Variable Neighborhood Search Method Research Articles

Cumulative Capacitated Colored Traveling Salesman Problem.

A colored traveling salesman problem (CTSP) is a generalization of the well-known multiple traveling salesman problem, which introduces colors to distinguish the accessibility of its cities to salesmen. This work proposes a city/customer-centric model called cumulative capacitated CTSP (C2-CTSP) to tackle some practical problems with fast response requirements. Its hypergraph and mathematical programming formulations are developed for the first time. A general variable neighborhood search (GVNS) metaheuristic is designed to solve it. Specifically, greedy backtracking is proposed to initialize a solution taking into account the cumulative cost and two constraints including colors and capacities. Next, 2-swap, reinsertion, and double-bridge operations are randomly selected and carried out to execute the perturbation. Moreover, neighborhood-list-2-opt, relocation move, and generalized partition crossover are organized as variable neighborhood descent to constitute the local search for better solutions. Extensive experiments are conducted to compare the proposed GVNS with four genetic algorithms, two hybrid ant colony systems, two variable neighborhood search methods, and a perturb-based local search in 20 regular and random cases. The statistical results demonstrate that GVNS is superior to all competitors tuned by irace package in terms of both search ability and convergence rate. In addition, the study of six GVNS variants lacking different operators validates the significant role of each corresponding operator in GVNS's outstanding performance.

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.

General VNS for asymmetric vehicle routing problem with time and capacity constraints

We consider a real-life transportation problem from a hypermarket company in Serbia that consists of delivering online ordered and possibly perishable goods from a single depot to multiple customers. It can be modeled as an asymmetric vehicle routing problem that requires visiting and serving all customers using a limited number of homogeneous vehicles and taking into account time and capacity constraints. The objective function to be minimized is the total distance traveled. We provide a mixed-integer programming (MIP) formulation of the problem and develop several Local Search based metaheuristic methods exploring combinatorial formulation of the considered problem: Multistart Local Search (MLS), Greedy Randomized Adaptive Search Procedure (GRASP), and several variants of General Variable Neighborhood Search (GVNS) methods. All methods are compared on real-life instances provided by the hypermarket company and benchmark instances from the relevant literature. The obtained results show the superiority of GVNS-based methods with respect to both solution quality and running time, confirming that systematic search procedures have more success when dealing with hard optimization problems.

An Artificial Bee Colony Algorithm for Coordinated Scheduling of Production Jobs and Flexible Maintenance in Permutation Flowshops

This research work addresses the integrated scheduling of jobs and flexible (non-systematic) maintenance interventions in permutation flowshop production systems. We propose a coordinated model in which the time intervals between successive maintenance tasks as well as their number are assumed to be non-fixed for each machine on the shopfloor. With such a flexible nature of maintenance activities, the resulting joint schedule is more practical and representative of real-world scenarios. Our goal is to determine the best job permutation in which flexible maintenance activities are properly incorporated. To tackle the NP-hard nature of this problem, an artificial bee colony (ABC) algorithm is developed to minimize the total production time (Makespan). Experiments are conducted utilizing well-known Taillard’s benchmarks, enriched with maintenance data, to compare the proposed algorithm performance against the variable neighbourhood search (VNS) method from the literature. Computational results demonstrate the effectiveness of the proposed algorithm in terms of both solution quality and computational times.

An ensemble of brain storm optimization and Q-learning methods for distributed flexible job shop scheduling problems with distribution operations

Distributed manufacturing scheduling problems have attracted much concern from both industrial and academic areas. Nevertheless, distributed scheduling problems with distribution operations are seldom studied. This work proposes a distributed flexible job shop scheduling problem with distribution operations. A set of jobs is handled at distributed flexible job shops, and then the finished jobs are transported to their corresponding customers following given due dates. First, a mixed integer programming model is established to minimize total tardiness. Second, an ensemble of brain storm optimization and Q-learning methods is developed to solve the formulated model. Six heuristics are hybridized to generate a high-quality initial population. A Q-learning method is devised by fully employing found search information to guide subsequent search processes instead of using fixed parameters as basic brain storm optimization. A variable neighborhood search method combining problem-specific knowledge is designed to further refine the found best individual. At last, the formulated model and method are compared with three state-of-the-art metaheuristics and a mathematical programming solver CPLEX via using a group of problem instances. The results and analysis demonstrate that the developed model and algorithm have more powerful competitiveness in addressing the studied problem.

