Variable Neighborhood Search Metaheuristic Research Articles

Self-adaptive General Variable Neighborhood Search algorithm for parallel machine scheduling with unrelated servers

This paper introduces a machine learning-augmented General Variable Neighborhood Search algorithm, termed Self-adaptive General Variable Neighborhood Search (SGVNS), for solving the two-identical parallel machine scheduling problem with unrelated servers. The studied problem is of high practical relevance in various industries and presents a significant gap in the existing literature. The motivation for this study stems from the healthcare industry, specifically surgery scheduling with limited anesthesiologists’ availability. Two mathematical formulations are presented to solve this scheduling problem. However, these formulations are limited to small-scale problems, prompting the need for an efficient metaheuristic. Therefore, a novel variant of the General Variable Neighborhood Search metaheuristic is developed, incorporating a self-adaption mechanism based on an Extreme Learning Machine (ELM) algorithm. Extensive experiments are conducted to assess the performance of the SGVNS metaheuristic on various classes of instances. The results demonstrate the effectiveness and efficiency of SGVNS in solving previously unsolved small-sized instances, outperforming both formulations while maintaining reasonable computation times.

Landscape properties of the very large-scale and the variable neighborhood search metaheuristics for the multidimensional assignment problem

We study the recent metaheuristic search algorithm for the multidimensional assignment problem (MAP) using fitness landscape theory. The analyzed algorithm performs a very large-scale neighborhood search on a set of feasible solutions to the problem. We derive properties of the landscape graphs that represent these very large-scale search algorithms acting on the solutions of the MAP. In particular, we show that the search graph is a generalization of a hypercube. We extend and generalize the original very large-scale neighborhood search to develop the variable neighborhood search. The new search is capable of searching even larger large-scale neighborhoods. We perform numerical analyses of the search graph structures for various problem instances of the MAP and different neighborhood structures of the MAP algorithm based on a very large-scale search. We also investigate the correlation between fitness (i.e., objective values) and distance (i.e., path lengths) of the local minima (i.e., sinks of the landscape). Our results can be used to design improved search-based metaheuristics for the MAP.

Optimizing Resources and Increasing the Coverage of Internet-of-Things (IoT) Networks: An Approach Based on LoRaWAN.

A resource optimization methodology is proposed for application in long range wide area networks (LoRaWANs). Using variable neighborhood search (VNS) and a minimum-cost spanning tree algorithm, it reduces the implementation and the maintenance costs of such low power networks. Performance evaluations were conducted in LoRaWANs with LoRa repeaters to increase coverage, in scenario where the number and the location of the repeaters are determined by the VNS metaheuristic. Parameters such as spread factor (SF), bandwidth and transmission power were adjusted to minimize the network's total energy per useful bit (Ebit) and the total data collection time. The importance of the SF in the trade-off between (Ebit) and time on-air is evaluated, considering a device scaling factor. Simulation results, obtained after model adjustments with experimental data, show that, in networks with few associated devices, there is a preference for small values of SF aiming at reduction of Ebit. The usage of large SF's becomes relevant when reach extensions are required. The results also demonstrate that, for networks with high number of nodes, the scaling of devices over time become relevant in the fitness function, forcing an equal distribution of time slots per SF to avoid discrepancies in the time data collection.

CAN LINEAR PROGRAMMING ASSIST METAHEURISTICS IN FOREST PRODUCTION PLANNING PROBLEM?

The planning of forest production requires the adoption of mathematical models to optimize the utilization of available resources. Hence, studies involving the improvement of decision-making processes must be performed. Herein, we evaluate an alternative method for improving the performance of metaheuristics when they are applied for identifying solutions to problems in forest production planning. The inclusion of a solution obtained by rounding the optimal solution of linear programming to a relaxed problem is investigated. Such a solution is included in the initial population of the clonal selection algorithm, genetic algorithm, simulated annealing, and variable neighborhood search metaheuristics when it is used to generate harvest and planting plans in an area measuring 4,210 ha comprising 120 management units with ages varying between 1 and 6 years. The same algorithms are executed without including the solutions mentioned in the initial population. Results show that the performance of the clonal selection algorithm, genetic algorithm, and variable neighborhood search algorithms improved significantly. Positive effects on the performance of the simulated annealing metaheuristic are not indicated. Hence, it is concluded that rounding off the solution to a relaxed problem is a good alternative for generating an initial solution for metaheuristics.

