Adaptive Variable Neighborhood Search Research Articles

Utilizing Heuristics and Metaheuristics for Solving the Set Covering Problem

A basic combinatorial optimization problem, the Set Covering Problem (SCP) finds extensive use in computer science, operations research, and logistics, among other domains. The SCP’s goal is to determine the smallest number of subsets, or sets, needed to cover every element precisely once given a finite set of items and a collection of subsets of these elements. Numerous practical uses for the SCP exist, such as crew scheduling, truck routing, and facility locating. This paper focuses on obtaining feasible solutions, applying to the obtained solutions constructive heuristics (CH), followed by a redundancy elimination procedure to remove unnecessary sets. To further optimize the quality of the solution, a local search method is also implemented based on the First and Best improvement algorithms. Additionally, the Greedy Randomized Adaptive Search Procedure (GRASP) and Variable Neighborhood Search (VNS) metaheuristics are designed and implemented. Each implemented heuristic underwent testing across 42 instances, with the average deviation from the optimal solution calculated for each instance. The GRASP heuristic demonstrated the most favorable performance, achieving a maximum deviation of 2.26% from the optimal solution, while the VNS approach yielded a maximum deviation of 11.46% from the optimal solution at its best.

Utilizing Heuristics and Metaheuristics for Solving the Set Covering Problem

A basic combinatorial optimization problem, the Set Covering Problem (SCP) finds extensive use in computer science, operations research, and logistics, among other domains. The SCP’s goal is to determine the smallest number of subsets, or sets, needed to cover every element precisely once given a finite set of items and a collection of subsets of these elements. Numerous practical uses for the SCP exist, such as crew scheduling, truck routing, and facility locating. This paper focuses on obtaining feasible solutions, applying to the obtained solutions constructive heuristics (CH), followed by a redundancy elimination procedure to remove unnecessary sets. To further optimize the quality of the solution, a local search method is also implemented based on the First and Best improvement algorithms. Additionally, the Greedy Randomized Adaptive Search Procedure (GRASP) and Variable Neighborhood Search (VNS) metaheuristics are designed and implemented. Each implemented heuristic underwent testing across 42 instances, with the average deviation from the optimal solution calculated for each instance. The GRASP heuristic demonstrated the most favorable performance, achieving a maximum deviation of 2.26% from the optimal solution, while the VNS approach yielded a maximum deviation of 11.46% from the optimal solution at its best.

Adaptive variable neighborhood search algorithm with Metropolis rule and tabu list for satellite range scheduling problem

Efficient scheduling of measurement and control resources plays a critical role in successful satellite operations. The tremendous growth in the number of satellites in orbit exacerbates resource scarcity, further enhancing the significance of the satellite range scheduling problem (SRSP). In order to maximize the benefits of measurement and control tasks, we propose an innovative algorithm to solve the SRSP with numerous constraints. Firstly, the SRSP operation flow is analyzed to establish a constraint satisfaction model. A task-resource matching algorithm based on fitness is then designed to generate an initial feasible solution with superior quality by heuristic criteria. Subsequently, an adaptive variable neighborhood search algorithm with Metropolis rule and tabu list (AVNS-MT) is proposed to solve the mathematical model. Three swap neighborhood structures are constructed to explore the solution space efficiently during the variable neighborhood descent search process. Meanwhile, three migration neighborhood structures are devised to enable the shaking of solutions and evasion from the local optimum. Moreover, the incorporation of the Metropolis rule and tabu search strategy will contribute to enhancing the algorithm convergence. Finally, we have conducted extensive simulations to verify the effectiveness and efficiency of the proposed AVNS-MT. Comparison experiments with several state-of-the-art methods validate the superiority of the proposed algorithm.

