Basic Variable Neighborhood Search Research Articles

A mathematical model and solution algorithms for optimising system-level configurations of reconfigurable single part flow lines

This study addresses a system-level configuration selection problem for reconfigurable single part flow lines (R-SPFLs) with parallel identical flexible machines at each stage. The problem is to determine the number of stages, the number of machines of a certain type at each stage and the assignment of operations to each stage in order to satisfy the demand of a part type. Precedence relations among the operations and space limitations are also considered. For the objective of minimising the sum of machine purchase and operation processing costs, a nonlinear integer programming model is developed that gives the optimal solutions. Then, due to the problem's complexity, a basic variable neighbourhood search algorithm is proposed that constructs an initial solution using a greedy-type heuristic and improves it using a shaking and a local search improvement methods. Moreover, the basic algorithm is extended to a general one that uses a variable neighbourhood descent method. Computational results show that the two algorithms outperform the previous one significantly in both solution quality and computation times, and the general algorithm improves the basic one significantly. Finally, the applicability of the variable neighbourhood search algorithms is shown by reporting a brief case study.

Airline capacity distribution under financial budget and resource consideration

Capacity distribution is a challenging issue for an airline under financial budget and resource consideration. It is a large-scale optimization problem covering both long-term planning and short-term operating arrangements. This study investigates on the airline capacity distribution problem with financial budget and resource consideration. It contains subproblems of financial budget arrangement, fleet introduction, and fleet assignment. Among them, financial budget is arranged in multiple decision periods, fleet introduction is decided under fixed time points, while fleet assignment is decided under all available time points. To tackle this problem, an integer programming model is formulated for descriptions. Then, an integrated algorithm of modified Variable Neighborhood Search (VNS) and Branch-and-bound (B&B) strategy is developed to find solutions. In detail, a greedy heuristic approach is utilized to generate an initial solution for fleet introduction, the modified B&B strategy is utilized to generate the optimal solution for fleet assignment and the modified VNS is applied to update current solution for a new one with better quality. In addition, budget limit checks are added for financial budget arrangements. Finally, the hybrid algorithm is tested on efficiency and stability. It is also compared to other algorithms which replace the modified VNS by basic VNS, differential evolution and genetic algorithm. Computational results show that performance of our approach is powerful in terms of objective value, convergence speed and stability.

A Dynamic Colored Traveling Salesman Problem With Varying Edge Weights

A colored traveling salesman problem (CTSP) is a generalization of the well-known multiple traveling salesman problem. In it, each city has one to multiple colors and allows a salesman in the same color to visit exactly once. This work presents for the first time a CTSP whose edge weights among the cities change over time. It can be applied to dynamic routing problems arising in logistic distribution systems with various goods accessibilities to different types of vehicles. A non-linear integer mathematical program is constructed. A Variable Neighborhood Search (VNS) algorithm with a direct-route encoding and random initialization is then presented to solve it. To increase the convergence rate and population diversity of VNS, it is further combined with two-stage greedy initialization and an appropriate population immigrant scheme to perform the population search in a dynamic environment. Then, off-line performance evaluation and Wilcoxon test of the proposed algorithms are performed. The results show that their solution quality is improved by 30% ~ 60% over the basic VNS’s. They can track the environmental changes of CTSP-VEW more rapidly and effectively. In the end, a case study with a practical scenario is conducted.

An Efficient Variable Neighborhood Search for Generalized Regenerator Location Problems

Optical networks are one of the fastest data communication networks, which use optical fiber cables for transmitting data in the form of light pulses between sender and receiver nodes. As the quality of optical signal deteriorates when increasing the distance among terminal nodes, expensive electronic devices (regenerators) must be deployed in the network to recover the signal quality. The objective of Generalized Regenerator Location Problem (GRLP) is to minimize the number of installed regenerators, while weighted variant (WGRLP) assumes different installation costs (weights) of potential regenerator locations and minimizes the sum of regenerator installation costs. In this study, an improved variant of Basic Variable Neighborhood Search (iBVNS) was developed as a metaheuristic solution approach to both GRLP and WGRLP. Computational results provided by the proposed iBVNS on all available data sets from the literature are compared with the results of existing solution methods for GRLP and WGRLP. The obtained results show that the proposed iBVNS quickly reaches optimal or near-optimal solutions and in many cases improves upper bounds provided by exact method. In addition, the conducted non-parametric statistical tests indicate that iBVNS outperforms all heuristic approaches proposed earlier in the literature for the considered problems.