Optimization of Static Patient Admission Scheduling using the Variable Neighborhood Search Method

Planning and resource management are important aspects of a company's operational sustainability. With good management, companies can achieve their targets while minimizing operational costs. The same goes for hospitals. Various challenges related to resources are experienced by hospitals, such as scheduling nurses, patient surgeries, and patient appointments. Therefore, this paper aim at optimizing patient admission scheduling in order to improve hospital resource efficiency. To be more specific, patient admission scheduling, also known as the Patient Admission Scheduling Problem (PASP), is a scheduling problem that considers patient preferences and needs, bed availability, resource efficiency, and utilization. This problem is highly relevant, especially for large hospitals. The number of rooms, specialists, and facilities makes manual scheduling extremely difficult. It is due to the varied preferences, needs, and lengths of stay for patients in hospital. Various methods, both heuristic and exact, have been proposed, including the use of integer programming methods. However, for a large search space, this method requires a very long computational time. To address the PASP, this study applies the Variable Neighborhood Search (VNS) algorithm and random selection as optimization algorithms. The method was chosen because it has been proven effective to solve some combinatorial optimization problems in prior studies. Seven types of neighborhoods are implemented to find the best combinations in optimizing the PASP. The results show that the VNS algorithm outperforms the random selection algorithm, as it is able to generate 5 out of 7 solutions that are better, reducing penalties by 27.84% to 55.29%. The expected impact of this study is to increase the hospital patient satisfaction whereas in the same time minimize the operational cost.

Hybrid Grey-Wolf Algorithm approach for Solving energy efficient permutation flowshop scheduling problem with Setup Times

Energy efficient permutation flowshop scheduling problem (PFSP) is widely studied to reduce the energy consumption in manufacturing systems. Most traditional studies make the premise that setup time is a component of processing time. However, this assumption does not satisfy the small batches, more varieties manufacturing models criterion. Therefore, energy efficient PFSP with setup times thus becomes a pressing problem that needs to be resolved. The contribution of this paper includes: (1) a permutation flowshop scheduling problem (PFSP) mathematical model by considering energy consumed and setup time by each machine in the system; (2) a grey-wolf algorithm optimization with variable neighborhood search (VNS) method (GWO_VNS) is proposed for the multi-objective PFSP model; (3) solved 9 benchmarks problems of Taillard (1993) [8] for the minimization of flowtime (FT) and energy consumption (EC). The performance of the proposed GWO_VNS algorithm is evaluated on the benchmark problems selected from the published literature [15]. It is noted that the proposed algorithm performed better on both the objectives i.e., FT and EC minimization. Overall, the proposed algorithm achieved 33.25% and 30.56% average improvement in FT and EC minimization respectively on benchmark problems.

Estimation of the stress-strength parameter under two-sample balanced progressive censoring scheme

In this paper, we obtain the stress-strength reliability estimation under balanced joint Type-II progressive censoring scheme for independent samples from two different populations. We simultaneously place two independent samples where the experimental units follow Weibull distributions with common shape parameter β and different scale parameters α, λ, respectively. The maximum likelihood estimators of the unknown parameters are derived. Further, the Bayesian inference is considered using Lindley's approximation and Gibbs sampling method. Extensive simulations are performed to see the effectiveness of the proposed estimation methods. Further, we derive the optimal censoring scheme in the Bayesian framework by using the variable neighbourhood search method proposed by [Bhattacharya et al. On optimum life-testing plans under type-ii progressive censoring scheme using variable neighbourhood search algorithm. Test. 2016;25(2):309–330]. Further, some simulation schemes are provided to compare the performances of the estimations under the jointly censored samples versus two separate censored samples.

Non-Crossing Anonymous MAPF for Tethered Robots

This paper deals with the anonymous multi-agent path finding (MAPF) problem for a team of tethered robots. The goal is to find a set of non-crossing paths such that the makespan is minimal. A difficulty comes from the fact that a safety distance must be maintained between two robots when they pass through the same subpath, to avoid collisions and cable entanglements. Hence, robots must be synchronized and waiting times must be added when computing the makespan. We show that bounds can be efficiently computed by solving linear assignment problems. We introduce a variable neighborhood search method to improve upper bounds, and a Constraint Programming model to compute optimal solutions. We experimentally evaluate our approach on three different kinds of instances.

