On the integrated charge planning with flexible jobs in primary steelmaking processes

The integrated charge planning (ICP) problem based on flexible jobs in an integrated steel plant is extremely difficult and valuable. The purpose of this paper is to improve the efficiency and feasibility of planning by minimising the number of charges, minimising the total production costs and maximising the total throughput, considering the hard constraints and soft constraints. A multi-objective mathematical programming model for the problem is formulated, and it is shown that the problem is NP-hard. Two new meta-heuristics are designed, one is guided variable neighbourhood search (GVNS) combined with harmony search, and the other is GVNS combined with simulated annealing. Compared with enumeration algorithm, tabu search, variable neighbourhood search (VNS), harmony search, extend next fit decreasing (ENFD) and skewed VNS (SVNS), variable neighbourhood descent (VND), the numerical results by actual production data have shown that the proposed model and GVNHS are feasible and effective for ICP.     

Multiple-variable neighbourhood search for the single-machine total weighted tardiness problem

The single-machine total weighted tardiness (SMTWT) problem is a typical discrete combinatorial optimization problem in the scheduling literature. This problem has been proved to be NP hard and thus provides a challenging area for metaheuristics, especially the variable neighbourhood search algorithm. In this article, a multiple variable neighbourhood search (m-VNS) algorithm with multiple neighbourhood structures is proposed to solve the problem. Special mechanisms named matching and strengthening operations are employed in the algorithm, which has an auto-revising local search procedure to explore the solution space beyond local optimality. Two aspects, searching direction and searching depth, are considered, and neighbourhood structures are systematically exchanged. Experimental results show that the proposed m-VNS algorithm outperforms all the compared algorithms in solving the SMTWT problem.     

A hybrid algorithm for total tardiness minimisation in flexible job shop: genetic algorithm with parallel VNS execution

This paper addresses the flexible-job-shop scheduling problem (FJSP) with the objective of minimising total tardiness. FJSP is the generalisation of the classical job-shop scheduling problem. The difference is that in the FJSP problem, the operations associated with a job can be processed on any set of alternative machines. We developed a new algorithm by hybridising genetic algorithm and variable neighbourhood search (VNS). The genetic algorithm uses advanced crossover and mutation operators to adapt the chromosome structure and the characteristics of the problem. Parallel-executed VNS algorithm is used in the elitist selection phase of the GA. Local search in VNS uses assignment of operations to alternative machines and changing of the order of the selected operation on the assigned machine to increase the result quality while maintaining feasibility. The purpose of parallelisation in the VNS algorithm is to minimise execution time. The performance of the proposed method is validated by numerical experiments on several representative problems and compared with adapted constructive heuristic algorithms’ (earliest due date, critical ratio and slack time per remaining operation) results.     

Integrated process planning and scheduling for large-scale flexible job shops using metaheuristics

In this paper, we discuss an integrated process planning and scheduling problem in large-scale flexible job shops (FJSs). We assume that products can be manufactured in different ways, i.e. using different bills of materials (BOM) and routes for the same product. The total weighted tardiness is the performance measure of interest. A Mixed Integer Programming formulation is provided for the researched problem. Because of the NP-hardness of the investigated problem, an iterative scheme is designed that is based on variable neighbourhood search (VNS) on the process planning level. Appropriate neighbourhood structures for VNS are proposed. Because the evaluation of each move within VNS requires the solution of a large-scale FJS scheduling problem instance, efficient heuristics based on local search from previous research are considered on the scheduling level. Extensive computational experiments based on new randomly generated problem instances are conducted. In addition, a parallel version of the VNS is investigated within the computational experiments. The proposed iterative scheme is benchmarked against a genetic algorithm (GA) from the literature that simultaneously considers process planning and scheduling for the special case where a single BOM is available for each product. It turns out that the new iterative scheme outperforms the GA and a memetic algorithm based on the GA. It is able to solve even large-size problem instances in reasonable amount of time.     

