neighborhood Search Research Articles

A Global Coverage Path Planning Method for Multi-UAV Maritime Surveillance in Complex Obstacle Environments

The study of unmanned aerial vehicle (UAV) coverage path planning is of great significance for ensuring maritime situational awareness and monitoring. In response to the problem of maritime multi-region coverage surveillance in complex obstacle environments, this paper proposes a global path planning method capable of simultaneously addressing the multiple traveling salesman problem, coverage path planning problem, and obstacle avoidance problem. Firstly, a multiple traveling salesmen problem–coverage path planning (MTSP-CPP) model with the objective of minimizing the maximum task completion time is constructed. Secondly, a method for calculating obstacle-avoidance path costs based on the Voronoi diagram is proposed, laying the foundation for obtaining the optimal access order. Thirdly, an improved discrete grey wolf optimizer (IDGWO) algorithm integrated with variable neighborhood search (VNS) operations is proposed to perform task assignment for multiple UAVs and achieve workload balancing. Finally, based on dynamic programming, the coverage path points of the area are solved precisely to generate the globally coverage path. Through simulation experiments with scenarios of varying scales, the effectiveness and superiority of the proposed method are validated. The experimental results demonstrate that this method can effectively solve MTSP-CPP in complex obstacle environments.

Optimization of water distribution networks using simulated annealing (SA) with variable neighbourhood search (VNS): a case study in the city of Malard

ABSTRACT Water distribution networks (WDNs) are essential for modern cities, as effective design can reduce construction costs and ensure reliable service. As cities expand, optimizing these large networks becomes increasingly complex. In this work, we introduce a novel approach by combining simulated annealing (SA) with variable neighbourhood search (VNS) into a single heuristic algorithm for WDN optimization, marking the first use of the SA-VNS method in this context. Additionally, we apply Taguchi's design of experiments (DOE) to tune the parameters of the SA-VNS algorithm specifically for water networks. We tested our new algorithm on four standard benchmark networks and a real-world WDN, including a case study of a large city. Our results demonstrate that the SA-VNS algorithm outperforms existing methods in terms of cost, speed, and overall effectiveness, making this research a significant advancement in both heuristic methods and parameter-tuning techniques for WDN optimization.

Analysis of the inter-city shared mobility system based on autonomous electric vehicles

While autonomous electric vehicles (AEVs) have been preliminarily implemented in shared travel services from both technical and theoretical perspectives, challenges such as dispersed fleets, limited service quality, and travel safety concerns have confined existing research to intra-city shared mobility, with few studies focusing on inter-city shared mobility for AEVs. With China’s metropolitan regions expanding and intercity travel rapidly increasing, examining the use of shared autonomous electric vehicles (SAEVs) for intercity travel is essential for future transportation systems. To address this issue, this study models the inter-city shared mobility problem utilizing mixed integer linear programming. The problem is defined on a directed graph and addressed using a variable neighborhood search algorithm. Numerical experiments are designed based on the actual shared mobility data between Yinchuan and Shizuishan, Ningxia Province, China. From the perspective of the operating platform, the potential influencing factors of the inter-city shared mobility system are analyzed, including passenger travel demand, fleet size, vehicle range, and the number of charging stations. The results demonstrate that increasing temporal and spatial imbalance in passenger travel demand and excessive fleet size will lead to lower total revenue of the operation platform. Conversely, within certain thresholds, increasing the number of charging stations, vehicle range, and fleet size will increase the total revenue. Continuing to increase the number of charging stations and vehicle range has no significant effect on total revenue and service rate but will lead to a waste of basic resources. The study is expected to provide a solution for building an inter-city shared mobility system based on SAEVs. By fully understanding the system’s limitations and advantages, we aim to provide a reference template for constructing future inter-city shared mobility systems.

