Parallel Variable Neighborhood Search Research Articles

A parallel variable neighborhood search for [formula omitted]-neighbor facility location problems

In this paper, we employ the less is more approach to develop a Parallel Variable Neighborhood Search (VNS) algorithm for the α-neighbor p-center problem (αNpCP) and the α-neighbor p-median problem (αNpMP). The αNpCP and the αNpMP are generalizations of the p-center (pCP) and p-median (pMP) problems, respectively. In the α-neighbor problems, one seeks to open p facilities and assign each of the n customers to their closest α ones. The objective is to minimize the maximum distance of a customer to its αth facility, in the case of the αNpCP, and the sum of the distances from each customer to their α nearest facilities, in the case of the αNpMP. Our VNS adapts simple but efficient algorithms and data structures from the pCP and pMP literature to the αNpCP and αNpMP context. We also introduce an updated objective function for the αNpCP, which adds more information to the solution cost and helps the VNS to escape from local optima. Several experimental tests show that our VNS outperforms more complex state-of-the-art algorithms. Regarding the αNpCP, on 120 instances derived from the OR-library set, our algorithm improved best-known solutions for 22, with an average improvement of 34.26%; the overall gap on the 120 instances is 6.18% in favor of our algorithm. Moreover, on 231 instances derived from the TSPLIB set, we improved the solutions for 115, with an average improvement of 5.30%, and an overall improvement gap of 2.47% for all 231 instances. Considering the αNpMP results, our heuristic obtained better results than a heuristic from literature in all 80 instances tested, finding optimal solutions in all these instances.

A multi-objective parallel variable neighborhood search for the bi-objective obnoxious p-median problem

Researchers and practitioners have addressed many variants of facility locations problems. Each location problem can be substantially different from each other depending on the objectives and/or constraints considered. In this paper, the bi-objective obnoxious p-median problem (Bi-OpM) is addressed given the huge interest to locate facilities such as waste or hazardous disposal facilities, nuclear power or chemical plants and noisy or polluting services, among others. The Bi-OpM aims to locate p facilities maximizing two different objectives: the distance between each customer and their nearest facility center and the dispersion among facilities. To address the Bi-OpM problem a Multi-objective Parallel Variable Neighborhood Search approach (Mo-PVNS) is implemented. Computational results indicate the superiority of the Mo-PVNS compared to the state-of-art algorithms.

A parallel variable neighborhood search for solving covering salesman problem

Covering salesman problem (CSP) is to construct a minimum length Hamiltonian cycle over a subset of vertices, in which the vertices not visited on the cycle must be covered by at least one visited vertex. In this paper, the CSP is reformulated as a bilevel CSP (BCSP) with a leader and a follower sub-problem. Two parallel variable neighborhood search (PVNS) heuristics, namely, synchronous “master–slave” PVNS and asynchronous cooperative PVNS, are proposed to solve the BCSP. To test the proposed algorithms, extensive computational experiments on the benchmark instances are performed, and the results indicate the effectiveness of the proposed approaches.

A parallel variable neighborhood search algorithm with quadratic programming for cardinality constrained portfolio optimization

Over the years, portfolio optimization remains an important decision-making strategy for investment. The most familiar and widely used approach in the field of portfolio optimization is the mean–variance framework introduced by Markowitz. Following this pioneering work, many researchers have extended this model to make it more practical and adapt to real-life problems. In this study, one of these extensions, the cardinality constrained portfolio optimization problem, is considered. Cardinality constraints transform the quadratic optimization model into the mixed-integer quadratic programming problem, which is proved to be NP-Hard, making it harder to obtain an optimal solution within a reasonable time by using exact solution methodologies. Hence, the vast majority of the researchers have taken advantage of approximate algorithms to overcome arising computational difficulties. To develop an efficient solution approach for cardinality constrained portfolio optimization, in this study, a parallel variable neighborhood search algorithm combined with quadratic programming is proposed. While the variable neighborhood search algorithm decides the combination of assets to be held in the portfolio, quadratic programming quickly calculates the proportions of assets. The performance of the proposed algorithm is tested on five well-known datasets and compared with other solution approaches in the literature. Obtained results confirm that the proposed solution approach is very efficient especially on the portfolios with low risk and highly competitive with state-of-the-art algorithms.