An improved water wave optimization algorithm with the single wave mechanism for the no-wait flow-shop scheduling problem

In this article, a water wave optimization algorithm with a single wave mechanism, called single water wave optimization (SWWO), is proposed to solve the no-wait flow-shop scheduling problem (NWFSP) with the objective of minimizing the makespan. In the proposed SWWO, an improved Nawaz–Enscore–Ham (NEH) heuristic is applied to construct a high-quality initial candidate. In the propagation operation, a self-adaptive block-shift operation is employed. In the breaking operation, a variable neighbourhood search operation is utilized to explore the local optimal solution. According to the schema theory as presented in genetic algorithms, a crossover operation is adopted as the refraction operation. Finally, the computational results based on several benchmarks and statistical performance comparisons are presented. The experimental results demonstrate the effectiveness and efficiency of the proposed SWWO for solving the NWFSP.     

A variable neighbourhood search for integrated production and preventive maintenance planning in multi-state systems

This paper presents a variable neighbourhood search (VNS) to the integrated production and maintenance planning problem in multi-state systems. VNS is one of the most recent meta-heuristics used for problem solving in which a systematic change of neighbourhood within a local search is carried out. In the studied problem, production and maintenance decisions are co-ordinated, so that the total expected cost is minimised. We are given a set of products that must be produced in lots on a multi-state production system during a specified finite planning horizon. Planned preventive maintenance and unplanned corrective maintenance can be performed on each component of the multi-state system. The maintenance policy suggests cyclical preventive replacements of components, and a minimal repair on failed components. The objective is to determine an integrated lot-sizing and preventive maintenance strategy of the system that will minimise the sum of preventive and corrective maintenance costs, setup costs, holding costs, backorder costs and production costs, while satisfying the demand for all products over the entire horizon. We model the production system as a multi-state system with binary-state components. The formulated problem can be solved by comparing the results of several multi-product capacitated lot-sizing problems. The proposed VNS deals with the preventive maintenance selection task. Results on test instances show that the VNS method provides a competitive solution quality at economically computational expense in comparison with genetic algorithms.     

A two-phase variable neighbourhood search algorithm for assembly line worker assignment and balancing problem type-II: an industrial case study

The assembly line worker assignment and balancing problem type-II (ALWABP-2) occurs when workers and tasks (where task times depend on workers’ skills) are to be simultaneously assigned to a fixed number of workstations with the goal of minimising the cycle time. In this study, a two-phase variable neighbourhood search (VNS) algorithm is proposed to solve the ALWABP-2 due to the NP-hard nature of this problem. In the first phase of the algorithm, a VNS approach is applied to assign tasks to workstations with the aim of minimising the cycle time while in the second phase, a variable neighbourhood descent method is applied to assign workers to workstations. The performance of the proposed algorithm is tested on well-known benchmark instances. In addition, the proposed algorithm has been used to solve a real case study from a consumer electronics company that manufactures LCD TVs. The results show that the algorithm is superior to the methods reported in the literature in terms of its higher efficiency and robustness. Furthermore, the algorithm is easy to implement and significantly improves the performance of the final assembly line for the investigated LCD TV real case study.     

Sequence based heuristics for two-dimensional bin packing problems

This article addresses several variants of the two-dimensional bin packing problem. In the most basic version of the problem it is intended to pack a given number of rectangular items with given sizes in rectangular bins in such a way that the number of bins used is minimized. Different heuristic approaches (greedy, local search, and variable neighbourhood descent) are proposed for solving four guillotine two-dimensional bin packing problems. The heuristics are based on the definition of a packing sequence for items and in a set of criteria for packing one item in a current partial solution. Several extensions are introduced to deal with issues pointed out by two furniture companies. Extensive computational results on instances from the literature and from the two furniture companies are reported and compared with optimal solutions, solutions from other five (meta)heuristics and, for a small set of instances, with the ones used in the companies.     