A Variable Neighborhood Search Method with a Tabu List and Local Search for Optimizing Routing in Trucks in Maritime Ports

Logistics problems represent an important class of real-world problems where even small improvements in solution quality can lead to significant decreases in operational costs. However, these problems are usually NP-hard; thus, they are mostly solved using metaheuristic methods. To improve their performance, there is substantial research on crafting new and refined metaheuristics to derive superior solutions. This paper considers a truck routing problem within a naval port, where the objective is to minimize the total distance traveled by all the vehicles to distribute a given set of containers. Due to the large volume of goods that are being transferred through ports, it is imperative to improve the operation times at such ports to improve the throughput. To achieve this goal, a novel variable neighborhood search method that integrates a tabu list, an iterative local search procedure, and parallelization of neighborhood generation is proposed and evaluated. The experimental results demonstrate that the proposed method achieves similar results to the state of the art, but in a smaller amount of time.

Multi-period scheduling problem of combination of home health care and outpatient services: based on Chinese family doctor contract services

Inspired by the service mode of family doctor contract service in China, this paper presents a multi-period problem of the combination of home health care and outpatient service over a planning horizon of multiple days. In the planning horizon, patients receive services with fixed frequencies and have different preferences for different dates. Taking the patients’ service date regulations and doctors’ working regulations into account, we propose a mixed-integer nonlinear and convex programming model, which aims to minimize the total operating costs and maximize the patients’ preference satisfaction. A hybrid tabu search algorithm with an embedded shake procedure is designed to solve the problem. Numerical experiment results imply that the hybrid tabu search algorithm performs well when compared with the exact method on small instances, and it can also provide higher quality solutions when compared with variable neighborhood search method. We also analyze problem properties and parameter sensitivities through some small instances.

Multi-objective home health care routing: a variable neighborhood search method.

Health and convenience are two indispensable indicators of the society promotion. Nowadays, to improve community health levels, the comfort of patients and those in need of health services has received much attention. Providing Home Health Care (HHC) services is one of the critical issues of health care to improve the patient convenience. However, manual nurse planning which is still performed in many HHC institutes results in a waste of time, cost, and ultimately lower efficiency. In this research, a multi-objective mixed-integer model is presented for home health care planning so that in addition to focusing on the financial goals of the institution, other objectives that can help increase productivity and quality of services are highlighted. Therefore, four different objectives of the total cost, environmental emission, workload balance, and service quality are addressed. Taking into account medical staff with different service levels, and the preferences of patients in selecting a service level, as well as different vehicle types, are other aspects discussed in this model. The epsilon-constraint method is implemented in CPLEX to solve small-size instances. Moreover, a Multi-Objective Variable Neighborhood Search (MOVNS) composed of nine local neighborhood moves is developed to solve the practical-size instances. The results of the MOVNS are compared with the epsilon-constraint method, and the strengths and weaknesses of the proposed algorithm are demonstrated by a comprehensive sensitivity analysis. To show the applicability of the algorithm, a real example is designed based on a case study, and the results of the algorithm over real data are evaluated.

Multi-Strategy Dynamic Evolution-Based Improved MOEA/D Algorithm for Solving Multi-Objective Fuzzy Flexible Job Shop Scheduling Problem

A scheduling model was developed to optimize the maximum completion time, total machine load, and maximum machine load for the fuzzy flexible job shop problem with uncertain processing times. To solve this problem, a multi-strategy dynamic evolution-based improved multi-objective evolutionary algorithm based on decomposition(IMOEA/D) was proposed. In order to enhance the quality of the non-dominated solution set and improve the algorithm efficiency. The algorithm firstly employs a strategy based on minimum processing time and workload, along with a non-dominated solution prioritization mechanism to generate the initial population. Secondly, three evolutionary strategies are incorporated, and their probabilities are dynamically adjusted with the increase of evolution generations. Finally, a variable neighborhood search method is introduced to improve the search performance of the algorithm. The effectiveness of the proposed algorithm was demonstrated through experimental validation.

