Hybrid Variable Neighborhood Search Research Articles

A stochastic hierarchical approach for the master surgical scheduling problem

For operating rooms in a hospital, the Master Surgical Scheduling Problem concerns the assignments of surgeons to time blocks over a planning horizon. This paper contributes mathematical models for this problem that consider multiple stakeholders and human and physical resources, including surgeons, machines, operating rooms, recovery ward beds, and patients. The models meet external waiting time targets, minimize differences between the actual and target number of patients, maximize the utilization of operating rooms, minimize variations in the assignments of surgeons to both weekdays and operating rooms, minimize the total number of expected patients in the recovery ward, and minimize variations in the recovery ward utilization. In addition to exact methods, hybrid variable neighbourhood search - genetic algorithm and late acceptance hill climbing heuristics are used to obtain solutions. Rival models from the literature are compared to this approach. Results from numerical experiments show that it is possible to develop master surgical schedules that achieve these goals while outperforming the rival models.

A hybrid variable neighborhood search approach for the multi-depot green vehicle routing problem

The Multi-Depot Green Vehicle Routing Problem (MDGVRP) is an extension of the well-known Green Vehicle Routing Problem (GVRP) where a fleet of alternative fuel-powered vehicles (AFVs) are used to serve the customers. GVRP consists of determining AFV tours such that the total distance travelled is minimum. The AFVs depart from the depot, serve a set of customers, and complete their tours at the depot without exceeding their driving range and the maximum tour duration. AFVs may refuel en-route at public refueling stations. In MDGVRP, the AFVs are dispatched from different depot locations and may refuel during the day at any depot or refueling station. We formulate MDGVRP as a mixed integer linear programming model and develop a hybrid General Variable Neighborhood Search and Tabu Search approach by proposing new problem-specific neighborhood structures to solve the problem effectively. We assess the performance of our method using the GVRP dataset from the literature. Our results show that the proposed method can provide high quality solutions in short computation times. Then, we extend these instances to the multi-depot case and compare our solutions for small-size instances with the optimal solutions. We also report our results for large-size problems and investigate the trade-offs associated with operating multiple depots and adopting different refueling policies to provide further insights for both academicians and practitioners.

Minimizing maximum tardiness on a single machine with family setup times and machine disruption

Due to the complexity of manufacturing processes, many industries today try to group their production components into families and use a common setup time to process every family. Also, the failure of machinery has an important impact on the planning of production systems. This paper deals with the problem of single machine scheduling with family setup times and randomly machine breakdown. It is assumed that there is disruption along the planning horizon with uncertain start and duration times based on a specific probability distribution function. The goal is to minimize the maximum expected tardiness. For this problem, a hill climbing based heuristic (HCO) and a novel hybrid variable neighborhood search metaheuristic (HVNS) have been developed. A branch and bound (BB) procedure is also proposed to optimally solve this problem using HCO and HVNS algorithms to derive upper bounds. Comparison of the solutions obtained from the presented algorithms with the mathematical programming model of the problem in small-scale instances shows that the solutions obtained from the proposed algorithms have a good quality in terms of the expected value of the objective function and the solving time. The computational results for executing the proposed algorithms on 36 series of various instances show that the BB procedure is able to solve 97.76% of the instances within the specified time frame and HVNS metaheuristic is capable to solve 41.07% of them, optimally. Also, the maximum mean deviation of HVNS solutions from the optimal solution is reported below 5% for hard instances and below 15% for instances with medium complexity. After performing a non-parametric hypothesis test, it is found that at a confidence level 99.9%, the deviation index for HVNS is less than 1.5% for difficult problems and less than 9% for semi-difficult ones. Finally, the results of solving large scale instances, demonstrate the efficiency of proposed metaheuristic.

