Variable Neighborhood Search Scheme Research Articles

A single-individual based variable neighborhood search algorithm for the blocking hybrid flow shop group scheduling problem

The Blocking Hybrid Flow Shop Group Scheduling Problem (BHFGSP) is prevalent within the manufacturing industry, where the ordering of groups poses a significant challenge for dispatchers. Moreover, the blocking constraints associated with jobs significantly influence energy consumption, yet these constraints are often overlooked in algorithm design. To address these issues effectively, a single-individual-based variable neighborhood search strategy is introduced. For the challenge of group ordering, a group-based neighborhood search strategy is proposed. This strategy is complemented by a job-based neighborhood search strategy to tackle the issues of blocking and job sequencing. These two neighborhood search strategies are designed to enhance the performance of the algorithm significantly. Furthermore, to augment the local search abilities of the proposed algorithm, the concept of a single-individual approach from the iterated greedy algorithm is integrated. The performance of the proposed algorithm is validated through 36 instances, demonstrating its efficiency in solving BHFGSPs compared to state-of-the-art algorithms. Notably, the proposed algorithm achieves a reduction in energy consumption by an average of 58% to 63.4% compared to previous best solutions.

A DQN-based memetic algorithm for energy-efficient job shop scheduling problem with integrated limited AGVs

AGVs have gained significant popularity in various industries. However, the existing literature rarely considers the integrated scheduling of production and logistics on the workshop due to the NP-hard property of both machine scheduling and AGV scheduling. The energy-efficient job shop scheduling problem with limited AGVs is investigated in this paper. A multi-objective memetic algorithm with deep Q-network (DQNMMA) is proposed to minimize the makespan and total energy consumption. In DQNMMA, ten features are selected to describe the current state of the population. This enables the DQN to dynamically adjust the crossover probability according to the population evolution. Formulas for calculating the head length and tail length of each node in the disjunctive graph model are presented for the first time to enable fast and accurate access to the critical paths. Building upon the analysis of critical paths, four problem properties are developed as the foundation for designing six neighborhood operators. Then, a property-based variable neighborhood search strategy is proposed to enhance the exploration capability of the algorithm. Numerous experimental results demonstrate that the proposed approaches can effectively enhance the performance of the algorithm, especially in solving large-scale problems. The comparative analysis with three other state-of-the-art multi-objective algorithms confirms the superiority and effectiveness of the proposed DQNMMA.

A multiobjective dynamic rebalancing evolutionary algorithm for free-floating bike sharing

The big challenge of free-floating bike sharing system is to rebalance the supply and demand in different places. Most studies are static rebalancing that moves bikes at night. Dynamic rebalancing considers the scheduling of transport vehicles during the day. It is more effective and difficult to solve. In this paper, a multiobjective dynamic rebalancing problem is solved. The two optimization objectives are considered: minimizing the total distance of rebalancing vehicle and minimizing the total demand unmet. A mathematic model is built to formulate the problem. A new algorithm SFMEA-AP (Sequence Flow Multiobjective Evolutionary Algorithm with Area Protected) that uses the sequence flow encoding is proposed. An novel area protected strategy that includes a non-dominated sorting with similarity comparison is proposed. It simultaneously considers the fairness and competitiveness in solution space. Six neighborhood search operators are designed. They are used as variable neighborhood search strategy. Computational experiments show that SFMEA-AP can obtain better solution quality than SFMEA-VNS, QMOEA, NSGA-II, ILS and LSMOVRPTW. The IGD values of non-dominated solutions of SFMEA-AP are better than those of SFMEA-VNS, QMOEA, NSGA-II, ILS and LSMOVRPTW. In addition, the non-dominated solution set of SFMEA-AP have good diversity.

Mathematical formulation and a novel two-stage algorithm for double-row layout problem with fixed loading and unloading points

Loading and unloading operations are frequent and important in the production workshop. Thus, this paper proposes a novel double-row layout problem, which involves the location planning of material loading and unloading points of the facility in the layout; It needs to solve the sequence and precise coordinates of facilities with safety clearance to ensure the safety of the layout. Subsequently, a mixed-integer programming model and an improved discrete differential evolution algorithm with linear programming are developed to minimize material handling costs. The algorithm includes four efficient operations in optimization: the annealing mechanism, random strategy, variable neighborhood search strategy, and double-threshold termination mode. Thereafter, compared with the computational results of benchmark cases, the validity of the model and the efficiency of the algorithm are verified. In the basic problem, the calculation results of the algorithm are compared with many algorithms in the literature, and the algorithm still performs well. Finally, the algorithm is applied to solve the reducer workshop and provides a better layout scheme.