General Variable Neighborhood Search for Maximum Diversity Problem with Capacity and Budget Constraints

General Variable Neighborhood Search for Maximum Diversity Problem with Capacity and Budget Constraints

Graph protection under multiple simultaneous attacks: A heuristic approach

This work focuses on developing a meta-heuristic approach to protect network nodes from simultaneous attacks, specifically addressing the k-strong Roman domination problem. The objective is to assign integer weights to the nodes, representing the number of stationed armies, to meet protection constraints while minimizing the total number of armies. A network is protected if it can repel any simultaneous attack on k nodes. A node is protected if it can defend itself or if a neighboring node provides an army while retaining at least one army for self-defense. This problem formulation can be used in practical scenarios, e.g. developing counter-terrorism strategies or in coping with supply chain disruptions. The problem is difficult as even verifying the feasibility of a single solution generally requires an exponential time. Two exact approaches are proposed in the literature but applicable to small random graphs. For larger graphs, we propose an effective variable neighborhood search, where the feasibility of a solution is verified by introducing the concept of relaxed feasibility. Experiments are conducted with random networks from the literature and two introduced ad-hoc wireless and real-world networks. Extensive experimental evaluations show the robustness of the proposed approach compared to the existing approaches from the literature by significantly outperforming them in all three benchmark sets. Furthermore, we demonstrate the practical application of the proposed variable neighborhood search approach, where its solution is used to position fire stations within the city so that simultaneous fires can be extinguished efficiently while reducing the number of required fire trucks.

A hybrid deep learning model-based LSTM and modified genetic algorithm for air quality applications.

Over time, computing power and storage resource advancements have enabled the widespread accumulation and utilization of data across various domains. In the field of air quality, analyzing data and developing air quality models have become pivotal in safeguarding public health. Despite significant progress in modeling, the critical need for accurate pollutant predictions persists. In addressing this challenge, deep learning models have garnered substantial attention in research due to their outstanding performance across diverse applications. However, the optimization of hyperparameters and features remains a challenging task. This study seeks to leverage historical data to construct the long short-term memory-based model for forecasting multistep PM10. To refine its architecture, a modified genetic algorithm is employed for automatic design. Furthermore, we explore principal component analysis and exhaustive feature selection to identify the optimal feature set. This paper introduces a novel hybrid deep learning model named EFS-GA-LSTM, tailored for multistep hourly PM10 forecasting. To assess its performance, we compare it with other hyperparameter optimization algorithms, including particle swarm optimization, variable neighborhood search, and Bayesian optimization with Gaussian process. The input dataset comprises hourly PM10 concentrations, meteorological variables, and time variables. The results reveal that for 3-h-ahead forecasting tasks, the EFS-GA-LSTM network demonstrates improvements in root mean square error, mean absolute percentage error, correlation coefficient, and coefficient of determination.

Multi-objective grey wolf optimizer based on reinforcement learning for distributed hybrid flowshop scheduling towards mass personalized manufacturing

As an emerging production paradigm, mass personalized manufacturing (MPM) realizes personalized product customization under the premise of ensuring large-scale production. In this paradigm, the rapid switching of the type and quantity of manufacturing tasks increases the difficulty of scheduling. Hence, this paper proposes the distributed hybrid flowshop scheduling problem with an order modularization and tasks assigning method (DHFSP-OMTA), where heterogeneous customer orders are decomposed into standard and personalized production tasks and assigned to different factories. Meantime, towards MPM, a novel mixed integer linear programming model is established to minimize the makespan and total energy consumption simultaneously. Considering the high complexity of DHFSP-OMTA, a multi-objective grey wolf optimizer based on reinforcement learning (MOGWO-RL) is designed. This paper contains the following three improvements. Firstly, the variable tasks splitting method combines two initial heuristic-rule to produce a high-quality population. Secondly, a variable neighborhood search based on reinforcement learning is designed to improve the search quality and jump out of the local optimum. Thirdly, an efficient merging batches method is presented to save transportation energy consumption. The advantages of the proposed algorithm are verified on 18 modified test instances based on the Taillard benchmark with the MPM feature. The results show that MOGWO-RL has the best effectiveness and stability of all comparison algorithms. Therefore, it can be used as a novel method to solve MPM’s scheduling problem.

A Space Telescope Scheduling Approach Combining Observation Priority Coding with Problem Decomposition Strategies

With the increasing number of space debris, the demand for telescopes to observe space debris is also constantly increasing. The telescope observation scheduling problem requires algorithms to schedule telescopes to maximize observation value within the visible time constraints of space debris, especially when dealing with large-scale problems. This paper proposes a practical heuristic algorithm to solve the telescope observation of space debris scheduling problem. In order to accelerate the solving speed of algorithms on large-scale problems, this paper combines the characteristics of the problem and partitions the large-scale problem into multiple sub-problems according to the observation time. In each sub-problem, a coding method based on the priority of the target going into the queue is proposed in combination with the actual observation data, and a decoding method matching the coding method is designed. In the solution process for each sub-problem, an adaptive variable neighborhood search is used to solve the space debris observation plan. When solving all sub-problems is completed, the observation plans obtained on all sub-problems are combined to obtain the observation plan of the original problem.

