Variable Neighborhood Decomposition Search Research Articles

Collaborative Planning in a Two-Stage Supply Chain: Transparent Coordination, Distributed Response, Integrated Optimization

In the competitive global market, large manufacturing enterprises are striving to achieve a competitive edge through constructing a transparent collaborative supply chain. One of the important and effective ways is to cooperate with distributed response from suppliers in the operation of the supply chain, such as production planning. This article proposes a new collaborative planning mode in a two-stage supply chain considering the supplier part production and product assembly simultaneously. In this context, a mathematical model is formulated and the integrated optimization method is proposed. To reduce the complexity of the problem, the part production decisions of suppliers are first addressed by some lemmas. Then, the transformation process of the mathematical model is described as the decision variables gradually decrease. On this basis, we further propose a LIMA-GVNDS (less is more approach-general variable neighborhood decomposition search) algorithm to solve the integrated supply chain planning problem for the assembly manufacturing enterprise. The objective is to minimize the total supply chain costs. A new neighborhood structure is designed according to the problem characteristics and a series of variable neighborhood descent (VND) variants are proposed. Some computational experiments are carried out, and the results show that the proposed LIMA-GVNDS algorithm has obtained an average 3.69%, 13.07%, 2.47%, and 2.99% improvement of objective value against the other four meta-heuristic algorithms. The model transformation and the integrated optimization method proposed in this article can provide a reference for large manufacturing enterprises to formulate collaborative planning in a transparent supply chain network.

Optimal allocating and sizing of passenger ferry fleet in maritime transport

Ferry service represents an important geostrategic, economic and social issues for the coastal regions that are using this mode of transport to satisfy demands of domicile population and tourists. The existing analyses report the significance of ferry service as an alternative mode of transport in narrow places that have a limited road infrastructure. We investigate the organization of transport policy establishing regular passenger ferry fleet service among a given set of routes and predetermined passenger preferences within the defined planning horizon. A Mixed Integer Programming (MIP), more precisely Mixed Integer Linear Programming (MILP) formulation for deterministic optimization problem related to the maximization of ferry operator's profit is developed. It considers the passenger ferry fleet sizing taking into account the employment of the existing and subcontracted fleet. The proposed model can be used to optimally solve instances by using a commercial exact solver. To deal with hard examples, we used three matheuristic methods: Variable Neighborhood Branching (VNB), Variable Neighborhood Decomposition Search for 0-1 MIP (VNDS 0–1 MIP) and Variable Intensity Neighborhood Search (VINS). Our experimental results show that in most of the cases matheuristics produce solutions of equal or higher quality in less computational time compared to the commercial exact solver.

A variable neighbourhood decomposition search approach applied to a global liner shipping network using a hub-and-spoke with sub-hub structure

This paper presents a new concept for a hub-and-spoke network structure, called “sub-hub”, applied to global operations of liner shipping. Hub-and-spoke networks are widely used in transportation due to the economy of scale offered to the demands between hubs. However, efficient network structures require more than an economy of scale with regard to transport costs. This study therefore, aims to demonstrate that lower transport costs are achievable by a hub-and-spoke with sub-hub structure because the economy of scale this model provides is combined with shorter alternative paths. A short sea operation in liner shipping is a circular route at cluster level (the hub and its allocated spokes). A deep sea operation functions as a direct connection between hubs. A sub-hub is an intersection point between two regional (cluster) routes, thereby allowing the transshipment of goods, for certain demands, without using hub nodes. Hubs and sub-hubs are selected between the existing ports (nodes), and installation costs are not included for these models. A cutting plane approach was implemented. Although the computation results of the models, which are classified as hub location-routing problems, were compared on small instances, a Variable Neighbourhood Decomposition Search (VNDS) was implemented to test large instances.