An Efficient and Improved Coronavirus Herd Immunity Algorithm Using Knowledge-Driven Variable Neighborhood Search for Flexible Job-Shop Scheduling Problems

By addressing the flexible job shop scheduling problem (FJSP), this paper proposes a new type of algorithm for the FJSP. We named it the hybrid coronavirus population immunity optimization algorithm. Based on the characteristics of the problem, firstly, this paper redefined the discretized two-stage individual encoding and decoding scheme. Secondly, in order to realize the multi-scale search of the solution space, a multi-population update mechanism is designed, and a collaborative learning method is proposed to ensure the diversity of the population. Then, an adaptive mutation operation is introduced to enrich the diversity of the population, relying on the adaptive adjustment of the mutation operator to balance global search and local search capabilities. In order to realize a directional and efficient neighborhood search, this algorithm proposed a knowledge-driven variable neighborhood search strategy. Finally, the algorithm’s performance comparison experiment is carried out. The minimum makespans on the MK06 medium-scale case and MK10 large-scale case are 58 and 201, respectively. The experimental results verify the effectiveness of the hybrid algorithm.

An improved memetic algorithm to solve the energy-efficient distributed flexible job shop scheduling problem with transportation and start-stop constraints.

In the current global cooperative production environment, modern industries are confronted with intricate production plans, demanding the adoption of contemporary production scheduling strategies. Within this context, distributed manufacturing has emerged as a prominent trend. Manufacturing enterprises, especially those engaged in activities like automotive mold production and welding, are facing a significant challenge in managing a significant amount of small-scale tasks characterized by short processing times. In this situation, it becomes imperative to consider the transportation time of jobs between machines. This paper simultaneously considers the transportation time of jobs between machines and the start-stop operation of the machines, which is the first time to our knowledge. An improved memetic algorithm (IMA) is proposed to solve the multi-objective distributed flexible job shop scheduling problem (MODFJSP) with the goal of minimizing maximum completion time and energy consumption. Then, a new multi-start simulated annealing algorithm is proposed and integrated into the IMA to improve the exploration ability and diversity of the algorithm. Furthermore, a new multiple-initialization rule is designed to enhance the quality of the initial population. Additionally, four improved variable neighborhood search strategies and two energy-saving strategies are designed to enhance the search ability and reduce energy consumption. To verify the effectiveness of the IMA, we conducted extensive testing and comprehensive evaluation on 20 instances. The results indicate that, when faced with the MODFJSP, the IMA can achieve better solutions in almost all instances, which is of great significance for the improvement of production scheduling in intelligent manufacturing.

An effective iterative greedy algorithm for distributed blocking flowshop scheduling problem with balanced energy costs criterion

With the increase in production levels, a pattern of industrial production has shifted from a single factory to multiple factories, resulting in a distributed production model. The distributed flowshop scheduling problem (DPFSP) is of great research significance as a frequent pattern in real production activities. In this paper, according to real-world scenarios, we have added blocking constraints and sequence-dependent setup times (SDST) to the DFSP and proposed a distributed blocking flowshop scheduling problem with sequence-dependent setup times (DBFSP_SDST). In a distributed environment, the allocation of resources and utilization have become an urgent problem to be solved. In addition, scheduling problems related to resource conservation have also attracted increasing attention. Therefore, we study DBFSP_SDST and consider minimizing the energy consumption cost of the critical factory (critical factory is the factory with maximum energy consumption cost) under resource balance. To tackle this problem, an effective iterated greedy algorithm based on a learning-based variable neighborhood search algorithm (VNIG) is proposed. In VNIG, an efficient construction heuristic is well designed. Two different local searches based on the characteristics of the proposed problem are developed to enhance the local exploitation by neighborhood searching. A learning-based selection variable neighborhood search strategy is designed to avoid the solution trapping in local optima. By conducting extensive simulation experiments, the proposed VNIG shows superior performance compared with artificial chemical reaction optimization (CRO, 2017), the discrete artificial bee colony algorithm (DABC, 2018), the iterative greedy algorithm with a variable neighborhood search scheme (IGR, 2021), and the evolution strategy approach (ES, 2022).