Mixed-model assembly line balancing problem considering learning effect and uncertain demand

An assembly line system is a manufacturing process in which parts are added in sequence from workstation to workstation until the final assembly is produced. In a mixed-model assembly line balancing problem, tasks belonging to different product models, are allocated to workstations according to their processing times and precedence relationships amongst tasks. The research parlayed two features, learning effect and uncertain demand, into the conventional mixed-model assembly line balancing model, which is the main contribution of our paper. Both features can affect the new decision appeared in the stated problem — the level of production. The problem setup as well as the new decisions considered in the problem are novel. The proposed model optimized two objectives, total expected cost and average cycle time. To solve the model, a mixed integer-based heuristic and a customized variable neighborhood search method is proposed. The algorithms are examined for two different system response time requirements. Computational results showed that the mixed integer-based heuristic is more efficient if there is enough response time for the decision making process. On the contrary, the customized variable neighborhood search method can deliver promising results under real-time conditions. The Pareto-optimal set can be generated, which provides the managers with multiple choices for different cost and cycle time combinations.

A reinforcement learning-Variable neighborhood search method for the capacitated Vehicle Routing Problem

Finding the best sequence of local search operators that yields the optimal performance of Variable Neighborhood Search (VNS) is an important open research question in the field of metaheuristics. This paper proposes a Reinforcement Learning method to address this question. We introduce a new hyperheuristic scheme, termed Bandit VNS, inspired by the Multi-Armed Bandit (MAB), a particular type of a single state reinforcement learning problem. In Bandit VNS, we utilize the General Variable Neighborhood Search metaheuristic and enhance it by a hyperheuristic strategy. We examine several variations of the Upper Confidence Bound algorithm to create a reliable strategy for adaptive neighborhood selection. Furthermore, we utilize Adaptive Windowing, a state of the art algorithm to estimate and detect changes in the data stream. Bandit VNS is designed for effective parallelization and encourages cooperation between agents to produce the best solution quality. We demonstrate this concept’s advantages in accuracy and speed by extensive experimentation using the Capacitated Vehicle Routing Problem. We compare the novel scheme’s performance against the conventional General Variable Neighborhood Search metaheuristic in terms of the CPU time and solution quality. The Bandit VNS method shows excellent results and reaches significantly higher performance metrics when applied to well-known benchmark instances. Our experiments show that, our approach achieves an improvement of more than 25% in solution quality when compared to the General Variable Neighborhood Search method using standard library instances of medium and large size.

Precedence-Constrained Colored Traveling Salesman Problem: An Augmented Variable Neighborhood Search Approach.

A colored traveling salesman problem (CTSP) as a generalization of the well-known multiple traveling salesman problem utilizes colors to distinguish the accessibility of individual cities to salesmen. This work formulates a precedence-constrained CTSP (PCTSP) over hypergraphs with asymmetric city distances. It is capable of modeling the problems with operations or activities constrained to precedence relationships in many applications. Two types of precedence constraints are taken into account, i.e., 1) among individual cities and 2) among city clusters. An augmented variable neighborhood search (VNS) called POPMUSIC-based VNS (PVNS) is proposed as a main framework for solving PCTSP. It harnesses a partial optimization metaheuristic under special intensification conditions to prepare candidate sets. Moreover, a topological sort-based greedy algorithm is developed to obtain a feasible solution at the initialization phase. Next, mutation and multi-insertion of constraint-preserving exchanges are combined to produce different neighborhoods of the current solution. Two kinds of constraint-preserving k -exchange are adopted to serve as a strong local search means. Extensive experiments are conducted on 34 cases. For the sake of comparison, Lin-Kernighan heuristic, two genetic algorithms and three VNS methods are adapted to PCTSP and fine-tuned by using an automatic algorithm configurator-irace package. The experimental results show that PVNS outperforms them in terms of both search ability and convergence rate. In addition, the study of four PVNS variants each lacking an important operator reveals that all operators play significant roles in PVNS.