Targets-Attackers-Defenders Game via Pairwise Outcomes

Decision algorithms are one of the key areas of focus in cluster confrontation research. In this paper, a Targets-Attackers-Defenders (TADs) game that includes an attacking team with [Formula: see text] Attackers, a target team with [Formula: see text] targets and a defending team with [Formula: see text] Defenders is considered. In this game, the players within each team cooperate with each other, and both cooperation and confrontation between the teams ensue. The defending team cooperates with the target team against the attacking team. The attacking team aims to capture [Formula: see text] Targets. The defending team protects [Formula: see text] Targets by intercepting Attackers or rendezvousing with Targets. We present a maximum matching algorithm considering both confrontation and cooperation by using relative distance and velocity parameters, and transform the TADs problem into a real-time target-assignment problem with strong confrontation. Finally, we propose an improved basic variable neighborhood search algorithm to solve the target-assignment problem and give the optimal dynamical strategy for each player.

A mixed integer linear programming model and a basic variable neighbourhood search algorithm for the repatriation scheduling problem

Commercial flights nearly halted due to the COVID-19 pandemic in the second quarter of 2020. Consequently, several countries have had to schedule repatriation flights to return their citizens stranded in other countries. Flight routes and schedules are known in normal circumstances, and passengers buy seats on these flights; however, the reverse steps happen in repatriation. Passengers express their need to travel, and flights are scheduled to satisfy their requests. The problem behind this flight schedule can be called the repatriation scheduling problem (RSP), in which we need to repatriate citizens from different countries. The objective of the RSP is to return the most vulnerable citizens first. The capacity of available airplanes and quarantine locations limit the number of repatriated citizens. To address this problem, we have developed a mixed-integer linear program (MILP) to model the RSP. Moreover, we suggest a basic variable neighbourhood search (BVNS) algorithm to solve the problem. We test the BVNS algorithm by creating and solving a set of 108 RSP instances and then comparing the BVNS solutions with the exact ones. Despite allocating only 20 s to run the BVNS algorithm compared to eight hours for a commercial exact solver’s branch and bound algorithm, the BVNS algorithm could find better results than the lower bounds for 62 instances and similar values for 17 instances.

Solving the Capacitated Dispersion Problem with variable neighborhood search approaches: From basic to skewed VNS

The topic of this paper is the Capacitated Dispersion Problem (CDP). To solve the problem, variable neighborhood search (VNS) based heuristics are proposed. The proposed heuristics are Basic VNS, General VNS and General Skewed VNS. Their performances are assessed on the benchmark instances from the literature and compared against the state-of-the-art ones. Comparing to the state-of-the-art results, it turns out that Basic VNS is able to provide competitive results, while General VNS and General Skewed VNS advance the state-of-the-art results by establishing 57 new best-known solutions on the data set of 100 instances. Twenty nine new best-known solutions are solely due to the proposed General Skewed VNS.

Two-dimensional bandwidth minimization problem: Exact and heuristic approaches

Reducing the bandwidth in a graph is an optimization problem which has generated significant attention over time due to its practical application in Very Large Scale Integration (VLSI) layout designs, solving system of equations, or matrix decomposition, among others. The bandwidth problem is considered as a graph labeling problem where each vertex of the graph receives a unique label. The target consists in finding an embedding of the graph in a line, according to the labels assigned to each vertex, that minimizes the maximum distance between the labels of adjacent vertices. In this work, we are focused on a 2D variant where the graph has to be embedded in a two-dimensional grid instead. To solve it, we have designed two constructive and three local search methods which are integrated in a Basic Variable Neighborhood Search (BVNS) scheme. To assess their performance, we have designed three Constraint Satisfaction Problem (CSP) models. The experimental results show that our CSP models obtain remarkable results in small or medium size instances. On the other hand, BVNS is capable of reaching equal or similar results than the CSP models in a reduced run-time for small instances, and it can provide high quality solutions in those instances which are not optimally solvable with our CSP models.

Basic variable neighborhood search for the minimum sitting arrangement problem

The minimum sitting arrangement (MinSA) problem is a linear layout problem consisting in minimizing the number of errors produced when a signed graph is embedded into a line. This problem has been previously tackled by theoretical and heuristic approaches in the literature. In this paper we present a basic variable neighborhood search (BVNS) algorithm for solving the problem. First, we introduce a novel constructive scheme based on the identification of cliques from the input graph, when only the positive edges are considered. The solutions obtained by the constructive procedure are then used as a starting point for the proposed BVNS algorithm. Efficient implementations of the several configurations of the local search procedure within the BVNS are described. The algorithmic proposal is then compared with previous approaches in the state of the art for the MinSA over different sets of referred instances. The obtained results supported by non-parametric statistical tests, indicate that BVNS can be considered as the new state-of-the-art algorithm for the MinSA.