Just-in-time scheduling for a distributed concrete precast flow shop system

This paper focuses on the distributed concrete precast flow shop scheduling problem to minimize total weighted earliness and tardiness. It is crucial for a precast manufacturer to schedule jobs effectively to meet shipping dates because of tight due date, limited inventory capacity and huge tardiness penalties. In order to respond quickly to customer demands, many concrete precast manufacturers have adopted the distributed-multiple-factory mode in which job assignment and scheduling have to be decided jointly. To solve this problem, through analyzing the characteristics of distributed precast production, we first develop a novel mixed integer nonlinear programming (MINLP) model and then transform it into an effective mixed integer linear programming (MILP) model by linearization techniques. Additionally, since the problem is more complex than the classical distributed flow shop scheduling problem, which is NP-hard in most cases, we propose a hybrid iterated greedy algorithm (HIG) by integrating due date related NEH-based heuristics, problem-specific knowledge, different local search methods, and mechanism of destruction and reconstruction. Subsequently, we propose a hybrid tabu search and iterated greedy (HTS_IG) in which a hybrid tabu search (HTS) is run at first and then an iterated greedy (IG) starts from the best solution obtained by HTS. Aimed at improving search efficiency, some structural properties of the schedules are explored and integrated into the local search steps of HIG and HTS_IG. We also develop a hybrid genetic algorithm and variable neighborhood search (HGA_VNS) and a two-phase heuristic method (TPHM) for comparison. Finally, extensive experiments and deep analysis are conducted on instances with different combination of problem parameters. Computational results show the effectiveness of the MILP model and the proposed algorithms. The computational analysis indicates that, on average, HTS_IG performs best among all the proposed metaheuristics. The effectivenesses of local search based on problem-specific knowledge (PSK) in HIG and HTS_IG are also verified.

Hybrid Variable Neighborhood Search for Multiple Maximum Scatter Traveling Salesperson Problems

Hybrid Variable Neighborhood Search for Multiple Maximum Scatter Traveling Salesperson Problems

An improved non-dominated sorting biogeography-based optimization algorithm for the (hybrid) multi-objective flexible job-shop scheduling problem

With the continuous advancement of intelligent manufacturing and industry 4.0, production scheduling has become a significant problem that most enterprises must deal with. Thereinto, (hybrid) multi-objective flexible job-shop scheduling problem, widely existing in the real-life manufacturing systems, is one of the NP-hard problems in various scheduling problems. Consequently, in this paper, an improved non-dominated sorting biogeography-based optimization (INSBBO) algorithm has been proposed to solve the problem. First of all, to overcome the pressure scarcity of individual selection in the Pareto dominance principle, especially in the late iteration of the algorithm, a novel V-dominance principle based on the volume enclosed by the normalized objective function values has been developed to enhance the convergence speed. Then, a hybrid variable neighborhood search (HVNS) structure is designed as a local search algorithm to amend the local search ability. Thereafter, for avoiding the loss of the partial (sub-)optimal solutions in the iteration, an elite storage strategy (ESS) is constructed to store the (sub-)optimal solutions. Additionally, we modify the internal habitat suitability index (HSI), migration and mutation operators of the NSBBO algorithm to further improve its performance. To evaluate the effectiveness of the above improved operations and the robustness of parameter setting, we compare the performances of each modified operation and critical parameter combination through multiple independent running the typical scheduling instance from the literature. The statistical results exhibit that each amended operation has a significant influence on the performance of INSBBO and its key parameter configuration is robust. Meanwhile, INSBBO has a better or similar performance among other state-of-the-art intelligent algorithms by comparing three classical benchmark scheduling datasets.