A variable neighborhood search approach to solve the order batching problem with heterogeneous pick devices

In this paper, we discuss the order batching problem in manual order picking systems. In such systems, order pickers move through a warehouse to collect items that are requested by customers. Customer orders have to be grouped into picking orders of limited size to ensure that the total length of the picker tours to collect all items is minimized. Motivated by real-world restrictions, we assume that the pick devices are heterogeneous, i.e., it is not necessarily possible to transport each customer order with each device. Since the order batching problem is NP-hard, we propose both serial and parallel versions of a variable neighborhood search (VNS) scheme to tackle large-sized problem instances in a reasonable amount of time. Moreover, the VNS scheme is hybridized with a set partitioning problem formulation. Based on computational experiments, we show that the proposed VNS scheme is a very fast approach that is able to provide solutions for benchmark instances with homogeneous pick devices that are of comparable quality or even partly superior to the best performing approaches from the literature. New benchmark instances for heterogeneous pick devices are proposed. High-quality solutions are obtained for these instances. We also consider large-scale problem instances from a real-world e-commerce warehouse. The VNS scheme outperforms the heuristic applied for order batching in this warehouse. Moreover, we demonstrate that a warehouse setup with heterogeneous pick devices is highly beneficial with respect to operating cost savings.

An effective water wave optimization algorithm with problem-specific knowledge for the distributed assembly blocking flow-shop scheduling problem

The distributed assembly blocking flow-shop scheduling problem (DABFSP), which is a promising area in modern supply chains and manufacturing systems, has attracted great attention from researchers and practitioners. However, minimizing the total tardiness in DABFSP has not captured much attention so far. For solving the DABFSP with the total tardiness criterion, a mixed integer linear programming method is utilized to model the problem, wherein the total tardiness during the production process and assembly process are optimized simultaneously. A constructive heuristic (KBNEH) and a water wave optimization algorithm with problem-specific knowledge (KWWO) are presented. KBNEH is designed by combining a new dispatching rule with an insertion-based improvement procedure to obtain solutions with high quality. In KWWO, effective technologies, such as the re-developed destruction–construction​ operator, four local search methods under the framework of the variable neighborhood search strategy (VNS), the path-relinking method are applied to improve the performance of the algorithm. Comprehensive numerical experiments based on 900 small-scale benchmark instances and 810 large-scale benchmark instances are conducted to evaluate the performance of the presented algorithm. The experimental results obtained by KWWO are 1 to 4 times better than those obtained by the other comparison algorithms, which demonstrate that the effectiveness of KWWO is superior to the compared state-of-the-art algorithms for the considered problem.

All-Directional DOA Estimation for Ultra-Wideband Regular Tetrahedral Array Using Wrapped PDoA.

In this paper, we proposed a Regular Tetrahedral Array (RTA) to cope with various types of sensors expected in Ultra-Wideband (UWB) localization requiring all-directional detection capability and high accuracy, such as indoor Internet-of-Things (IoT) devices at diverse locations, UAVs performing aerial navigation, collision avoidance and takeoff/landing guidance. The RTA is deployed with four synchronized Ultra-Wideband (UWB) transceivers on its vertexes and configured with arbitrary aperture. An all-directional DOA estimation algorithm using combined TDoA and wrapped PDoA was conducted. The 3D array RTA was decomposed into four planar subarrays solved as phased Uniform Circular Array (UCA) respectively. A new cost function based on geometric identical and variable neighborhood search strategy using TDoA information was proposed for ambiguity resolution. The results of simulation and numerical experiments demonstrated excellent performance of the proposed RTA and corresponding algorithm.

Generating bicriteria schedules for correlated parallel machines involving tardy jobs and weighted completion time

This research focuses on studying the correlated parallel machine scheduling problem with release dates to minimize the number of tardy jobs and the total weighted completion time to find Pareto optima of all non-dominated solutions for both criteria. First, a mixed integer programming (MIP) model to find the entire efficient frontier for the studied problem has been proposed. Next, a bicriteria heuristic, named UTWC, and three artificial bee colony (ABC) variant algorithms have been proposed to tackle the studied problem. The three ABC variant algorithms are ABC, ABC with variable neighborhood search scheme (ABC_VNS), and ABC with simulated annealing scheme (ABC_SA). For small problem instances, we compare the proposed heuristic UTWC and three ABC variant algorithms with the efficient frontier generated by solving the MIP model. For large problem instances, we compare the UTWC and three ABC variant algorithms with an existing multi-objective tabu search algorithm (TSA). We create a reference set by combining the solutions from the three ABC variant algorithms and the TSA. The computational results indicate that the UTWC heuristic can find a set of non-dominated solutions that are uniformly distributed above the efficient frontier. The proposed ABC_VNS algorithm outperforms all the compared algorithms in both small and large problem instances.