A new hybrid particle swarm optimization and parallel variable neighborhood search algorithm for flexible job shop scheduling with assembly process

PurposeThe purpose of this paper is to present a mathematical model and a new hybrid algorithm for flexible job shop scheduling problem with assembly operations. In this problem, each product is produced by assembling a set of several different parts. At first, the parts are processed in a flexible job shop system, and then at the second stage, the parts are assembled and products are produced.Design/methodology/approachAs the problem is non-deterministic polynomial-time-hard, a new hybrid particle swarm optimization and parallel variable neighborhood search (HPSOPVNS) algorithm is proposed. In this hybrid algorithm, particle swarm optimization (PSO) algorithm is used for global exploration of search space and parallel variable neighborhood search (PVNS) algorithm for local search at vicinity of solutions obtained in each iteration. For parameter tuning of the metaheuristic algorithms, Taguchi approach is used. Also, a statistical test is proposed to compare the ability of metaheuristics at finding the best solution in the medium and large sizes.FindingsNumerical experiments are used to evaluate and validate the performance and effectiveness of HPSOPVNS algorithm with hybrid particle swarm optimization with a variable neighborhood search (HPSOVNS) algorithm, PSO algorithm and hybrid genetic algorithm and Tabu search (HGATS). The computational results show that the HPSOPVNS algorithm achieves better performance than competing algorithms.Practical implicationsScheduling of manufacturing parts and planning of assembly operations are two steps in production systems that have been studied independently. However, with regard to many manufacturing industries having assembly lines after manufacturing stage, it is necessary to deal with a combination of these problems that is considered in this paper.Originality/valueThis paper proposed a mathematical model and a new hybrid algorithm for flexible job shop scheduling problem with assembly operations.

Cooperative versus non-cooperative parallel variable neighborhood search strategies: a case study on the capacitated vehicle routing problem

The capacitated vehicle routing problem (CVRP) is a well-known NP-hard combinatorial optimization problem with numerous real-world applications in logistics. In this work, we present a literature review with recent successful parallel implementations of variable neighborhood search regarding different variants of vehicle routing problems. We conduct an experimental study for the CVRP using well-known benchmark instances, and we present and investigate three parallelization strategies that coordinate the communication of the multiple processors. We experimentally evaluate a non-cooperative and two novel cooperation models, the managed cooperative and the parameterized cooperative strategies. Our results constitute a first proof-of-concept for the benefits of this new self-adaptive parameterized cooperative approach, especially in computationally hard instances.

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.

Multi-Objective Parallel Variable Neighborhood Search for Energy Consumption Scheduling in Blocking Flow Shops

Blocking flow shop scheduling problem has been extensively studied because of its widespread industrial applications. However, the existing research mostly aims at makespan or total flow time minimization and ignores the criterion for energy saving. This paper investigates the blocking flow shop scheduling problem with both makespan and energy consumption criteria. First, the multi-objective model of blocking flow shop scheduling is formulated in consideration of machine energy consumed in blocking and idle time. Then, a multi-objective parallel variable neighborhood search (MPVNS) algorithm is proposed to solve this problem. An improved Nawaz–Enscore–Ham-based heuristic is developed to generate initial solutions, and a variable neighborhood search is designed to explore these solutions in parallel. Furthermore, an insertion-based pareto local search method is embedded to enhance the exploitation of the algorithm. Finally, in order to validate its effectiveness, the MPVNS is compare with other two effective multi-objective metaheuristics by computational experiments based on well-known benchmark instances. The experimental results illustrate that the proposed algorithm is superior to non-dominated sorting genetic algorithm (II) and bi-objective multi-start simulated annealing algorithm in terms of set coverage and hypervolume measures.

A hybrid CPU-GPU parallelization scheme of variable neighborhood search for inventory optimization problems

In this paper, we study various parallelization schemes for the Variable Neighborhood Search (VNS) metaheuristic on a CPU-GPU system via OpenMP and OpenACC. A hybrid parallel VNS method is applied to recent benchmark problem instances for the multi-product dynamic lot sizing problem with product returns and recovery, which appears in reverse logistics and is known to be NP-hard. We report our findings regarding these parallelization approaches and present promising computational results.

A parallel variable neighborhood search for the vehicle routing problem with divisible deliveries and pickups

A well-known variant of the vehicle routing problem involves backhauls, where vehicles deliver goods from a depot to linehaul customers and pick up goods from backhaul customers to the depot. The vehicle routing problem with divisible deliveries and pickups (VRPDDP) allows vehicles to visit each client once or twice for deliveries or pickups. In this study, a very efficient parallel approach based on variable neighborhood search (VNS) is proposed to solve VRPDDP. In this approach, asynchronous cooperation with a centralized information exchange strategy is used for parallelization of the VNS approach, called cooperative VNS (CVNS). All available problem sets of VRPDDP have been successfully solved with the CVNS, and the best solutions available in the literature have been significantly improved.