Hybrid VNS–LP algorithm for online optimal coordination of directional overcurrent relays

Optimal coordination of directional overcurrent relays (DOCRs) in interconnected power systems is a highly constrained, non-convex and non-linear optimisation problem. In this study, use of a series of linear programming (LP) problems in a variable neighbourhood search (VNS) framework is proposed, in which pickup current settings can be considered either as continuous or discrete variables. Therefore, the proposed hybrid algorithm (VNS–LP) is suitable for coordination problem-solving in a network with different types of DOCRs. Furthermore, two versions of the VNS algorithm are proposed, the first of which is very easy to implement, while, the other is somewhat more sophisticated, and at the same time much faster and possibly suitable for online coordination in smart grids applications. One advantage of the second algorithm is that it relies only on elementary arithmetic and requires low RAM, which makes it implementable in any low-level programming environment. This, in turn, can increase the interoperability, which is of crucial importance when automating tasks. The efficiency of the proposed algorithm was investigated in several test systems. Numerical results indicate that the two proposed approaches outperform the previous methods. Moreover, the coordination problem is solved in a reasonably short time using a faster approach.

A hybrid DBH-VNS for high-end equipment production scheduling with machine failures and preventive maintenance activities

The high-end equipment features with high value, complicated manufacturing process, and high status, and it thus brings a huge challenge to increase reliability, quality, and productivity during the production. In order to tackle this challenge and achieve automation, integration, and intelligence this paper proposes a hybrid metaheuristic for an integrated order scheduling and maintenance planning model with position-based processing time, parallel-batching processing, and multiple manufacturers. During the production, the continuous operation of the machine increases the probability of failure, and the repair work can eliminate the failure For each order, we derive some useful lemmas and develop an optimal algorithm to schedule jobs within it. Then, given the order assignment and sequence in the manufacturers, we propose a dynamic programing algorithm to make the decision on the maintenance planning. Subsequently, the investigated problem is proved to be NP-hard, thus, we propose a hybrid discrete black hole algorithm and variable neighborhood search (DBH-VNS) approach to solve the integrated problem. Some improvements are integrated into the proposed algorithm to obtain the competitive results, which include discrete encoding-based population updating scheme, the modified neighborhoods, and the VNS-based local search. Finally, we conduct computational experiments and the results demonstrate the effectiveness and validity of the proposed hybrid metaheuristic.

Two calibrated meta-heuristics to solve an integrated scheduling problem of production and air transportation with the interval due date

Contrary to previous methods in production management, today’s approaches mainly focus on the whole supply chain parties’ considerations. Considering production planning and distribution, as the two main functions in supply chain (SC) management, in an integrated manner in order to enhance the SC advantages is one of today’s main dilemma. Here, we have firstly proposed and investigated the integrated production and air transportation scheduling problem with time windows for the due date to minimize the total SC costs. Since the problem was NP-hard, two new coordinated and integrated solution procedures have been presented based on meta-heuristics. Four algorithms (i.e., simulated annealing (SA), genetic algorithm, particle swarm optimization/district PSO (PSO/DPSO), and hybrid variable neighborhood search–simulated annealing (H-VNS–SA)) have been developed in both procedures. For the first time in literature, we probe different encoding schemes in the proposed algorithms. In addition, by using Taguchi experimental design, the parameters of the algorithms have been tuned. Besides, to study the behavior of the algorithms, different problem sizes have been generated and the results of two procedures have been compared together and discussed. Finally, a comparison of the proposed algorithms with some state-of-art optimized algorithms has been presented to prove statistically better performance of the proposed algorithms in most cases.

A VNS-EDA Algorithm-Based Feature Selection for Credit Risk Classification

Many quantitative credit scoring models have been developed for credit risk assessment. Irrelevant and redundant features may deteriorate the performance of credit risk classification. Feature selection with metaheuristic techniques can be applied to excavate the most significant features. However, metaheuristic techniques suffer from various issues such as being trapped in local optimum and premature convergence. Therefore, in this article, a hybrid variable neighborhood search and estimation of distribution technique with the elitist population strategy is proposed to identify the optimal feature subset. Variable neighborhood search with the elitist population strategy is used to direct its local searching in order to optimize the ergodicity, avoid premature convergence, and jump out of the local optimum in the searching process. The probabilistic model attempts to capture the probability distribution of the promising solutions which are biased towards the global optimum. The proposed technique has been tested on both publicly available credit datasets and a real-world credit dataset in China. Experimental analysis demonstrates that it outperforms existing techniques in large-scale credit datasets with high dimensionality, making it well suited for feature selection in credit risk classification.