A Matheuristic Approach Based on Variable Neighborhood Search for the Static Repositioning Problem in Station-Based Bike-Sharing Systems

In this paper, we study a novel static bike-sharing repositioning problem. There is a set of stations spread over a given area, each containing a number of operative bikes, damaged bikes, and free slots. The customers may pick up an operative bike from a station, use it, and return it to another station. Each station should have a target number of operative bikes to make it likely to meet customer demands. Furthermore, the damaged bikes should be removed from the stations. Given a fleet of available vehicles, the repositioning problem consists of designing the vehicles’ routes and calculating the number of operative (usable) and damaged (unusable) bikes that will be moved (loading instructions/loading policy) between stations and/or the depot. The objective is to minimize the weighted sum of the deviation from the target number of bikes for each station, the number of damaged bikes not removed, and the total time used by vehicles. To solve this problem, we propose a matheuristic based on a variable neighborhood search combined with several improving algorithms, including an integer linear programming model to optimize loading instructions. The algorithm was tested in instances based on real-world data and could find good solutions in reasonable computing times.

Optimizing floating crane operations for efficient bulk product transshipments on inland waterways

In the realm of global supply chains, the optimization of floating crane operations for bulk product transshipment via inland waterways emerges as a crucial necessity to address economic, operational, and environmental imperatives. This research identifies a significant gap in existing methodologies for the scheduling, routing, and assignment of floating cranes, which are essential for improving efficiency and sustainability in maritime logistics. To bridge this gap, we propose the Reinforcement Learning Variable Neighbourhood Strategy Adaptive Search (RL-VaNSAS) algorithm, a novel integration of reinforcement learning with variable neighbourhood search strategies. This advanced model aims to holistically minimize energy consumption, labor costs, and penalty costs, while simultaneously enhancing service efficiency. Through rigorous simulations, RL-VaNSAS was benchmarked against conventional methods such as Differential Evolution (DE), Genetic Algorithm (GA), and the original Variable Neighbourhood Search Adaptive Strategy (VaNSAS), revealing its superior capability in significantly reducing annual energy costs to $1,211,948, labor costs to $270,948, penalty costs to $19,948, and operational hours to 12,087. Demonstrating notable advancements in operational efficiency and cost reduction, RL-VaNSAS offers a sustainable solution to the dynamic challenges of maritime logistics, characterized by fluctuating vessel arrivals and diverse cargo requirements. The findings illuminate the critical need for innovative optimization techniques in enhancing the sustainability and efficiency of maritime logistics operations. RL-VaNSAS not only fills the identified research gap but also sets a new standard for future endeavors in global supply chain management, underlining the importance of adopting advanced optimization strategies for sustainable production and economic growth.

Variable Neighborhood Search and Alternating Direction Method of Multipliers for Integrated Optimization of Maintenance Windows and Train Timetables

Variable Neighborhood Search and Alternating Direction Method of Multipliers for Integrated Optimization of Maintenance Windows and Train Timetables

Modeling and Optimization Algorithm for Rotational Irrigation Group Based on Connectivity Weighted Index

Abstract Manual calculations for rotational irrigation groups are inefficient, and a single objective cannot provide farmers with diverse options. Based on considering both engineering standards and practical needs, this study designs a connectivity index and proposes a new model with the optimization objectives of balanced flow and minimum connectivity. To address infeasible solutions and constraint issues, A hybrid genetic algorithm based on variable neighborhoods is adopted to enhance the search capability of the classical non-dominated sorting genetic algorithm. The effectiveness and universality of the model and algorithm are verified through multiple real-world cases. The research shows that the proposed multi-objective model is more practical than a single-objective model, and farmers can be provided with diverse Pareto solutions by adjusting the weight index ω. The variable neighborhood search algorithm enhances the search capability within the radius threshold, improves population diversity, and analyzes the radius threshold and branch pipe flow parameters to explore factors that affect algorithm performance and indicators.