Improving the performance of embedded systems with variable neighborhood search

Embedded systems have become an essential part of our lives, mainly due to the evolution of technology in the last years. However, the power consumption of these devices is one of their most important drawbacks. It has been proven that an efficient use of the memory of the device also improves its energy performance. This work efficiently solves the dynamic memory allocation problem, which can be formally defined as follows: given a program that has to be executed by a circuit, the objective is to fit that program in memory in such a way that the computing time required to execute it is minimized. In this work, we propose a parallel variable neighborhood search strategy to address this problem. We additionally compare this parallel procedure with the sequential version of the algorithm and with the best previous approach. Computational results show the superiority of our proposal, backed up with statistical tests.

Parallel variable neighborhood search for the min–max order batching problem

AbstractWarehousing is a key part of supply chain management. It primarily focuses on controlling the movement and storage of materials within a warehouse and processing the associated transactions, including shipping, receiving, and picking. From the tactical point of view, the main decision is the storage policy, that is, to decide where each product should be located. Every day a warehouse receives several orders from its customers. Each order consists of a list of one or more items that have to be retrieved from the warehouse and shipped to a specific customer. Thus, items must be collected by a warehouse operator. We focus on situations in which several orders are put together into batches, satisfying a fixed capacity constraint. Then, each batch is assigned to an operator, who retrieves all the items included in those orders grouped into the corresponding batch in a single tour. The objective is then to minimize the maximum retrieving time for any batch. In this paper, we propose a parallel variable neighborhood search algorithm to tackle the so‐called min–max order batching problem. We additionally compare this parallel procedure with the best previous approach. Computational results show the superiority of our proposal, confirmed with statistical tests.

Parallel VNS for Bus Terminal Location Problem

This paper considers the Bus Terminal Location Problem (BTLP) which incorporates characteristics of both the p-median and maximal covering problems. We propose a parallel variable neighborhood search algorithm (PVNS) for solving BTLP. Improved local search, based on efficient neighborhood interchange, is used for the p-median problem, and is combined with a reduced neighborhood size for the maximal covering part of the problem. The proposed parallel algorithm is compared with its non-parallel version. Parallelization yielded significant time improvement in function of the processor core count. Computational results show that PVNS improves all existing results from the literature, while using significantly less time. New larger instances, based on rl instances from the TSP library, are introduced and computational results for those new instances are reported.

Solving dynamic memory allocation problems in embedded systems with parallel variable neighborhood search strategies

Embedded systems have become an essential part of our lives, thanks to their evolution in the recent years, but the main drawback is their power consumption. This paper is focused on improving the memory allocation of embedded systems to reduce their power consumption. We propose a parallel variable neighborhood search algorithm for the dynamic memory allocation problem, and compare it with the state of the art. Computational results and statistical tests applied show that the proposed algorithm produces significantly better outcomes than the previous algorithm in shorter computing time.

A note on “Parallel variable neighborhood search for solving fuzzy multi-objective dynamic facility layout problem”

Abedzadeh et al. (Int J Adv Manuf Technol 65:197–211, 2013) proposed a mixed integer programming formulation for dynamic flexible bay layout problem with three objectives: minimizing material handling and relayout cost, maximizing adjacency ratio, and minimizing shape ratio difference. In this paper, we correct the formulation proposed by Abedzadeh et al. (Int J Adv Manuf Technol 65:197–211, 2013). This correction is mainly focused on the three objectives of their formulation. It is shown that the relayout cost was miscalculated, the adjacency ratio was improperly linearized, the third objective was incorrectly linearized and fuzzy programming technique for multi-objective linear programming problems was not applied correctly for this problem.

A novel hybrid genetic algorithm for the multidepot periodic vehicle routing problem

AbstractA genetic algorithm is a metaheuristic proposed to derive approximate solutions for computationally hard problems. In the literature, several successful applications have been reported for graph-based optimization problems, such as scheduling problems. This paper provides one definition of periodic vehicle routing problem for single and multidepots conforming to a wide range of real-world problems and also develops a novel hybrid genetic algorithm to solve it. The proposed hybrid genetic algorithm applies a modified approach to generate a population of initial chromosomes and also uses an improved heuristic called the iterated swap procedure to improve the initial solutions. Moreover, during the implementation a hybrid algorithm, cyclic transfers, an effective class of neighborhood search is applied. The author uses three genetic operators to produce good new offspring. The objective function consists of two terms: total traveled distance at each depot and total waiting time of all customers to take service. Distances are assumed Euclidean or straight line. These conditions are exactly consistent with the real-world situations and have received little attention in the literature. Finally, the experimental results have revealed that the proposed hybrid method can be competitive with the best existing methods as asynchronous parallel heuristic and variable neighborhood search in terms of solution quality to solve the vehicle routing problem.