VNS Metaheuristic Based on Thresholding Functions for Brain MRI Segmentation

Image segmentation is a very crucial step in medical image analysis which is the first and the most important task in many clinical interventions. The authors propose in this paper to apply the variable neighborhood search (VNS) metaheuristic on the problem of brain magnetic resonance images (MRI) segmentation. In fact, by reviewing the literature, they notice that when the number of classes increases the computational time of the exhaustive methods grows exponentially with the number of required classes. That's why they exploit the VNS algorithm to optimize two maximizing thresholding functions which are the between-class variance (the Otsu's function) and the entropy thresholding (the Kapur's function). Thus, two versions of the VNS metaheuristic are respectively obtained: the VNS-Otsu and the VNS-Kapur. These two novel proposed thresholding methods are tested on a set of benchmark brain MRI to show their robustness and proficiency.

Clustering approach in maintenance of capillary railway network

Maintenance optimization of railway infrastructure includes several kinds of aspects, such as safety, economic, operational, organization and regulatory issues. Among them the regulatory issues, that are fixed, increase the maintenance costs significantly. This is especially true in so-called capillary networks (local regional railway networks), where only the freight transport exists. Hence, the question is how to minimize maintenance costs with respect to regulatory issues? To solve this problem, we propose a clustering approach. The idea is to cluster tracks, considering elements of railway infrastructure as attributes. Once railway tracks are clustered in groups with similar attributes, then the maintenance can be organized more efficiently. In this paper, Variable Neighborhood Search metaheuristic is developed to solve minimum sum of squares clustering problem. Based on the results of clustering and available real and simulated data we report 22% savings in maintenance schedule for clusters.

A heuristic hybrid framework for vector job scheduling

We examine the first phase of a known NP-hard 2-stage assembly problem. It consists of sequencing a set of jobs having multiple components to be processed. Each job has to be worked on independently on a specific machine. We consider these jobs to form a vector of tasks. Our objective is to schedule jobs on the particular machines in order to minimize the completion time before the second stage starts. We first develop a new mathematical programming formulation of the problem and test it on a small problem instance using an integer programming solver. Then, we develop a heuristic algorithm based on Ant Colony Optimization and Variable Neighborhood Search metaheuristics in order to minimize the total completion time. The performance of our implementation appears to be efficient and effective.

A VNS-based Heuristic for Solving the Vehicle Routing Problem with Time Windows and Vehicle Preventive Maintenance Constraints

We address a vehicle routing problem with time windows (VRPTW) that also contains vehicle with preventive maintenance constraints (VRPTW-PM) and propose a MIP mathematical formulation as well as a general variable neighborhood search metaheuristic (VNS) to solve with large instance the problematic situation. First we create a initial solution using Solomon heuristic then we minimize the number of used routes, and then the total travelled distance by all vehicles is minimized. Computational results show the efficiency of the proposed approach.

Heuristics for the network design problem with connectivity requirements

We consider the NP-complete problem of finding a spanning $$k$$k-tree of minimum weight in a complete weighted graph. This problem has a number of applications in designing reliable backbone telecommunication networks. We propose effective algorithms based on a greedy strategy and several variable neighborhood search metaheuristics. We also develop an integer linear programming model for calculating a lower bound. Preliminary numerical experiments using random and real-word data sets are reported to show the effectiveness of our approach. In addition, we compare our approach with known metaheuristics.

Otimização da escala mensal de motoristas de ônibus urbano utilizando a heurística Variable Neighborhood Search

One of the last stage from public transportation planning concerns to defining the scale of urban bus drivers for short term period, called Crew Rostering Problem (CRT). This problem aims to generate sequences of daily shifts, includ-ing weekdays, Saturdays and Sundays, respecting labor laws and operational constraints. Moreover, a good crew roster should provide a better division of workload among the crews and still to reduce the overtime costs paid by the company. The model proposed in this paper is able to generate solutions satisfying a fixed scheme called 5/1 of day-off, beyond the labor laws and operational constraints imposed by the company. The Variable Neighborhood Search metaheuristic (VNS) was implemented using different neighborhood structures, varying the number of modifications performed on the current solution. The implementation was tested with data from a midsize company and the results show significant improvements compared to the solution adopted by the company.

A Variable Neighborhood Search Metaheuristic for Cellular Manufacturing with Multitask Machine Tools

Traditionally in metal cutting, it is assumed that a machine tool can process at most one operation at a time since machine tools have one spindle and one turret. Yet, with advent of machine tools with multiple spindles and multiple turrets, this assumption does not hold anymore. This paper deals with the integrated problem of process planning and production scheduling for a parallel processing manufacturing cells with multitasking machines. A novel Variable Neighborhood Search (VND) metaheuristic is proposed to solve the problem. This algorithm employs novel operators that cover mechanisms to combine and improve, replace and shake plans and individuals of the VNS population-based search.