A hybrid Pareto-based local search algorithm for multi-objective flexible job shop scheduling problems

This paper presents a hybrid Pareto-based local search (PLS) algorithm for solving the multi-objective flexible job shop scheduling problem. Three minimisation objectives are considered simultaneously, i.e. the maximum completion time (makespan), the total workload of all machines, and the workload of the critical machine. In this study, several well-designed neighbouring approaches are proposed, which consider the problem characteristics and thus can hold fast convergence ability while keep the population with a certain level of quality and diversity. Moreover, a variable neighbourhood search (VNS) based self-adaptive strategy is embedded in the hybrid algorithm to utilise the neighbouring approaches efficiently. Then, an external Pareto archive is developed to record the non-dominated solutions found so far. In addition, a speed-up method is devised to update the Pareto archive set. Experimental results on several well-known benchmarks show the efficiency of the proposed hybrid algorithm. It is concluded that the PLS algorithm is superior to the very recent algorithms, in term of both search quality and computational efficiency.     

Coordinated scheduling of production and transportation in a two-stage assembly flowshop

To enhance the overall performance of supply chains, coordination among production and distribution stages has recently received an increasing interest. This paper considers the coordinated scheduling of production and transportation in a two-stage assembly flowshop environment. In this problem, product components are first produced and assembled in a two-stage assembly flowshop, and then completed final products are delivered to a customer in batches. Considering the NP-hard nature of this scheduling problem, two fast heuristics (SPT-based heuristic and LPT-based heuristic) and a new hybrid meta-heuristic (HGA-OVNS) are presented to minimise the weighted sum of average arrival time at the customer and total delivery cost. To guide the search process to more promising areas, the proposed HGA-OVNS integrates genetic algorithm with variable neighbourhood search (VNS) to generate the offspring individuals. Furthermore, to enhance the effectiveness of VNS, the opposition-based learning (OBL) is applied to establish some novel opposite neighbourhood structures. The proposed algorithms are validated on a set of randomly generated instances, and the computation results indicate the superiority of HGA-OVNS in quality of solutions.     

An integrated CPU–GPU heuristic inspired on variable neighbourhood search for the single vehicle routing problem with deliveries and selective pickups

Environmental issues have become increasingly important to industry and business in recent days. This trend forces the companies to take responsibility for product recovery, and proper recycling and disposal, moving towards the design of sustainable green supply chains. This paper addresses the backward stream in transportation of products, by means of reverse logistics applied to vehicle routing. This problem, called single vehicle routing problem with deliveries and selective pickups, consists in finding a route that starts from the depot and visits all delivery customers. Some pickup customers may also be visited, since the capacity of the truck is not exceeded, and there is also a revenue associated with each pickup. We develop an algorithm inspired on the variable neighbourhood search metaheuristic that explores the power of modern graphics processing unit (GPU) to provide routes in reasonable computational time. The proposed algorithm called four-neighbourhood variable neighbourhood search (FN-VNS) includes a novel high-quality initial solution generator, a CPU–GPU integrated perturbation strategy and four different neighbourhood searches implemented purely in GPU for the local search phase. Our experimental results show that FN-VNS is able to improve the quality of the solution for 51 instances out of 68 instances taken from the literature. Finally, we obtained speedups up to 14.49 times, varying from 17.42 up to 76.84 for each local search, measured over a set of new large-size instances.     

Fast local neighborhood search algorithm for the no-wait flow shop scheduling with total flow time minimization

A fast local neighbourhood search (FLNS) algorithm is proposed in this paper to minimise the total flow time in the no-wait flow shop scheduling problem, which is known to be NP-hard for more than two machines. In this work, an unscheduled job sequence is constructed firstly according to the total processing time and standard deviation of jobs on the machines. This job sequence is undergone an initial optimisation using basic neighbourhood search algorithm. Then, an innovative local neighbourhood search scheme is designed to search for the partial neighbourhood in each iterative processing and calculate the neighbourhood solution with an objective increment method. This not only improves the solution quality significantly, but also speeds up the convergence of the solution of the algorithm. Moreover, a probabilistic acceptance criterion is adopted to help our method escape from the local optima. Based on Taillard’s benchmarks, the experimental results show that the proposed FLNS algorithm is superior to major existing algorithms (IHA, IBH_LS, GA-VNS and DHS) in terms of both quality and robustness, and can provide best upper bounds. The in-depth statistical analysis demonstrates that the promising performance of our proposed algorithm is also statistically significant.     