The container drayage problem for heterogeneous trucks with multiple loads: A revisit

In this study, we revisit the container drayage problem for heterogeneous trucks with multiple loads in view of its practical significance. We first propose a tailored mixed-integer linear programming (MILP) model explicitly to reflect the reality of container drayage operations. To solve medium-scale problems more effectively, two relaxed MILP models are built to provide a solution that is close to optimal with less computational time. These two relaxed models are proven to work as intended and provide optimal solutions under certain conditions. Moreover, an effective hybrid heuristic method incorporating the cheapest feasible insertion mechanism and the variable neighborhood search scheme is designed to solve large-scale problems. Extensive numerical experiments demonstrate the scalability of the heuristic method in real-world applications.

Application of dynamic firework algorithm considering variable neighborhood strategy in flexible job shop scheduling problem

Aiming at the flexible job shop scheduling problem, this paper constructs a dual-objective mathematical model to minimize the maximum completion time and the minimum total processing cost. The traditional firework algorithm introduces a variable neighborhood search strategy, which is generated during the explosion of the algorithm. On the basis of explosive spark and Gaussian spark, the algorithm is further avoided from falling into the dilemma of local optimization. The product of completion time and processing cost is used as the fitness value of the plan, so that the firework algorithm is suitable for solving the two objective scheduling problems in this paper, and the ratio of fitness value and congestion is used as a comprehensive index for the selection of the optimal plan . In this paper, the selected 5×6 calculation examples are solved, and the completion time of the optimal scheduling scheme is reduced by 12.9%, and the total production cost is reduced by 17.67%, which verifies the feasibility and efficiency of the method.

An Improved Whale Optimization Algorithm for the Traveling Salesman Problem

The whale optimization algorithm is a new type of swarm intelligence bionic optimization algorithm, which has achieved good optimization results in solving continuous optimization problems. However, it has less application in discrete optimization problems. A variable neighborhood discrete whale optimization algorithm for the traveling salesman problem (TSP) is studied in this paper. The discrete code is designed first, and then the adaptive weight, Gaussian disturbance, and variable neighborhood search strategy are introduced, so that the population diversity and the global search ability of the algorithm are improved. The proposed algorithm is tested by 12 classic problems of the Traveling Salesman Problem Library (TSPLIB). Experiment results show that the proposed algorithm has better optimization performance and higher efficiency compared with other popular algorithms and relevant literature.

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.

Effective Hot Rolling Batch Scheduling Algorithms in Compact Strip Production

This paper studies a hot rolling batch scheduling problem in compact strip production (CSP), which is decomposed into a two-stage problem. The first stage is the strip combination problem aimed at determining the strip combination of each rolling turn and the number of rolling turns with the objective of minimizing the number of virtual strips, and the second is the strip allocation and sequencing problem aimed at optimizing the allocation and rolling sequence of the strips in each rolling turn. We first model this two-stage problem considering a set of production constraints and then design an optimal approach to solve the strip combination problem. Subsequently, we design an evolutionary algorithm (i.e., artificial bee colony algorithm) with a novel search strategy for employed bees, a dynamic strategy for onlooker bees, a variable neighborhood search strategy for a scout bee, and an enhanced strategy to solve the problem in the second stage. Computational experiments demonstrate the effectiveness of the proposed algorithms. Note to Practitioners —The hot rolling batch scheduling process is crucial in linking the casting and rolling processes of iron and steel productions. In the rolling batch scheduling problem of CSP, there is no buffer between the casting and rolling processes, and virtual strips must be added to satisfy production constraints. Most rolling batch scheduling methods do not consider the addition of virtual strips. In this paper, we mathematically characterize the hot rolling batch scheduling problem in CSP with flexible production constraints. We then show how the optimal approach and artificial bee colony algorithm are designed. Finally, the effectiveness of the proposed algorithms is demonstrated by comparisons with other well-known metaheuristic algorithms. This paper can be extended to other hot rolling batch scheduling problems with buffers and hybrid flowshop scheduling problems.