The home health care routing with heterogeneous electric vehicles and synchronization

AbstractThis paper studies the problem of heterogeneous electric vehicles, fast chargers, and synchronized jobs that have time windows in home healthcare routing and scheduling. We consider a problem that aims to establish daily routes and schedules for healthcare nurses to provide a variety of services to patients located in a scattered area. Each nurse should be assigned to an electric vehicle (EV) from a heterogeneous fleet of EVs to perform the assigned jobs within working hours. We consider three different types of EVs in terms of battery capacity and energy consumption. We aim to minimize the total cost of energy consumption, fixed nurse cost, and costs arising from the patients that cannot be served within the working day. We model the problem as a mixed integer programming formulation. We develop a hybrid metaheuristic based on a greedy random adaptive search procedure heuristic, to generate good quality initial solutions quickly, and an adaptive variable neighborhood search algorithm to generate high quality solutions in reasonable time. The hybrid metaheuristic employs a set of new advanced efficient procedures designed to handle the complex structure of the problem. Through extensive computational experiments, the performance of the mathematical model and the hybrid metaheuristic are evaluated. We conduct analyses on the robustness of the metaheuristic and the performance contribution of employing adaptive probabilities. We analyze the impact of problem parameters such as competency requirements, job duration, and synchronized jobs.

The pollution traveling salesman problem with refueling

This study presents the Pollution Traveling Salesman Problem with Refueling, a novel optimization problem which integrates two recently proposed variants of the Traveling Salesman Problem: the Pollution Traveling Salesman Problem and the Traveling Salesman Problem with Refueling. The proposed problem captures the operational dynamics of a real-world routing scenario involving a single vehicle originating from a central depot and delivering products to end customers. When considering the vehicle’s fuel tank capacity and fuel consumption during the routing process, the need to visit fuel stations for refueling arises. To address this complex problem, a new mixed integer linear programming model was developed, and the Gurobi solver was employed to solve smaller instances. For the effective resolution of larger practical problem cases, a two-stage double adaptive general variable neighborhood search method was proposed. The proposed methodology exhibits comparable efficiency to a commercial solver, demonstrating notably low execution time requirements. To further assess its performance, a comparative study was conducted on TSPLib instances. In comparison to various solution approaches documented in the open literature, encompassing both Variable Neighborhood Search-based and alternative methods, our proposed approach consistently yields highly competitive results within low execution times.

Hybrid truck-drone delivery system with multi-visits and multi-launch and retrieval locations: Mathematical model and adaptive variable neighborhood search with neighborhood categorization

Drones have recently been suggested as a means of performing last-mile deliveries, as they have several advantages compared to traditional delivery vehicles. A recent research avenue is to adopt a hybrid truck-drone delivery system that integrates drones with traditional delivery methods such as trucks. This paper deals with the problem of optimizing the delivery operation of a truck working in tandem with a drone capable of visiting multiple customers per dispatch. We also introduce practical attributes such as allowing the truck to launch and retrieve the drone from both customer and non-customer nodes as well as permitting cyclic and acyclic drone operations. An integer linear programming model is first formulated followed by the development of an effective variable neighborhood search (VNS)-based approach. The novelty of the latter is that it incorporates an effective categorisation of neighborhoods due to their large number that is needed while retaining their individual impact through an adaptive selection scheme. The performance of this powerful VNS-based heuristic is empirically assessed against three variants of the VNS. The VNS heuristic was also shown to be flexible and effective at handling the issue of synchronization. A sensitivity analysis, based on some of the critical parameters of the drone, is conducted alongside highlights of some interesting insights.

Vehicle routing problem with time windows and carbon emissions: a case study in logistics distribution.

Logistics and transportation industry is not only a major energy consumer, but also a major carbon emitter. Developing green logistics is the only way for the sustainable development of the logistics industry. One of the main factors of environmental pollution is caused by carbon emissions in the process of vehicle transportation, and carbon emissions of vehicle transportation are closely related to routing, road conditions, vehicle speed, and speed fluctuations. The low-carbon vehicle routing problem with high granularity time-dependent speeds, speed fluctuations, road conditions, and time windows is proposed and formally described. In order to finely evaluate the effects of vehicle speed and speed fluctuations on carbon emissions, a graph convolutional network (GCN) is used to predict the high granularity time-dependent traffic speeds. To solve this complicated low-carbon vehicle routing problem, a hybrid genetic algorithm with adaptive variable neighborhood search is proposed to obtain vehicle routing with low carbon emissions. Finally, this method is validated using a case study with the logistics and traffic data in Jingzhou, China, and also the results show the effectiveness of this proposed method.