Development of Both the AIS and PSO for Solving the Flexible Job Shop Scheduling Problem

The flexible job shop scheduling problem (FJSP) is to assign each operation to an appropriate machine and to sequence the operations on the machines. The paper describes the development and the application of the artificial immune system (AIS) and the particle swarm optimization (PSO) for solving the flexible job shop scheduling problem with sequence-dependent setup times (SDST-FJSP). A series of the experiments have been designed using the analysis of variance to recognize best settings of parameters. Finally, 30 examples of the different sizes in the SDST-FJSP with the objective of minimizing makespan and mean tardiness have been used to verify the performance of the proposed algorithms, and to compare them with the existing meta-heuristic algorithms in the literature, such as the genetic algorithm (GA), the parallel variable neighborhood search (PVNS), and the variable neighborhood search (VNS). The obtained results show that the proposed PSO outperforms the GA and the PVNS approaches. It is found that the average best-so-far solutions obtained from the proposed AIS are better than those produced by the GA, the PVNS, the VNS, and the PSO algorithms for all the examples.

A parallel variable neighborhood search for the multi-objective sustainable post-sales network design problem

Abstract Environmental and sustainability awareness in societies has attracted many academics and professionals from various disciplines to revise their thoughts and philosophies such as supply chain management. In particular, implementation of reverse logistics systems and closed-loop supply chain often results in reduced environmental pollution and costs, as well as increased customer satisfaction. In this study, a multi-objective post-sales network design model considering strategic and tactical decisions is proposed to minimize total fixed and variable costs, total tardiness, and environmental pollution. In addition to common network design decisions, various decisions such as technology and capacity level decisions as well as product selection at recovery facilities are considered. To tackle the proposed model, a parallel multi-objective heuristic based on variable neighborhood search (VNS) is developed to find Pareto-optimal solutions. The efficiency of proposed method is compared with an available efficient multi-objective memetic algorithm (MOMA). In addition, its results are compared with those of branch and bound methods of two commercial optimization packages for small and medium-sized test instances. Computational results demonstrate the superiority of the proposed algorithm in terms of solution quality and computational time over MOMA as well as the single-thread and multi-thread branch and bound methods. Furthermore, comparing the proposed heuristic with a standard VNS demonstrates the success of parallelization in thoroughly exploring solution space as well as improving number and quality of Pareto-optimal solutions.

Parallel variable neighborhood search for solving fuzzy multi-objective dynamic facility layout problem

In spite of the classic approaches of solution of dynamic facility layout problem, which only material handling and rearrangement costs are considered as objective function, these problems are the multi-objective problems. In this paper, a mixed integer linear programming formulation is presented for multi-objective dynamic facility layout problem concerning flexible bay structure. In addition, three current objectives in dynamic facility layout problems including minimizing material handling and rearrangement costs, maximizing adjacency rate, and minimizing shape ratio difference have been considered. Also, for solving this problem, two methods including the GAMS software and proposed parallel variable neighborhood search (PVNS) algorithm are used. So, it is worth mentioning that four test problems are solved by them, and the results show that the proposed PVNS algorithm is more efficient than the GAMS software.

Flexible job-shop scheduling with parallel variable neighborhood search algorithm

Flexible job-shop scheduling problem (FJSP) is an extension of the classical job-shop scheduling problem. FJSP is NP-hard and mainly presents two difficulties. The first one is to assign each operation to a machine out of a set of capable machines, and the second one deals with sequencing the assigned operations on the machines. This paper proposes a parallel variable neighborhood search (PVNS) algorithm that solves the FJSP to minimize makespan time. Parallelization in this algorithm is based on the application of multiple independent searches increasing the exploration in the search space. The proposed PVNS uses various neighborhood structures which carry the responsibility of making changes in assignment and sequencing of operations for generating neighboring solutions. The results obtained from the computational study have shown that the proposed algorithm is a viable and effective approach for the FJSP.