Hybridizing Basic Variable Neighborhood Search With Particle Swarm Optimization for Solving Sustainable Ship Routing and Bunker Management Problem

This paper studies a novel sustainable ship routing problem considering a time window concept and bunker fuel management. Ship routing involves the decisions corresponding to the deployment of vessels to multiple ports and time window concept helps to maintain the service level of the port. Reducing carbon emissions within the maritime transportation domain remains one of the most significant challenges as it addresses the sustainability aspect. Bunker fuel management deals with the fuel bunkering issues faced by different ships, such as selection of bunkering ports and total bunkered amount at a port. A novel mathematical model is developed capturing the intricacies of the problem. A hybrid particle swarm optimization with a basic variable neighborhood search algorithm is proposed to solve the model and compared with the exact solutions obtained using Cplex and other popular algorithms for several problem instances. The proposed algorithm outperforms other popular algorithms in all the instances in terms of the solution quality and provides good quality solutions with an average cost deviation of 5.99% from the optimal solution.

Less is more approach: basic variable neighborhood search for the obnoxious p‐median problem

AbstractThe goal of the less is more approach (LIMA) for solving optimization problems that has recently been proposed in Mladenović et al. (2016) is to find the minimum number of search ingredients that make a heuristic more efficient than the currently best. In this paper, LIMA is successfully applied to solve the obnoxious p‐median problem (OpMP). More precisely, we developed a basic variable neighborhood search for solving the OpMP, where the single search ingredient, the interchange neighborhood structure, is used. We also propose a new simple local search strategy for solving facility location problems, within the interchange neighborhood structure, which is in between the usual ones: first improvement and best improvement strategies. We call it facility best improvement local search. On the basis of experiments, it appeared to be more efficient and effective than both first and best improvement. According to the results obtained on the benchmark instances, our heuristic turns out to be highly competitive with the existing ones, establishing new state‐of‐the‐art results. For example, four new best‐known solutions and 133 ties are claimed in testing the set with 144 instances.

Variable neighbourhood search for financial derivative problem

We propose a new matching problem for combinatorial optimization in financial markets. The problem studied here has arisen from the financial regulators that collect transaction data across regulated assets classes. Unlike previous matching problems, our focus is to identify any unhedged/unmatched derivative, Contract for Difference (CFD) with its corresponding underlying asset that has been reported to the corresponding component authorities. The underlying asset and CFD transaction contain variables like volume and price. Therefore, we are looking for a combination of underlying asset variables that may hedge/match the equivalent CFD variables. Our aim is to identify unhedged /unmatched CFD?s. This problem closely relates to the goal programming problem with variable parameters. In this paper, we construct and implement a variant of BasicVariable Neighborhood Search (BVNS) with our newly constructed local search techniques that performs efficient neighbourhood search to solve these types of problems. Computational results show that the proposed approach achieve good solutions.

A variable neighborhood search approach for the vertex bisection problem

The Vertex Bisection Problem (VBP) belongs to the family of well-known graph partitioning problems, where the main goal is to find a partition of the vertices maximizing or minimizing a given objective function. These optimization problems have relevant application in the context of scientific computing, VLSI design circuit, or task scheduling in multi-processor systems. This family of problems has gained importance due to its application in clustering and detection of cliques in social, pathological, and biological networks.In this paper we use Basic Variable Neighborhood Search (BVNS) methodology to solve the VBP. In particular, we propose three constructive procedures and six improvement methods. We introduce a novel scheme for calculating the objective function which substantially reduces the computing time as compared with the direct implementation. After a set of preliminary experiments, the best BVNS design is compared with the state-of-the-art over the same set of instances obtaining better results for both, quality of the solutions and execution time. These results are further confirmed by non-parametric statistical tests.

A parallel variable neighborhood search approach for the obnoxious p‐median problem

AbstractThe obnoxious p‐median problem consists of selecting p locations, considered facilities, in a way that the sum of the distances from each nonfacility location, called customers, to its nearest facility is maximized. This is an ‐hard problem that can be formulated as an integer linear program. In this paper, we propose the application of a variable neighborhood search (VNS) method to effectively tackle this problem. First, we develop new and fast local search procedures to be integrated into the basic VNS methodology. Then, some parameters of the algorithm are tuned in order to improve its performance. The best VNS variant is parallelized and compared with the best previous methods, namely branch and cut, tabu search, and GRASP over a wide set of instances. Experimental results show that the proposed VNS outperforms previous methods in the state of the art. This fact is finally confirmed by conducting nonparametric statistical tests.

Variable neighborhood search based approaches to a vehicle scheduling problem in agriculture

AbstractA vehicle scheduling problem (VSP) that arises from sugar beet transportation within minimum working time under the set of constraints reflecting a real‐life situation is considered. A mixed integer quadratically constrained programming (MIQCP) model of the considered VSP and reformulation to a mixed integer linear program (MILP) are proposed and used within the framework of Lingo 17 solver, producing optimal solutions only for small‐sized problem instances. Two variants of the variable neighborhood search (VNS) metaheuristic—basic VNS (BVNS) and skewed VNS (SVNS) are designed to efficiently deal with large‐sized problem instances. The proposed VNS approaches are evaluated and compared against Lingo 17 and each other on the set of real‐life and generated problem instances. Computational results show that both BVNS and SVNS reach all known optimal solutions on small‐sized instances and are comparable on medium‐ and large‐sized instances. In general, SVNS significantly outperforms BVNS in terms of running times.