Synchronizing delivery and installation with vehicle sharing: A hybrid adaptive large neighborhood search

This paper presents the real-life synchronized delivery and installation with vehicle sharing problem (SDIVSP). Two fleets of vehicles serve a set of customers within their specified time windows. Delivery vehicles drop products to customers while installation vehicles drop and pick up technicians without necessarily waiting for them. Delivery must precede installation. This paper models SDIVSP as a mixed integer linear program, which solves small-sized instances. For large instances, this paper proposes a heuristic HALNS that hybridizes adaptive large neighborhood search and variable neighborhood search. Extensive experimentation provides computational evidence of the superiority of HALNS when solving well-known benchmark instances of (synchronized) vehicle routing problems with time windows and its effectiveness in tackling newly proposed SDIVSP instances. HALNS outperforms two state-of-the-art algorithms by an average 6.41% and 12.43% on synchronized vehicle routing with time windows benchmark sets. It further provides computational evidence of the benefits of shared installation vehicles: Total cost decreases by 41.72% and 35.35% as the installation vehicle capacity increases for tight and large time windows respectively.

Variable Neighborhood Search Algorithm for the Single Assignment Incomplete Hub Location Problem with Modular Capacities and Direct Connections

In distribution systems such as airlines and express package delivery, the use of hub-and-spoke networks is common, and flow consolidation at hub facilities is essential for cost reduction. While a constant discount factor is typically used to model cost reduction in interhub links, this paper explores an extension of the incomplete hub location problem with modular capacity that enables direct connections between non-hub nodes. The modified approach, called MHLPDC, aims to locate a set of hub facilities, connect each non-hub node to a hub, and activate hub facility links, access arc links, and direct links between non-hub nodes to minimize network costs. The MHLPDC integrates link activation decisions into the decision-making process and utilizes modular arc costs to model the flow dependence of transportation costs in all arcs. To solve the problem, the paper presents a mixed-integer mathematical programming formulation and heuristic algorithm based on a greedy randomized adaptive search and variable neighborhood search approach. The proposed algorithm produces high-quality solutions, as demonstrated through computational experiments on benchmark instances with up to 40 nodes. Furthermore, a sensitivity analysis of the optimal network structure indicates that increasing the discount factor, by varying hub and access arc capacities as well as the associated variable costs, results in fewer hubs being established and more direct shipments between non-hub nodes being permitted.

Effective and Interpretable Rule Mining for Dynamic Job-Shop Scheduling via Improved Gene Expression Programming with Feature Selection

Gene expression programming (GEP) is frequently used to create intelligent dispatching rules for job-shop scheduling. The proper selection of the terminal set is a critical factor for the success of GEP. However, there are various job features and machine features that can be included in the terminal sets to capture the different characteristics of the job-shop state. Moreover, the importance of features in the terminal set varies greatly between scenarios. The irrelevant and redundant features may lead to high computational requirements and increased difficulty in interpreting generated rules. Consequently, a feature selection approach for evolving dispatching rules with improved GEP has been proposed, so as to select the proper terminal set for different dynamic job-shop scenarios. First, the adaptive variable neighborhood search algorithm was embedded into the GEP to obtain a diverse set of good rules for job-shop scenarios. Secondly, based on the fitness of the good rules and the contribution of features to the rules, a weighted voting ranking method was used to select features from the terminal set. The proposed approach was then compared with GEP-based algorithms and benchmark rules in the different job-shop conditions and scheduling objectives. The experimentally obtained results illustrated that the performance of the dispatching rules generated using the improved GEP algorithm after the feature selection process was better than that of both the baseline dispatching rules and the baseline GEP algorithm.

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.

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.