Multiple vehicle synchronisation in a full truck-load pickup and delivery problem: A case-study in the biomass supply chain

The search for higher efficiency in transportation planning processes in real life applications is challenging. The synchronisation of different vehicles performing interrelated operations can enforce a better use of vehicle fleets and decrease travelled distances and non-productive times, leading to a reduction of logistics costs. In this work, the full truck-load pickup and delivery problem with multiple vehicle synchronisation (FT-PDP-mVS) is presented. This problem is motivated by a real-life application in the biomass supply chain “hot-system”, where it is necessary to simultaneously perform chipping and transportation operations at the forest roadside. The FT-PDP-mVS consists in determining the integrated routes for three distinct types of vehicles, which need to perform interrelated operations with minimum logistics costs. We extend existing studies in synchronisation of multiple routes by acknowledging several synchronisation aspects, such as operations and movement synchronisation. A novel mixed integer programming model (MIP) is presented, along with valid inequalities to tighten the formulation. A solution method approach is developed based on the fix-and-optimise principles under a variable neighbourhood decomposition search. Results of its application to 19 instances based on a real-world case-study demonstrate its performance. For a baseline instance, the synchronisation aspects tackled in this problem allowed for significant gains when compared to the company’s current planning approach. Furthermore, the proposed approach can enhance planning and decision making processes by providing valuable insights about the impact of key parameters of biomass logistics over the routing results.

VNDS for the min-power symmetric connectivity problem

We consider the NP-hard problem of synthesis of optimal spanning communication subgraph in a given arbitrary simple edge-weighted graph. This problem occurs in the wireless networks while minimizing total transmission power consumptions. We propose a new method based on the variable neighborhood decomposition search metaheuristic for the approximate solution to the problem. We have performed a numerical experiment where the proposed algorithm was executed on the randomly generated test instances. For these instances, on average, our algorithm significantly outperforms the previously known heuristics, comparing solutions obtained after the same run time. The advantage of the proposed algorithm becomes more noticeable with increasing dimensions of the problem.

A VNDS Approach for the Liner Shipping Transport in a Structure of Hub-and-Spoke with Sub-Hub

In this work, a network structures type hub-and-spoke combining short alternative paths and economy of scale is provided trying to minimize the demand routing cost in liner shipping transport. Deep sea operation is done by direct connections between hubs and short sea operation is represented by circular route inside each cluster (regions). Developed models are classified as hub location-routing problems. A structure with sub-hubs (nodes with multiple allocation), allowing alternative paths, is compared with a structure without sub-hub. A Variable Neighborhood Decomposition Search (VNDS) was implemented for testing large problem instances.

Ascent–descent variable neighborhood decomposition search for community detection by modularity maximization

In this paper we propose a new variant of the Variable Neighborhood Decomposition Search (VNDS) heuristic for solving global optimization problems. We call it Ascent-Descent VNDS since it performs “boundary effect”, or local search step, even if the improvement in solving the subproblem has not been obtained. We apply it in detecting communities in large networks by modularity maximization, the criterion which is, despite of some recent criticism, most widely used. Computational analysis is performed on 22 instances from the 10th DIMACS Implementation Challenge. On 13 instances where optimal solutions were not known, we got the improved best known solutions on 9 instances and on 4 instances the solution was equal to the best known. Thus, the proposed new heuristic outperforms the current state-of-the-art algorithms from the literature.

The competitive facility location problem under disruption risks

Two players sequentially locate a fixed number of facilities, competing to capture market share. Facilities face disruption risks, and each customer patronizes the nearest operational facility, regardless of who operates it. The problem therefore combines competitive location and location with disruptions. This combination has been absent from the literature. We model the problem as a Stackelberg game in which the leader locates facilities first, followed by the follower, and formulate the leader’s decision problem as a bilevel optimization problem. A variable neighborhood decomposition search heuristic which includes variable fixing and cut generation is developed. Computational results suggest that high quality solutions can be found quickly. Interesting managerial insights are drawn.

A bi-layer optimization approach for a hybrid flow shop scheduling problem involving controllable processing times in the steelmaking industry

A steelmaking-continuous casting (SCC) scheduling problem is an example of complex hybrid flow shop scheduling problem (HFSSP) with a strong industrial background. This paper investigates the SCC scheduling problem that involves controllable processing times (CPT) with multiple objectives concerning the total waiting time, earliness/tardiness and adjusting cost. The SCC scheduling problem with CPT is seldom discussed in the existing literature. This study is motivated by the practical situation of a large integrated steel company in which the just-in-time (JIT) and cost-cutting production strategy have become a significant concern. To address this complex HFSSP, the scheduling problem is decomposed into two subproblems: a parallel machine scheduling problem (PMSP) in the last stage and an HFSSP in the upstream stages. First, a hybrid differential evolution (HDE) algorithm combined with a variable neighborhood decomposition search (VNDS) is proposed for the former subproblem. Second, an iterative backward list scheduling (IBLS) algorithm is presented to solve the latter subproblem. The effectiveness of this bi-layer optimization approach is verified by computational experiments on well-designed and real-world scheduling instances. This study provides a new perspective on modeling and solving practical SCC scheduling problems.