A risk-averse latency location-routing problem with stochastic travel times

In this paper, a latency location-routing problem with stochastic travel times is investigated. The problem is cast as a two-stage stochastic program. The ex-ante decision comprises the location of the depots. The ex-post decision regards the routing, which adapts to the observed travel times. A risk-averse decision-maker is assumed, which is conveyed by adopting the latency CVaRα as the objective function. The problem is formulated mathematically. An efficient multi-start variable neighborhood search algorithm is proposed for tackling the problem when uncertainty is captured by a finite set of scenarios. This procedure is then embedded into a sampling mechanism so that realistic instances of the problem can be tackled, namely when the travel times are represented by random vectors with an infinite support. An extensive computational analysis is conducted to assess the methodological developments proposed and the relevance of capturing uncertainty in the problem. Additional insights include the impact of the risk level in the solutions.

Proactive scheduling of steelmaking-continuous casting with uncertain processing times under carbon emission reduction

To solve the proactive scheduling problem of steelmaking-continuous casting with uncertain processing time, a fuzzy scheduling model is established to minimize the total completion time, maximum elapsed time, and carbon emission, considering machine energy consumption. An improved multi-objective beluga whale optimization algorithm (MOBWO-VNS) is proposed to solve it. In MOBWO-VNS, the process-machine matching rule is used to enhance the quality of initial solutions, an adaptive layered evolution strategy is designed to improve the convergence speed, and a variable neighborhood search strategy is introduced to strengthen the algorithm's local search capability. The diversity and convergence of the algorithm are verified by the benchmark function. A comparison experiment between deterministic scheduling and fuzzy scheduling is carried out using the actual production data of a steel plant, and the feasibility and robustness of fuzzy scheduling are verified. Large-scale scheduling evaluation experiments are designed using large-scale data, and the results show that the proposed model and algorithm reduce the total completion time, maximum elapsed time, and carbon emissions by 7.6 %, 19.2 %, and 2.2 %, respectively. Results show that this study can optimize the time and energy consumption targets, improve the production efficiency of enterprises, and provide strong support for the green transformation of steel enterprises.

Proximal Policy Optimization with Population-based Variable Neighborhood Search Algorithm for Coordinating Photo-Etching and Acid-Etching Processes in Sustainable Storage Chip Manufacturing

In the complex process of manufacturing storage chips, the photo-etching and acid-etching stages play a crucial role, significantly affecting energy consumption and environmental impact. This paper introduces a novel Bi-Level Programming Model for Storage Chip Manufacturing (BLPM-SCM) aimed at optimizing the coordination between these two stages. The upper-level model focuses on minimizing the time it takes to complete wafer production, while the lower-level model seeks to reduce the number of acid-etching tanks used, thereby balancing production efficiency with resource utilization. To address the inherent complexity of the bi-level model, we present a hybrid meta-heuristic algorithm that combines Proximal Policy Optimization (PPO) with a Population-based Variable Neighborhood Search (PVNS) method. The PPO-PVNS algorithm enhances the intensification phase by adaptively selecting shaking and local search strategies, while PVNS supports the diversification phase, ensuring comprehensive exploration of the search space through iterative updates of the solution population. Extensive numerical experiments demonstrate the algorithm's superior performance and generalization capabilities in optimizing the manufacturing process. It significantly improves the coordination between the photo-etching and acid-etching stages, achieving dual optimization of energy consumption and environmental benefits. Furthermore, this study provides valuable insights and decision-making tools for industry practitioners, offering innovative solutions for scheduling optimization in the semiconductor sector and promoting more sustainable and efficient production practices.

Improved Whale Optimization Algorithm with Variable Neighbourhood Search Strategy (WOA-VNS) in Solving Vehicle Routing Problem (VRP) for Recommending Multi-days Tourist Routes in Yogyakarta

Improved Whale Optimization Algorithm with Variable Neighbourhood Search Strategy (WOA-VNS) in Solving Vehicle Routing Problem (VRP) for Recommending Multi-days Tourist Routes in Yogyakarta

VNS-BA*: An Improved Bidirectional A* Path Planning Algorithm Based on Variable Neighborhood Search.