An Improved Sparrow Search Algorithm for Solving the Energy-Saving Flexible Job Shop Scheduling Problem

Due to emerging requirements and pressures related to environmental protection, manufacturing enterprises have expressed growing concern for adopting various energy-saving strategies. However, environmental criteria were usually not considered in traditional production scheduling problems. To overcome this deficiency, energy-saving scheduling has drawn more and more attention from academic scholars and industrial practitioners. In this paper, an energy-saving flexible job shop scheduling problem (EFJSP) is introduced in accordance with the criterion of optimizing power consumption and processing costs simultaneously. Since the classical FJSP is strongly NP-hard, an Improved Sparrow Search Algorithm (ISSA) is developed for efficiently solving the EFJSP. In the ISSA, a Hybrid Search (HS) method is used to produce an initial high-quality population; a Quantum Rotation Gate (QRG) and a Sine–Cosine Algorithm (SCA) are integrated to intensify the ability of the ISSA to coordinate exploration and exploitation; the adaptive adjustment strategy and Variable Neighborhood Search (VNS) are applied to strengthen diversification of the ISSA to move away from local optima. Extensive computational experiments validate that the ISSA outperforms other existing algorithms in solving the EFJSP due to the advantages of intensification and diversification mechanisms in the ISSA.

A customer-oriented method to support multi-task green scheduling with diverse time-of-use prices in Cloud Manufacturing

Green manufacturing has become a hot topic globally, and Cloud Manufacturing (CMfg) provides a novel approach to support green manufacturing through manufacturing services (MS) composition. In this study, we design a customer-oriented method for supporting multi-task green scheduling in CMfg. First, we aim to minimize the total energy consumption during scheduling. Second, because CMfg is a type of customer-oriented manufacturing, the just-in-time objective is used to meet the customers on-time requirements. Subsequently, we study the different time-of-use prices of MS in CMfg. The price of utilizing MS is related not only to cost but also to the supply-demand relationship, which results in diverse time-of-use prices for MS. After establishing the scheduling model, a hybrid artificial bee colony algorithm is designed to solve the scheduling model. For the algorithm, we design a guiding mechanism to enhance the global search ability and an adaptive variable neighborhood search for improving the local search ability. To verify the performance of our algorithm, we compared it with similar algorithms, and the results indicate the high-level performance of our work.

A two-echelon fuzzy clustering based heuristic for large-scale bike sharing repositioning problem

This paper considers the large-scale bike sharing repositioning problem (BSRP) frequently encountered in modern bike sharing systems. To cope with customer demand fluctuations, BSRP aims to identify the optimal routes traveled by homogeneous vehicles to fulfill the inventory needs at each bike-sharing station in order to minimize the total cost. It is computationally intractable to obtain promising solutions, especially for large-scale instances, given its NP-hardness. This paper adapts the two-echelon structure from the vehicle routing problem (VRP) to BSRP, proposes the two-echelon BSRP model and demonstrates its competitiveness. First, a novel fuzzy clustering strategy quantitatively considering the correlation between stations is designed to construct the clusters with satellites and their corresponding customers to form the two-echelon structure. Then, a tailored fuzzy correlation based adaptive variable neighborhood search (FC-AVNS) with newly designed neighborhood structures and several feasibility and satisfaction check mechanisms is proposed to construct the routes within and between the clusters. Performance of the proposed method is compared with that of a exact model solved by CPLEX and other three state-of-the-art methods. Also, comparisons are made between the presented fuzzy clustering strategy and the other two classical clustering methods taken from the literature. Computational experiments based on medium- and large-scale instances involving 100 to 519 stations are performed and the results validate the superior performance of the proposed method with respect to solution efficiency and stability.