A hybrid variable neighbourhood search and dynamic programming approach for the nurse rostering problem

Nurse Rostering is the activity of assigning nurses to daily shifts in order to satisfy the cover requirements, taking into account the operational requirements and nurses' preferences. The problem is usually modeled as sets of hard and soft constraints with an objective function to minimize violations of soft constraints. The nurse rostering problem is known to be NP-hard. Many metaheuristics were used to tackle this problem. One of the frequently used heuristics is the Variable Neighbourhood Search (VNS). The VNS is usually used as a standalone method or in integration with another exact or heuristic method. In this paper, a new hybrid VNS and Dynamic Programming based heuristic approach is proposed to handle the nurse rostering problem. In the proposed approach, two perturbation mechanisms are adopted simultaneously. The proposed approach is tested on two different benchmark data sets. A comparison with state-of-the-art methods from literature revealed the competitive performance of the proposed approach.

A Scalable Privacy Preserving Distributed Parallel Optimization for a Large-Scale Aggregation of Prosumers With Residential PV-Battery Systems

A novel scalable and privacy-preserving distributed parallel optimization that allows the participation of large-scale aggregation of prosumers with residential PV-battery systems in the market for the ancillary service (ASM) is proposed in this paper. To consider both reserve capacity and energy, day-ahead and real-time stages in the ASM are considered. A method based on hybrid Variable Neighborhood Search (VNS) and distributed parallel optimization is designed for the day ahead and real-time optimization. Different distributed optimization methods are compared and designed and a new distributed optimization method based on Linear Programming (LP) is proposed that outperforms previous methods based on integer and Quadratic programming (QP). The proposed LP-based optimization can be easily coded up and implemented on microcontrollers and connected to a designed Internet of Things (IoT) based architecture. As confirmed by simulation results, carried out considering different realistic case studies, both day-ahead and real-time proposed optimization methods, by allocating the computational effort among local resources, are highly scalable and fulfil the privacy of prosumers.

A Hybrid Water Flow-Like Algorithm and Variable Neighbourhood Search for Traveling Salesman Problem

Various metaheuristic methods have been proposed earlier and applied for solving the Travelling Salesman Problem (TSP). Water Flow Algorithm (WFA) is one of the recent population-based metaheuristic optimization techniques used for solving this problem. Past research has shown that improving WFA local search strategy has a significant impact on the algorithm performance. Therefore, this paper aims to solve TSP by enhancing WFA searching strategy based on a Variable Neighbourhood Search (VNS) known as hybrid WFA-VNS. It is a mixture of the exploration of WFA and the exploitation capability of VNS. This study is conducted in two stages: Pre-experiment and initial experiment. The objective of doing pre-experiment is to select four neighborhood structures to be used for the initial experiment. At the first stage, three instances are used, and there are five neighborhood structures involved. Those neighborhood structures are two opt, three opt, four opt, swapping, and insertion move. Because of pre-experiment, it discovers four best neighborhood structures, which are two opt, three opt, exchanging and insertion move. These neighborhood structures will be used in the initial experiment, which an improvement approach is employed. In an initial experiment, the performance of the proposed hybrid WFA-VNS is further studied and tested on 26 established benchmarked symmetric TSP datasets using four neighborhood structures selected in pre-experiment earlier. The TSP datasets involved are categorized into three types: small datasets, medium datasets, and large datasets. Selected neighborhood structures obtained in pre-experiment are applied and generated randomly to intensify the initial solution achieved at an earlier stage of hybrid WFA-VNS. The results of the comparison show that this hybrid approach represents an improvement and able to produce competitive results.