Uma meta-heurística de busca decomposta em vizinhança variável para o problema bidimensional de agrupamento de entregas em veículos de uma frota heterogênea

Este artigo trata do problema de distribuição física que envolve o agrupamento e alocação de entregas a uma frota de veículos visando minimizar o frete total. Este problema surge em diferentes situações práticas em que os pontos a serem atendidos estão suficientemente próximos entre si de tal modo que as distâncias percorridas entre paradas consecutivas podem ser consideradas irrelevantes para o custo total de entregas da frota e, portanto, podem ser desconsideradas para o cálculo dos fretes pagos a terceiros que realizam esse serviço. Este trabalho propõe um método de resolução para um problema de binpacking generalizado com restrições adicionais encontrado em situações práticas de logística e transporte de cargas. Neste trabalho é proposta uma meta-heurística de Busca Decomposta em Vizinhança Variável (VNDS) para a resolução desse problema. Experimentos computacionais com instâncias de problemas benchmarking da literatura evidenciam que essa meta-heurística produz bons resultados (obteve a solução ótima ou próxima do limite inferior em todas as instâncias testadas) em tempos de processamento bastante reduzidos (até 5,10% mais rápido do que o VNS).

New variable neighbourhood search based 0-1 MIP heuristics

In recent years many so-called matheuristics have been proposed for solving Mixed Integer Programming (MIP) problems. Though most of them are very efficient, they do not all theoretically converge to an optimal solution. In this paper we suggest two matheuristics, based on the variable neighbourhood decomposition search (VNDS), and we prove their convergence. Our approach is computationally competitive with the current state-of-the-art heuristics, and on a standard benchmark of 59 0-1 MIP instances, our best heuristic achieves similar solution quality to that of a recently published VNDS heuristic for 0-1 MIPs within a shorter execution time.

Variable neighborhood search for the pharmacy duty scheduling problem

In this paper, we study on the Pharmacy Duty Scheduling (PDS) problem, where a subset of pharmacies should be on duty on national holidays, at weekends and at nights in order to be able to satisfy the emergency drug needs of the society. PDS problem is a multi-period p-median problem with special side constraints and it is an NP-Hard problem. We propose four Variable Neighborhood Search (VNS) heuristics. The first one is the basic version, BVNS. The latter two, Variable Neighborhood Decomposition Search (VNDS) and Variable Neighborhood Restricted Search (VNRS), aim to obtain better results in less computing time by decomposing or restricting the search space. The last one, Reduced VNS (RVNS), is for obtaining good initial solutions rapidly for BVNS, VNDS and VNRS. We test BVNS, VNRS and VNDS heuristics on randomly generated instances and report the computational test results. We also use VNS heuristics on real data for the pharmacies in central İzmir and obtain significant improvements.

Routing of barge container ships by mixed-integer programming heuristics

We investigate the optimization of transport routes of barge container ships with the objective to maximize the profit of a shipping company. This problem consists of determining the upstream and downstream calling sequence and the number of loaded and empty containers transported between any two ports. We present a mixed integer linear programming (MILP) formulation for this problem. The problem is tackled by the commercial CPLEX MIP solver and improved variants of the existing MIP heuristics: Local Branching, Variable Neighborhood Branching and Variable Neighborhood Decomposition Search. It appears that our implementation of Variable Neighborhood Branching outperforms CPLEX MIP solver both regarding the solution quality and the computational time. All other studied heuristics provide results competitive with CPLEX MIP solver within a significantly shorter amount of time. Moreover, we present a detailed case study transportation analysis which illustrates how the proposed approach can be used by managers of barge shipping companies to make appropriate decisions and solve real life problems.