The A* algorithm is an effective method for path planning; however, it has certain drawbacks, such as a high number of turns, low planning efficiency, and redundant searches. To address these issues, this paper proposes an improved bidirectional A* global path planning algorithm based on a variable neighborhood search strategy, named VNS-BA*. The new algorithm first employs an 8-11-13 neighborhood search method for node expansion. Then, the bidirectional search strategy is optimized by using the current nodes of the opposite path and the global target point, enabling the two paths to meet in the middle of the map. Finally, redundant turns are removed from the path, and cubic spline interpolation is applied to achieve local smoothing at the turns. The effectiveness of the improved algorithm was validated on different maps and compared with A* and its three derived improved versions. The simulation results indicate that VNS-BA* shows significant improvements in terms of the number of path turns, turn angles, and planning efficiency.

Fuzzy flexible job shop dynamic scheduling considering machine remaining processing capacity

Dynamic fuzzy flexible job shop scheduling (DFFJSP) is significant in the medical equipment industry. Generally the dynamic flexible job shop scheduling problem considers a single dynamic factor or ignores resources such as machine itself also plays a huge role in dealing dynamic issues. Thus fuzzy processing time and machine breakdowns are considered in this paper. In order to copy with two problems mentioned above, the model of DFFJSP containing two objectives of makespan and energy consumption is established. To solve this problem, the remaining processing capacity of broken machine is applied to weaken the impacts of machine breakdowns and a multi-objective evolutionary algorithm (NG-WOA) is proposed, which integrating NSGA-II and whale optimal algorithm (WOA). Furthermore, the joining of variable neighborhood search makes NG-WOA skip the local optimum solution in time. Through experiments, the validity of remaining processing capacity is verified in rescheduling scheme. Then NG-WOA algorithm is proven can find better solutions when compared with other two algorithms according to the distribution of pareto forefront solutions in benchmark examples. The results of this paper show that the remaining processing capacity has greater advantages in guaranteeing the stability of dynamic scheduling problems, because the machine’s processing capacity can be utilized fully compared to previous strategies for fault disturbances.

Open shop scheduling with group and transportation operations by learning-driven hyper-heuristic algorithms

Open shop scheduling problems (OSSPs) are complex scheduling problems, which have been extensively studied in the literature. Group and transportation activities are two important aspects of OSSPs that still need attention. This work considers an OSSP with group and transportation operations to minimize maximum completion time by solving three key sub-problems: job assignment among groups, job sequence in groups and group sequence on machines. Firstly, an integer programming model is formulized to define the problem. Secondly, a learning-driven hyper-heuristic algorithm is developed by incorporating a Q-learning method and four meta-heuristics, i.e., genetic algorithm, artificial bee colony optimization, variable neighborhood search method and Jaya algorithm. The Q-learning method is devised to select the most promising meta-heuristic for performing at each iteration. Three neighborhood structures are designed by integrating critical machines and critical paths. Finally, the developed model is verified by an exact solver CPLEX, and the comparison results exhibit that CPLEX is effective for instances with ten jobs. For the instances with more than ten jobs, the developed algorithm wins CPLEX in terms of computation accuracy and efficiency, signifying its excellent performance in finding better solutions. Furthermore, four meta-heuristics mentioned above and three state-of-the-art meta-heuristics are employed for comparisons in solving a set of benchmark test instances. The results confirm that the formulated model and algorithm have stronger competitiveness in handling the considered problems.

Changeover minimization in the production of metal parts for car seats

We tackle a capacitated lot-sizing and scheduling problem (CLSP) with the main objective of minimizing changeover time in the production of metal parts for car seats. Changeovers occur when a machine (or production line) is reconfigured to produce a different product or part, leading to production downtime and loss of efficiency. In this study, we first provide a mixed-integer programming (MIP) formulation of the problem. We test the limits of solving the problem with commercial mathematical programming software. We also propose two approaches to tackle instances found in practice for which the mathematical programming model is not a viable solution method. Both approaches are based on partitioning the entire production of a part into production runs (or work slots). In the first approach, the work slots are assigned to machines and sequenced by a metaheuristic that follows the search principles of the GRASP (greedy randomized adaptive procedure) and VNS (variable neighborhood search) methodologies. In the second approach, we develop a Hexaly Optimizer (formerly known as LocalSolver) model to assign and sequence work slots. The study provides insights into how to minimize changeovers and improve production efficiency in metal parts manufacturing for car seats. The findings of this study have practical implications for the auto-part manufacturing industry, where efficient and cost-effective production is critical to meet the demands of the market.