Green Job Shop Scheduling Problem With Discrete Whale Optimization Algorithm

In the last few decades, production scheduling problems have been studied for optimizing production efficiency involving the time-related indicators, such as completion time, earliness/tardiness time, or flow time. Currently, with the consideration of sustainable development, the green scheduling problem has been paid more and more attention. Here, a green job shop scheduling problem is considered to minimize the sum of energy-consumption cost and completion-time cost in the workshop. In this paper, a mathematical model is first established with the consideration of multi-speed machines. A discrete whale optimization algorithm (DWOA) is then proposed for solving the model. In the proposed algorithm, a two-string encoding is adopted to represent the two sub-problems: job permutation and speed selection. Then, a heuristic method is used to initialize the population to enhance the quality of initial solutions. By considering the discrete characteristics of the problem, the individual updating operators are redesigned to ensure the algorithm work directly in a discrete scheduling domain. In addition, a variable neighborhood search strategy is embedded to further improve the search ability. The extensive experiments have been performed to test the DWOA. The computational data reveal the promising advantages of the DWOA on the considered problem.

A Proactive Robust Scheduling Method for Aircraft Carrier Flight Deck Operations with Stochastic Durations

The operations on the aircraft carrier flight deck are carried out in a time-critical and resource-constrained environment with uncertainty, and it is of great significance to optimize the makespan and obtain a robust schedule and resource allocation plan for a greater sortie generation capacity and better operational management of an aircraft carrier. In this paper, a proactive robust optimization method for flight deck scheduling with stochastic operation durations is proposed. Firstly, an operation on node-flow (OONF) network is adopted to model the precedence relationships of multi-aircraft operations, and resource constraints categorized into personnel, support equipment, workstation space, and supply resource are taken into consideration. On this basis, a mathematical model of the robust scheduling problem for flight deck operation (RSPFDO) is established, and the goal is to maximize the probability of completing within the limitative makespan (PCLM) and minimize the weighted sum of expected makespan and variance of makespan (IRM). Then, in terms of proactive planning, both serial and parallel schedule generation schemes for baseline schedule and robust personnel allocation scheme and equipment allocation adjustment scheme for resource allocation are designed. In terms of executing schedules, an RSPFDO-oriented preconstraint scheduling policy (CPC) is proposed. To optimize the baseline schedule and resource allocation, a hybrid teaching-learning-based optimization (HTLBO) algorithm is designed which integrates differential evolution operators, peak crossover operator, and learning-automata-based adaptive variable neighborhood search strategy. Simulation results shows that the HTLBO algorithm outperforms both some other state-of-the-art algorithms for deterministic cases and some existing algorithms for stochastic project scheduling, and the robustness of the flight deck operations can be improved with the proposed resource allocation schemes and CPC policy.

Solutions to No-Wait Flow Shop Scheduling Problem Using the Flower Pollination Algorithm Based on the Hormone Modulation Mechanism

A flower pollination algorithm is proposed based on the hormone modulation mechanism (HMM-FPA) to solve the no-wait flow shop scheduling problem (NWFSP). This algorithm minimizes the maximum accomplished time. Random keys are encoded based on an ascending sequence of components to make the flower pollination algorithm (FPA) suitable for the no-wait flow shop scheduling problem. The hormone modulation factor is introduced to strengthen information sharing among the flowers and improve FPA cross-pollination to enhance the algorithm global search performance. A variable neighborhood search strategy based on dynamic self-adaptive variable work piece blocks is constructed to improve the local search quality. Three common benchmark instances are applied to test the proposed algorithm. The result verifies that this algorithm is effective.

Optimal sub-tree scheduling for wireless sensor networks with partial coverage

In this paper, we consider the problem of scheduling optimal sub-trees at different time intervals for wireless sensor network (WSN) communications with partial coverage. More precisely, we minimize the total power consumption of the network while taking into account time dimension and multichannel diversity where different disjoint subsets of nodes are required to be active and connected under a tree topology configuration. Optimization problems of these types may arise when designing new wireless communication protocols in order to increase network lifetime. We propose mixed integer quadratic and linear programming (resp. MIQP and MILP) models to compute optimal solutions for the problem. Subsequently, we propose Kruskal-based variable neighborhood search (VNS) and simulated annealing (SA) meta-heuristic procedures. In particular, we introduce a new embedded guided local search strategy in our VNS algorithm to further strengthen the solutions obtained. Our numerical results indicate that some of the proposed models allow to obtain optimal solutions with CPLEX in significantly less CPU time. Similarly, VNS and SA algorithms proved to be highly efficient when compared to the optimal solutions and allow to obtain near optimal solutions for large instances. In particular, VNS and guided VNS strategies allow to obtain solutions in less CPU time whilst SA methods can reach better solutions at higher CPU times. Finally, optimizing over time dimension allows one to obtain important reductions in power savings which has never been reported before in the literature.