A variable neighborhood decomposition search algorithm for multilevel capacitated lot-sizing problems

Abstract The multi-level capacitated lot-sizing problem (MLCLSP) has been an important part of material requirement planning (MRP) system. In this paper we combine variable neighborhood decomposition search and accurate mixed integer programming (VNDS-MIP) to solve MLCLSP. This method is based on the variable neighborhood search, and with the use of exact LP/MIP solvers ILOG CPLEX, it's proved to be very efficient in solving MLCLSP problem. Computational experiments are carried out on three classes of benchmark instances and VNDS-MIP shows good performance in solving the lot-sizing problem. For the 300 small-sized instances, the VNDS-MIP algorithm can find 97.67% of the optimal solutions in several seconds; for the 150 medium-sized instances, the VNDS-MIP algorithm is better than the other methods.

Combining the principles of variable neighborhood decomposition search and the fix&optimize heuristic to solve multi-level lot-sizing and scheduling problems

In this paper a new heuristic is proposed to solve general multi-level lot-sizing and scheduling problems. The idea is to cross-fertilize the principles of the meta-heuristic Variable Neighborhood Decomposition Search (VNDS) with those of the MIP-based Fix&Optimize heuristic. This combination will make it possible to solve the kind of problems that typically arise in the consumer goods industry due to sequence-dependent setups and shifting bottlenecks. In order to demonstrate the strength of this procedure, a GLSP variant for multiple production stages is chosen as a representative. With the help of artificial and real-world instances, the quality of the solution as well as the computational performance of the new procedure is tested and compared to a standard MIP-solver.

Hybrid Variable Neighbourhood Decomposition Search for 0-1 Mixed Integer Programming Problem

Abstract In this paper we propose new hybrid heuristics for the 0-1 mixed integer programming problem, based on the variable neighbourhood decomposition search principle and on exploiting information obtained from a series of relaxations. In the case of a maximization problem, we add iteratively pseudo-cuts to the problem in order to produce a sequence of lower and upper bounds of the problem, so that integrality gap is reduced. We validate our approaches on the well-known 0-1 multidimensional knapsack problem, in which the general-purpose CPLEX MIP solver is used as a black box for solving subproblems generated during the search process. The results obtained with these methods are comparable with the current state-of-the-art heuristics on a set of large scale instances.

Variable neighbourhood decomposition search for 0–1 mixed integer programs

In this paper we propose a new hybrid heuristic for solving 0–1 mixed integer programs based on the principle of variable neighbourhood decomposition search. It combines variable neighbourhood search with a general-purpose CPLEX MIP solver. We perform systematic hard variable fixing (or diving) following the variable neighbourhood search rules. The variables to be fixed are chosen according to their distance from the corresponding linear relaxation solution values. If there is an improvement, variable neighbourhood descent branching is performed as the local search in the whole solution space. Numerical experiments have proven that exploiting boundary effects in this way considerably improves solution quality. With our approach, we have managed to improve the best known published results for 8 out of 29 instances from a well-known class of very difficult MIP problems. Moreover, computational results show that our method outperforms the CPLEX MIP solver, as well as three other recent most successful MIP solution methods.

Solving 0–1 Mixed Integer Programs with Variable Neighbourhood Decomposition Search

Abstract In this paper we propose a new heuristic for solving 0–1 mixed integer programs based on the variable neighbourhood decomposition search principle. It combines variable neighbourhood search with general-purpose CPLEX MIP solver. We perform systematic hard variables fixing (or diving) following the variable neighbourhood search rules. Variables to be fixed are chosen according to their distance from the corresponding linear relaxation solution values. If there is an improvement, variable neighbourhood descent branching is performed as the local search in the whole solution space. Numerical experiments have proven that by exploiting boundary effects in this way, solution quality can be considerably improved. With our approach, we have managed to improve the best known published results for 8 out of 29 instances from a well-known class of very difficult MIP problems. Moreover, computational results show that our method outperforms CPLEX MIP solver, as well as three other recent most successful MIP solution methods.

Variable Neighbourhood Decomposition Search with Bounding for Multidimensional Knapsack Problem

Abstract In this paper we propose a new heuristic for solving multidimensional knapsack problem, based on the variable neighbourhood decomposition search principle. The set of neighbourhoods is generated by exploiting information obtained from a series of relaxations. In each iteration, we add new constraints to the problem in order to produce a sequence of lower and upper bounds around the optimal value, with the goal to reduce the gap between them. General-purpose CPLEX MIP solver is used as a black box for solving subproblems generated during the search process. With this approach, we have managed to obtain promising results on a set of large scale multidimensional knapsack problem instances. The results are comparable with the current state-of-the-art techniques for solving multidimensional knapsack problem.

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,