Bi-Objective Colored Traveling Salesman Problems

As a generalization of the well-known multiple traveling salesman problem, a colored traveling salesman problem (CTSP) utilizes colors to describe the accessibility of individual cities to salesmen. To expand its application scope, this work presents a bi-objective CTSP (BCTSP) over hypergraphs, taking into account the balance of workload among salesmen. To solve it, a bi-objective variable neighborhood search (BVNS) is proposed as a solution framework. In BVNS, we exploit a two-stage initialization and a probability-based insertion to produce feasible solutions and generate their neighborhood. Next, population-based multi-insertion, color-preserving exchange and 2-opt constitute a powerful local search procedure, where color-preserving exchange improves the solutions by modifying the route intersections among distinct salesmen. Besides, Delaunay triangulation is utilized to prepare candidates for multi-insertion, thereby increasing the possibility to find an optimal route by shortening links among vertices. Extensive experiments are conducted on 20 cases. To make a comprehensive comparison, four existing methods, i.e., two genetic algorithms and two variable neighborhood search methods, are adapted by exploiting an elitist non-dominated sorting for solving BCTSP instances. The experimental results show that BVNS is superior to its peers in achieving Pareto optima in terms of three popular performance metrics, i.e., hypervolume, inverted generational distance, and C-metric. In addition, the study of four BVNS variants reveals that probability-based insertion, population-based multi-insertion, and color-preserving exchange play significant roles in BVNS’s high performance.

A memetic algorithm for the inventory routing problem

In this article, we study an Inventory Routing Problem with deterministic customer demand in a two-tier supply chain. The supply chain network consists of a supplier using a single vehicle with a given capacity to deliver a single product type to multiple customers. We are interested in population-based algorithms to solve our problem. A Memetic Algorithm (MA) is developed based on the Genetic Algorithm (GA) and Variable Neighborhood Search methods. The proposed meta-heuristics are tested on small and large reference benchmarks. The results of the MA are compared to those of the classical GA and to the optimal solutions in the literature. The comparison shows the efficiency of using MA and its ability to generate high quality solutions in a reasonable computation time.

Many-Objective Flexible Job Shop Scheduling Problem with Green Consideration

With the increasingly customized product requirements of customers, the manufactured products have the characteristics of multi-variety and small-batch production. A high-quality production scheduling scheme can reduce energy consumption, improve production capacity and processing quality of the enterprise. The high-dimensional many-objective green flexible job shop scheduling problem (Ma-OFJSSP) urgently needs to be solved. However, the existing optimization method are difficult to effectively optimize the Ma-OFJSSP. This study proposes a many-objective flexible job shop scheduling model. An optimization method SV-MA is designed to effectively optimize the Ma-OFJSSP model. The SV-MA memetic algorithm combines an improved strength Pareto evolution method (SPEA2) and the variable neighborhood search method. To effectively distinguish the better solutions and increase the selection pressure of the non-dominated solutions, the fitness calculation method based on the shift-based density estimation strategy is adopted. The SV-MA algorithm designs the variable neighborhood strategy which combines with scheduling knowledge. Finally, in the workshop scheduling benchmarks and the machining workshop engineering case, the feasibility and effectiveness of the proposed model and SV-MA algorithm are verified by comparison with other methods. The production scheduling scheme obtained by the proposed model and SV-MA optimization algorithm can improve production efficiency and reduce energy consumption in the production process.

Meta-Heuristic Algorithms for the Generalized Extensible Bin Packing Problem With Overload Cost

In this paper, we consider a generalized the extensible bin packing problem with overload cost, first proposed by Denton et al. [1] in 2010, in which the total size of items packed into a bin is allowed to exceed its capacity, and the cost incurred each bin is equal to the fixed cost plus the overload cost, the objective is to minimize the total cost of all bins. According to the characteristics of the problem, we first propose an improved ant colony optimization algorithm (IACO), which enhances the positive feedback effect of ACO by improving the update method of pheromone and the adaptive adjustment parameters. We also introduce a variable neighborhood search method in ACO to improve the convergence of the algorithm and get rid of the phenomenon of local extrema. Then, we present a discrete particle swarm optimization algorithm (DPSO) to solve the problem. In order to ensure the uniform distribution and high quality of the initial particle swarm, we use some heuristic methods in the initialization process of the swarm, so that the initial particle can cover the entire search space with a large probability, which effectively improves the performance of DPSO algorithm. Finally, we compare and analyze the performance of these proposed algorithms through two sets of computational experimental frameworks. Compared with some algorithms in the literature, computational results signify that the improved ACO algorithm and MDPSO algorithm are more competitive than some other metaheuristic algorithms..