Heuristic approaches for the car sequencing problems with block batches

Motivated by the practical supply chain management of the automobile industry, we study the car sequencing problem (CSP) that minimizes the conflicts occur when sequentially manufacturing cars on an assembly line. The CSP is a well-established problem, subject to the paint batching constraints to decrease the energy consumption for color changeovers and production rate constraints in the assembly shop to ensure a smooth usage of car options. However, the existing solution algorithms to this problem do not take into account the block batches, which desires a consecutive production batch of cars requiring a certain option. This requirement often occurs when specialized labor time window is short in the customized car production scenario, and renders additional complexities to the traditional car sequencing problem. In this paper, we present a novel model to deal with these constraints and simultaneously generate the sequencing and replenishment decisions. Besides, we develop two math-heuristic algorithms to solve the proposed large-scale CSP. The presented heuristics are on the basis of relax-and-fix procedures, fix-and-optimize procedures and adaptive variable neighborhood search. To solve the large-sized instances (commercial solvers, i.e., Cplex, cannot obtain a feasible result within 1 h), we design and implement a reinforced parameter tuning mechanism to dynamically select the parameter values, so as to speed up the search process. The proposed models and heuristics are tested on representative instances generated from the benchmark in the literature (CSPLib), as well as large-sized instances generated from real-world cases. We report on extensive computational experiments and provide basic managerial insights into the planning process.

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.

Interrelated trips in the rural dial-a-ride problem with autonomous vehicles

Nowadays, the rural population is still dependent on motorized individual transportation due to the little offers of public transport there. Autonomous vehicles have the potential to close this mobility gap as shifting the task of driving from humans to machines facilitates new possibilities for vehicle sharing and lifts economical and service time limitations (e.g., labor costs and working hour regulations). However, mobility service operators are then probably responsible for serving the holistic travel demands of users. This might involve interrelated trips, where users ask for simultaneous arrival at meeting locations, where round trips involve a stay time at some destination locations, or the like. Accordingly, in this work, we present a problem variant of the dial-a-ride problem that allows for interrelated trips. We formulate the problem as a mixed-integer program and propose an adaptive variable neighborhood search heuristic (AVNS) based on a sophisticated solution representation. Our computational results for instances considering characteristics of rural areas reveal that the heuristic performs very well and that it is clearly superior to standard MIP solvers. We further investigate the impact of different types of trip interrelations on the solvability of the problem, service quality, and total transportation costs of the solutions.

HA-CCP: A Hybrid Algorithm for Solving Capacitated Clustering Problem.

The capacitated clustering problem (CCP) divides the vertices of the undirected graph into several disjoint clusters so that the sum of the node weights in each cluster meets the capacity limit while maximizing the sum of the weight of the edges between nodes in the same cluster. CCP is a typical NP-hard problem with a wide range of engineering applications. In recent years, heuristic algorithms represented by greedy random adaptive search program (GRASP) and variable neighborhood search (VNS) have achieved excellent results in solving CCP. To improve the efficiency and quality of the CCP solution, this study proposes a new hybrid algorithm HA-CCP. In HA-CCP, a feasible solution construction method is designed to adapt to the CCP with stricter upper and lower bound constraints and an adaptive local solution destruction and reconstruction method is designed to increase population diversity and improve convergence speed. Experiments on 90 instances of 4 types show that the best average solution obtained by HA-CCP on 58 instances is better than all comparison algorithms, indicating that HA-CCP has better solution stability. HA-CCP is also superior to all comparison algorithms in average solving efficiency.

A new hybrid matheuristic of GRASP and VNS based on constructive heuristics, set-covering and set-partitioning formulations applied to the capacitated vehicle routing problem

This paper develops a hybrid matheuristic in two stages to solve Capacitated Vehicle Routing Problem (CVRP) by applying Greedy Randomized Adaptive Search Procedure (GRASP), mathematical models and Variable Neighborhood Search (VNS). The CVRP consists of designing a set of routes for a fleet of identical vehicles to attend a set of customers at shortest distance traveled. In the proposed method, a routing is performed using constructive heuristics and the Set-covering problem (SCP). SCP employs local optima solutions found in previous iterations of VNS to create a partial tour which is filled by a constructive heuristic if needed. Then, the built solution undergoes a local search phase by VNS. This process is repeated as the main loop of the GRASP. As last step of the method, the Set-partitioning problem (SPP) provides a new improved solution with regard to solutions found in the GRASP. We tested our algorithm with seven benchmarks and compared it with some other heuristics in the literature. Computational experiments showed that the proposed algorithm is competitive in terms of the quality of the solutions reported in recent works.