Hybrid Real-Coded Genetic Algorithm and Variable Neighborhood Search for Optimization of Product Storage

Agricultural product storage has a problem that need to be noticedbecause it has an impact in gaining the profit according to the number ofproducts and the capacity of storage. Inappropriate combination of productcauses high expenses and low profit. To solve the problem, we propose geneticalgorithm (GA) as the optimization method. Although GA is good enough tosolve the problem, GA not always gives an optimum result in complex searchspaces because it is easy to be trapped in local optimum. Therefore, we presenta hybrid real-coded genetic algorithm and Variable Neighborhood Search(HRCGA-VNS) to solve the problem. VNS is applied after reproductionprocess of GA to repair the offspring and improve GA exploitation capabilitiesin local area to get better result. The test results show that the optimal popsizeof GA is 180, number of generations is 80, combination of cr and mr is 0.7 and0.3 while optimum Kmax of VNS is 40 with number of iterations 50. Eventhough HRCGA-VNS need longer computational time, HRCGA-VNS hasproven to provide a better result based on higher fitness value compared withclassical GA and VNS.

Optimizing the Low-Carbon Flexible Job Shop Scheduling Problem with Discrete Whale Optimization Algorithm

The flexible job shop scheduling problem (FJSP) is a difficult discrete combinatorial optimization problem, which has been widely studied due to its theoretical and practical significance. However, previous researchers mostly emphasized on the production efficiency criteria such as completion time, workload, flow time, etc. Recently, with considerations of sustainable development, low-carbon scheduling problems have received more and more attention. In this paper, a low-carbon FJSP model is proposed to minimize the sum of completion time cost and energy consumption cost in the workshop. A new bio-inspired metaheuristic algorithm called discrete whale optimization algorithm (DWOA) is developed to solve the problem efficiently. In the proposed DWOA, an innovative encoding mechanism is employed to represent two sub-problems: Machine assignment and job sequencing. Then, a hybrid variable neighborhood search method is adapted to generate a high quality and diverse population. According to the discrete characteristics of the problem, the modified updating approaches based on the crossover operator are applied to replace the original updating method in the exploration and exploitation phase. Simultaneously, in order to balance the ability of exploration and exploitation in the process of evolution, six adjustment curves of a are used to adjust the transition between exploration and exploitation of the algorithm. Finally, some well-known benchmark instances are tested to verify the effectiveness of the proposed algorithms for the low-carbon FJSP.

Solving fuzzy capacitated location routing problem using hybrid variable neighborhood search and evolutionary local search

A fuzzy capacitated location routing problem (FCLRP) is solved by using a heuristic method that combines variable neighborhood search (VNS) and evolutionary local search (ELS). Demands of the customer and travel times between customers and depots are considered as fuzzy and deterministic variables, respectively in FCLRP. Heterogeneous and homogeneous fleet sizes are performed together to reach the least multi-objective cost in a case study. The multi-objective cost consists of transportation cost, additional cost, vehicle waiting cost and delay cost. A fuzzy chance constrained programming model is added by using credibility theory. The proposed method reaches the solution by performing four stages. In the first stage, initial solutions are obtained by using a greedy heuristic method, and then VNS heuristic, which consists of seven different neighborhood structures, is performed to improve the solution quality in the second stage. In the third stage, a perturbation procedure is applied to the improved solution using ELS algorithm, and then VNS heuristic is applied again in the last stage. The combination of VNS and ELS is called VNSxELS algorithm and applied to a case study, which has fifty-seven customers and five distributing points, effectively in a reasonable time.

A novel location-routing problem in electric vehicle transportation with stochastic demands

With the development of the electric vehicle (EV) technology, the electric vehicle routing problems (EVRPs) have become a current focus for research. Although customer demands in the logistics service industry are often uncertain during the route planning stage, these demands have seldom been discussed in the existing literature on the EVRPs. This study presents an electric vehicle battery swap station (BSS) location-routing problem with stochastic demands, with the aim to determine a minimum cost scheme including the optimal number and location of BSSs with an optimal route plan based on stochastic customer demands. Furthermore, the classical recourse policy and preventive restocking policy are extended by considering the influences of both battery and vehicle capacity simultaneously. Subsequently, the concept of Pareto optimality is applied to the EVRP to expedite the selection of BSS sequences. To solve such a hybrid problem, a hybrid variable neighborhood search (HVNS) algorithm is proposed, which integrates the binary particle swarm optimization and variable neighborhood search to solve the location and routing problems interactively. In experimental studies, the HVNS is compared to five heuristic algorithms to verify its performance.