Less is more: basic variable neighborhood search heuristic for balanced minimum sum-of-squares clustering

Clustering addresses the problem of finding homogeneous and well-separated subsets, called clusters, from a set of given data points. In addition to the points themselves, in many applications, there may exist constraints regarding the size of the clusters to be found. Particularly in balanced clustering, these constraints impose that the entities be equally spread among the different clusters. In this work, we present a basic variable neighborhood search heuristic for balanced minimum sum-of-squares clustering, following the recently proposed “Less Is More Approach”. Computational experiments and statistical tests show that the proposed algorithm outperforms the current state-of-the-art algorithm for the problem, indicating that non sophisticated and easy to implement metaheuristic methods can be sufficient to produce successful results in practice.

Application of a Basic Variable Neighborhood Search Algorithm in the Coordinated Tuning of PSS and POD Controllers

This paper proposes the application of a Basic Variable Neighborhood Search algorithm in the coordinated and simultaneous tuning of the parameters of damping controllers known as power system stabilizer and thyristor-controlled series capacitor–power oscillation damping. The controllers are inserted into the multi-machine power system New England (10 generators, 39 buses and 46 transmission lines) in order to guarantee its small-signal stability. A current injection model for the thyristor-controlled series capacitor is presented and incorporated into the current sensitivity model, which is used to represent the electric power system and its components. The performance of the method proposed in this work is compared to three other methods found in the literature: local search, iterated local search and particle swarm optimization. The results show that, of the techniques analyzed, the Basic Variable Neighborhood Search is the most efficient for this type of problem, presenting high convergence rates and the shortest processing times with robust solutions considering different scenarios with load variations.

Model and metaheuristics for a scheduling problem integrating procurement, sale and distribution decisions

This paper presents an integrated approach for short-term supply chain management (SCM) at a fast moving consumer goods production plant. The problem is to determine the production quantities, to provide a detailed production schedule, to trigger the relevant express deliveries of raw material, and to manage the distribution. We propose a linear integer model, which integrates all of these decisions within scheduling. To find high quality solutions in a reasonable amount of time, various solution methods are proposed, such as a greedy constructive heuristic, two tabu search metaheuristics, a basic variable neighborhood search and an enhanced one, which uses a variable shaking operator. Experiments on realistic instances show that the latter method is efficient and robust. This paper is a contribution to the SCM literature (indeed, only few references address the integration of short term decisions) and to the general metaheuristics field (as the variable neighborhood search paradigm is extended).

A single-machine scheduling problem with multiple unavailability constraints: A mathematical model and an enhanced variable neighborhood search approach

AbstractThis research focuses on a scheduling problem with multiple unavailability periods and distinct due dates. The objective is to minimize the sum of maximum earliness and tardiness of jobs. In order to optimize the problem exactly a mathematical model is proposed. However due to computational difficulties for large instances of the considered problem a modified variable neighborhood search (VNS) is developed. In basic VNS, the searching process to achieve to global optimum or near global optimum solution is totally random, and it is known as one of the weaknesses of this algorithm. To tackle this weakness, a VNS algorithm is combined with a knowledge module. In the proposed VNS, knowledge module extracts the knowledge of good solution and save them in memory and feed it back to the algorithm during the search process. Computational results show that the proposed algorithm is efficient and effective.Highlights A scheduling problem with multiple unavailability is proposed and formulated. A knowledge-based variable neighborhood search algorithm is proposed. Extensive computational tests confirm the good capability of the proposed model and algorithm.

A variable neighbourhood search method for solving the long-term care facility location problem

This article deals with a problem of determining locations for installing long-term care facilities in the given network, in order to minimize the maximum number of patients that are assigned to a single installed facility. The problem is known as the Long-Term Care Facility Location Problem (LTCFLP). We propose an improved mathematical formulation for the LTCFLP and evaluate its efficiency through a set of computational experiments on test instances with up to 80 potential facility locations. To solve instances of larger problem dimensions, we develop a metaheuristic method based on a Variable Neighbourhood Search (VNS). A reduced VNS algorithm is employed to provide a good-quality initial solution, which is then used as a starting point of the basic VNS method. A local search procedure with efficient fast interchange method is implemented in the proposed VNS-based approach. The algorithm is benchmarked on a large-scale dataset involving up to 400 potential facility locations. Presented computational results show that the proposed VNS quickly reaches all optimal solutions from the literature, and in most cases outperforms existing heuristic methods for solving the LTCFLP.