Skewed Variable Neighborhood Search Research Articles

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.

Skewed general variable neighborhood search for the cumulative capacitated vehicle routing problem

AbstractThe cumulative capacitated vehicle routing problem (CCVRP) is a relatively new version of the classical capacitated vehicle routing problem, and it is equivalent to a traveling repairman problem with capacity constraints and a homogeneous vehicle fleet, which aims to minimize the total arrival time at customers. Many real‐world applications can be modeled by this problem, such as the important application resulting from the humanitarian aid following a natural disaster. In this paper, two heuristics are proposed. The first one is a constructive heuristic to generate an initial solution and the second is the skewed variable neighborhood search (SVNS) heuristic. The SVNS algorithm starts with the initial solution. At each iteration, the perturbation phase and the local search phase are used to improve the solution of the CCVRP, and the distance function in acceptance criteria phase is used to improve the exploration of faraway valleys. This algorithm is applied to a set of benchmarks, and the comparison results show that the proposed algorithms provide better solutions than those reported in the previous literature on memetic algorithms and adaptive large neighborhood search heuristics.

Variable neighborhood search with memory for a single-machine scheduling problem with periodic maintenance and sequence-dependent set-up times

In this paper we study the problem of sequencing jobs in a single machine with programmed preventive maintenance and sequence-dependent set-up times. This is an NP-hard problem that has practical relevance because of its industrial applications (textile industry, chemical industry, manufacturing of printed circuit boards, etc.), in which machines need periodic preventive maintenance. An improved formulation of this problem is proposed. Using this new formulation computational experiments show that commercial software can solve exactly not only small-sized instances but also almost all medium-sized instances as well. For solving large-sized instances a heuristic method based on the Variable Neighborhood Search (VNS) is proposed. Specifically, a Skewed VNS with memory, that is, it allows, under certain conditions, the current solution to move to a worse solution and for the incorporation of memory in the search process. Computational experiments show the good performance of our proposed VNS-based method. For small- and medium-sized instances specifically, this method obtains very close-to-optimal solutions, finding the optimal solution in the almost every case. In larger instances our method performs better than previously published algorithms. Several statistical tests support these conclusions. All instances used in computational experiments have been taken from the literature.

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.

Solving the capacitated clustering problem with variable neighborhood search

Variable neighborhood search (VNS) is a proven heuristic framework for finding good solutions to combinatorial and global optimization problems. In this paper two VNS-based heuristics are proposed for solving the capacitated clustering problem. The first follows a standard VNS approach, and the second a skewed VNS that allows moves to inferior solutions. The performance of the two heuristics is assessed on benchmark instances from the literature. We also compare their performance against a recently published iterated VNS procedure. All VNS procedures outperform the state-of-the-art, but the Skewed VNS is best overall. This would suggest that using acceptance criteria before allowing moves to inferior solutions in Skewed VNS is preferable to the random shaking approach that is used in Iterated VNS to move to new regions of the solution space.

General Metaheuristic Algorithm for a Set of Rich Vehicle Routing Problems

This paper studies a set of rich vehicle routing problems incorporating various complexities found in real-life applications. The rich vehicle routing problem considers simultaneously four multiple constraints: multiple depots, multiple time windows, multiple trips, and multiple vehicle types. A metaheuristic algorithm called the general vehicle routing algorithm, based on the skewed variable neighborhood search, was designed to address the problem of any combination on five features. A slice of operators and heuristic approaches developed for the specific constraints is embedded in the general vehicle routing algorithm. Six combination vehicle routing problem types were investigated. The computational results demonstrated that the proposed algorithm is competitive for both benchmark instances and generated instances in accuracy of solution and computational time.

Enhancing variable neighborhood search by adding memory: Application to a real logistic problem

This paper addresses a real problem of designing the routes over a planning period with flexibility in the dates of delivery. Specifically, a method based on the strategy Variable Neighborhood Search (VNS) is designed for this problem. The VNS-based method takes some ideas from routing-first cluster-second strategies for routing problems. In addition, it has two important features: it uses a memory-based shaking procedure and it allows, under some conditions, to move from the current solution to a worse solution (Skewed VNS). This procedure performs better than its basic version (no memory, not skewed). Computational experiments with real-data-based instances show that our VNS obtains better results than previous methods for this problem. The method is simple, with an easy implementation and can be adapted to other routing problems.

A variable neighborhood search method for the orienteering problem with hotel selection

Abstract In this paper, we present the orienteering problem with hotel selection (OPHS), an extension of the orienteering problem (OP). In the OPHS, a set of vertices with a score and a set of hotels are given. The goal is to determine a fixed number of connected trips that visits some vertices and maximizes the sum of the collected scores. Each trip is limited in length and should start and end in one of the hotels. We formulate the problem mathematically, explain the differences with related optimization problems and indicate what makes this problem inherently more difficult. We use a skewed variable neighborhood search that consists of a constructive initialization procedure and an improvement procedure. The algorithm is based on a neighborhood search operator designed specifically for the hotel selection part of this problem, as well as some typical neighborhoods for the regular OP. We generate a set of 224 benchmark instances of varying sizes with known optimal solutions. For 102 of these instances our algorithm finds the optimal solution. The average gap with the optimal solution over all these instances is only 1.44% and the average computation time is 1.91 s.