A SA-VNS approach for the High School Timetabling Problem

The High School Timetabling Problem consists in assigning timeslots and resources to events, satisfying constraints which heavily depend on the specific institution. This work deals with the problem of the ongoing III International Timetabling Competition (ITC), which includes a diverse set of instances from many educational institutions around the world. We proposed an approach based on Simulated Annealing and Variable Neighborhood Search metaheuristics. One important structural feature of our approach is the use of the Kingston’s High School Timetabling Engine (KHE) to generate initial solutions combined with the multi-neighborhood search. Such approach led us to the finals of the ongoing competition.

A Method for Selecting Pareto Optimal Solutions in Multiobjective Optimization

In many real-life multiobjective optimization problems and particularly in combinatorial ones, a common methodology is to determine a Pareto optimal set. These sets can be extremely large or may contain an infinite number of solutions. It is then difficult to choose among these solutions, one that corresponds to the best compromise according to the decision-maker's preferences. In this paper, we propose a model to select a restricted set of solutions. These sets should be structurally different and the most representative of the Pareto-optimal solutions. Our model is implemented using hierarchical algorithms and variable neighborhood search metaheuristics.

Primal-Dual Variable Neighborhood Search for the Simple Plant-Location Problem

The variable neighborhood search metaheuristic is applied to the primal simple plant-location problem and to a reduced dual obtained by exploiting the complementary slackness conditions. This leads to (i) heuristic resolution of (metric) instances with uniform fixed costs, up to n=15,000 users, and m=n potential locations for facilities with an error not exceeding 0.04%; (ii) exact solution of such instances with up to m=n=7,000; and (iii) exact solutions of instances with variable fixed costs and up to m=n=15,000.

A modified VNS metaheuristic for max-bisection problems

Variable neighborhood search (VNS) metaheuristic as presented in Festa et al. [Randomized heuristics for the MAX-CUT problem, Optim. Methods Software 17 (2002) 1033–1058] can obtain high quality solution for max-cut problems. Therefore, it is worthwhile that VNS metaheuristic is extended to solve max-bisection problems. Unfortunately, comparing with max-cut problems, max-bisection problems have more complicated feasible region via the linear constraint e T x = 0 . It is hard to directly apply the typical VNS metaheuristic to deal with max-bisection problems. In this paper, we skillfully combine the constraint e T x = 0 with the objective function, obtain a new optimization problem which is equivalent to the max-bisection problem, and then adopt a distinct greedy local search technique to the resulted problem. A modified VNS metaheuristic based on the greedy local search technique is applied to solve max-bisection problems. Numerical results indicate that the proposed method is efficient and can obtain high equality solution for max-bisection problems.

A variable neighborhood decomposition search method for supply chain management planning problems

Few models have been developed for the integrated planning and scheduling of the inventory, production and distribution functions. In this paper, we consider a three-stage supply chain, for which a sustainable inventory–production–distribution plan over a multi-period horizon is constructed. The associated program takes the form of a general mixed-integer program, for which the sole reliance upon exact methods is shown to be insufficient. We use a solution algorithm based on the variable neighborhood decomposition search metaheuristics, that can be seen as a stagewise exploration of increasingly large neighborhoods. The stages are related to the decomposition scheme, i.e., the order on which integrality conditions are restored. Within each stage, a sequence of neighborhoods is defined relying on the variable neighborhood search metaheuristics, while the exploration of the successive neighborhoods is performed using a branch-and-bound algorithm. The methodology is validated through its application to a problem faced by a large supply chain. Empirical results show that (i) the methodology performs best when the decomposition scheme accounts for the possibility of resources bottleneck, (ii) the primary source of savings originates from the distribution function and (iii) congestion must be defined with respect to the availability of the distribution resources at the periods with high requirements.

Heuristic Procedures for Solving the Discrete Ordered Median Problem

We present two heuristic methods for solving the Discrete Ordered Median Problem (DOMP), for which no such approaches have been developed so far. The DOMP generalizes classical discrete facility location problems, such as the p-median and p-center. The first procedure proposed in this paper is based on a genetic algorithm developed by Moreno Vega (1996) for p-median and p-center problems. Additionally, a second heuristic approach based on the Variable Neighborhood Search metaheuristic (VNS) proposed by Hansen and Mladenovic (1997) for the p-median problem is described. An extensive numerical study is presented to show the efficiency of both heuristics and compare them.

Variable neighborhood search for extremal graphs: 1 The AutoGraphiX system

Finding extremal graphs for expressions involving one or more invariants is viewed as a problem of combinatorial optimization. The recent Variable Neighborhood Search metaheuristic is used to solve it. Neighborhoods are defined by addition, removal or exchange of edges, removal of pendant vertices and similar transformations. First results, obtained with the system AutoGraphiX, are presented: many extremal graphs are determined, three conjectures from Graffiti are refuted, other conjectures are sharpened and new ones proposed.