An integrated disaster relief model based on covering tour using hybrid Benders decomposition and variable neighborhood search: Application in the Iranian context

This research developed an integrated model for relief operations in critical situations. The model is aimed at minimizing the late arrival of relief vehicles that cross points en route to disaster locations. It locates temporary relief centers in affected areas and accordingly allocates and routes the first-aid commodities required by the centers. Vehicle routing in the model is underlain by the covering tour approach given that such method considerably increases the operational speed of a disaster logistics system, especially in terms of dispatching vehicles that carry essential commodities. Under the approach, vehicles pass through a small number of points where relief centers are established as temporary facilities. The model solves the issue of late arrival through hybrid benders decomposition and variable neighborhood search. The numerical results of application in Iran demonstrated the efficiency, quality, and speed of the proposed model.

Outsourcing and rescheduling for a two-machine flow shop with the disruption of new arriving jobs: A hybrid variable neighborhood search algorithm

This paper addresses the two-machine flow shop outsourcing and rescheduling problem (TFSORP) in response to an unexpected arrival of new jobs, in which each job can be processed in the in-house shop or outsourced to a single subcontractor. An efficient schedule is constructed for the in-house jobs, and its performance is measured by the makespan. Each of the outsourced jobs requires paying an outsourcing cost. The objective is to minimize the sum of the in-house makespan and total outsourcing cost, subject to a limit on the number of original jobs processed by the subcontractor after disruption. To solve this NP-hard problem, a mixed integer programming formulation and helpful optimization properties are first established, and then a hybrid variable neighborhood search algorithm (HVNS) that incorporates one-dimensional array representation and three problem-specific neighborhood structures is developed. At the initialization stage, either of two well-designed constructive heuristics, i.e., job addition heuristic (JAH) and job removal heuristic (JRH) is employed. At the iterative search stage, an adaptive best-improvement procedure based on three neighborhood structures is devised to play the role of local search. An extensive experimental calibration for main factors in HVNS is carried out by a full-factorial design of experiments. To validate the calibrated HVNS, computational experiments are conducted upon the test suite of various instances. As demonstrated in the results, the calibrated HVNS gains the advantage over both the commercial optimizer and exhaustive approach in terms of computation time for small-sized instances, while it also outperforms an existing meta-heuristic algorithm and two canonical ones (based on the principles of genetic algorithm and simulated annealing) in the optimizing capability.

An Effective Hybrid Genetic Algorithm and Variable Neighborhood Search for Integrated Process Planning and Scheduling in a Packaging Machine Workshop

Process planning and scheduling are modeled sequentially in the traditional manufacturing system. However, because of their complementarity, the increasing need to integrate them has emerged to enhance the manufacturing productivity significantly. Therefore, the integrated process planning and scheduling (IPPS) is becoming a hotspot in providing a blueprint for efficient manufacturing system. This paper proposes a novel algorithm hybridizing the genetic algorithm with strong global searching ability and variable neighborhood search with strong local searching ability for the IPPS problem. To improve the searching ability, a novel procedure, encoding method, and local search method have been designed. Effective operators have been adopted. Three experiments with totally 37 well-known benchmark problems are employed to evaluate the performance of the proposed method. Based on the results, the proposed algorithm outperforms the state-of-the-art methods and finds the new solutions (the best solutions found so far) for some problems. The proposed method has also been applied on a real-world case from a nonstandard equipment production workshop for the packaging machine of a machine tool company in China. The solution demonstrates that it can solve real-world cases very well.