Multiobjective metaheuristics for frequency assignment problem in mobile networks with large‐scale real‐world instances

PurposeThe purpose of this paper is to address a multiobjective FAP (frequency assignment problem) formulation. More precisely, two conflicting objectives – the interference cost and the separation cost – are considered to characterize FAP as an MO (multiobjective optimization) problem.Design/methodology/approachThe contribution to this specific telecommunication problem in a real scenario follows a recent approach, for which the authors have already accomplished some preliminary results. In this paper, a much more complete analysis is performed, including two well‐known algorithms (such as the NSGA‐II and SPEA2), with new results, new comparisons and statistical studies. More concretely, in this paper five different algorithms are presented and compared. The popular multiobjective algorithms, NSGA‐II and SPEA2, are compared against the Differential Evolution with Pareto Tournaments (DEPT) algorithm, the Greedy Multiobjective Variable Neighborhood Search (GMO‐VNS) algorithm and its variant Greedy Multiobjective Skewed Variable Neighborhood Search (GMO‐SVNS). Furthermore, the authors also contribute with a new design of multiobjective metaheuristic named Multiobjective Artificial Bee Colony (MO‐ABC) that is included in the comparison; it represents a new metaheuristic that the authors have developed to address FAP. The results were analyzed using two complementary indicators: the hypervolume indicator and the coverage relation. Two large‐scale real‐world mobile networks were used to validate the performance comparison made among several multiobjective metaheuristics.FindingsThe final results show that the multiobjective proposal is very competitive, clearly surpassing the results obtained by the well‐known multiobjective algorithms (NSGA‐II and SPEA2).Originality/valueThe paper provides a comparison among several multiobjective metaheuristics to solve FAP as a real‐life telecommunication engineering problem. A new multiobjective metaheuristic is also presented. Preliminary results were enhanced with two well‐known multiobjective algorithms. To the authors' knowledge, they have never been investigated for FAP.

Skewed VNS enclosing second order algorithm for the degree constrained minimum spanning tree problem

We develop ideas to enhance the performance of the variable neighborhood search (VNS) by guiding the search in the shaking phase, and by employing the Skewed strategy. For this purpose, Second Order algorithms and Skewed functions expressing structural differences are embedded in an efficient VNS proposed in the literature for the degree constrained minimum spanning tree problem. Given an undirected graph with weights associated with its edges, the degree constrained minimum spanning tree problem consists in finding a minimum spanning tree of the given graph, subject to constraints on node degrees. Computational experiments are conducted on the largest and hardest benchmark instances found in the literature to date. We report results showing that the VNS with the proposed strategies improved the best known solutions for all the hardest benchmark instances. Moreover, these new best solutions significantly reduced the gaps with respect to tight lower bounds reported in the literature.

Introduction to the special issue on variable neighborhood search

Variable Neighborhood Search (VNS) is a metaheuristic for solving optimization problems based on systematic changes of structure within a search that may be performed in a deterministic way (Variable Neighborhood Descent, VND) or randomly (reduced VNS). Basic VNS combines random selection of a point in a shaking or perturbation step followed by a deterministic local search from that point. There are several extensions and hybrids of the basic VNS scheme suggested in the literature: if VND is used instead of local search, we have general VNS; the variable neighbourhood decomposition search (VNDS) method extends the basic VNS into a two-level VNS scheme based upon decomposition of the problem; the skewed VNS allows moves to a slightly worse but far solutions, etc. VNS has been successfully applied to a wide range of combinatorial and global optimization problems. In this special issue of Journal of Heuristics we collect several new successful applications of VNS as well as studies of advanced characteristics of VNS. Most of them were presented at the XVIII Mini EURO Conference (MEC), which was held at Tenerife, Spain, in November 2005. On that meeting, 61 VNS contributions by researches from 14 different countries and 4 continents were presented. The papers that make up this special issue on Variable Neighborhood Search illustrate breadth and depth of research in variable neighborhood search since they show some advanced features of the metaheuristic. Michael Polacek, Karl F. Doerner, Richard F. Hartl and Vittorio Maniezzo develop a basic variable neighborhood search algorithm to solve the Capacitated Arc Routing Problem with Intermediate Facilities that outperforms all known heuristics on four benchmark sets. The method uses only one exchange operator, the CROSS-exchange,

Variable neighborhood search: Principles and applications

Systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization, called variable neighborhood search (VNS). We present a basic scheme for this purpose, which can easily be implemented using any local search algorithm as a subroutine. Its effectiveness is illustrated by solving several classical combinatorial or global optimization problems. Moreover, several extensions are proposed for solving large problem instances: using VNS within the successive approximation method yields a two-level VNS, called variable neighborhood decomposition search (VNDS); modifying the basic scheme to explore easily valleys far from the incumbent solution yields an efficient skewed VNS (SVNS) heuristic. Finally, we show how to stabilize column generation algorithms with help of VNS and discuss various ways to use VNS in graph theory, i.e., to suggest, disprove or give hints on how to prove conjectures, an area where metaheuristics do not appear to have been applied before.