Modelling and a tabu search solution for the slab reallocation problem in the steel industry

This paper considers a slab reallocation problem arising from operations planning in the steel industry. The problem involves reallocating steel slabs to customer orders to improve the utilisation of slabs and the level of customer satisfaction. It can be viewed as an extension of a multiple knapsack problem. We firstly formulate the problem as an integer nonlinear programming (INLP) model. With variable replacement, the INLP model is then transformed into a mixed integer linear programming (MILP) model, which can be solved to optimality by MILP optimisers for very small instances. To obtain satisfactory solutions efficiently for practical-sized instances, a heuristic algorithm based on tabu search (TS) is proposed. The algorithm employs multiple neighbourhoods including swap, insertion and ejection chain in local search, and adopts solution space decomposition to speed up computation. In the ejection chain neighbourhood, a new and more effective search method is also proposed to take advantage of the structural properties of the problem. Computational experiments on real data from an advanced iron and steel company in China show that the algorithm generates very good results within a short time. Based on the model and solution approach, a decision support system has been developed and implemented in the company.     

Variable neighbourhood search for dual-resource constrained flexible job shop scheduling

Dual-resource constrained flexible job shop scheduling problem (FJSP) is considered and an effective variable neighbourhood search (VNS) is presented, in which the solution to the problem is indicated as a quadruple string of the ordered operations and their resources. Two neighbourhood search procedures are sequentially executed to produce new solutions for two sub-problems of the problem, respectively. The search of VNS is restarted from a slightly perturbed version of the current solution of VNS when the determined number of iterations is reached. VNS is tested on some instances and compared with methods from literature. Computational results show the significant advantage of VNS on the problem.     

A reliability/availability approach to joint production and maintenance scheduling with multiple preventive maintenance services

In classical scheduling problems, it is often assumed that the machines are available during the whole planning horizon, while in realistic environments, machines need to be maintained and therefore may become unavailable within production periods. Hence, in this paper we suggest a joint production and maintenance scheduling (JPMS) with multiple preventive maintenance services, in which the reliability/availability approach is employed to model the maintenance aspects of a problem. To cope with the suggested JPMS, a mixed integer nonlinear programming model is developed and then a population-based variable neighbourhood search (PVNS) algorithm is devised for a solution method. In order to enhance the search diversification of basic variable neighbourhood search (VNS), our PVNS uses an epitome-based mechanism in each iteration to transform a group of initial individuals into a new solution, and then multiple trial solutions are generated in the shaking stage for a given solution. At the end of the local search stage, the best obtained solution by all of the trial solutions is recorded and the worst solution in population is replaced with this new solution. The evolution procedure is continued until a predefined number of iterations is violated. To validate the effectiveness and robustness of PVNS, an extensive computational study is implemented and the simulation results reveal that our PVNS performs better than traditional algorithms, especially in large size problems.     

An efficient iterated local search algorithm for the total tardiness blocking flow shop problem

This paper deals with the blocking flow shop problem and proposes an Iterated Local Search (ILS) procedure combined with a variable neighbourhood search (VNS) for the total tardiness minimisation. The proposed ILS makes use of a NEH-based procedure to generate the initial solution, and uses a local search to intensify the exploration that combines the insertion and swap neighbourhood and uses a perturbation mechanism consisting of three neighbourhood operators to diversify the search. The computational evaluation has shown the effectiveness of combining the insertion and swap neighbourhood during the search despite the insertion neighbourhood being more effective than the swap neighbourhood for this problem. Finally, the computation of this algorithm when evaluated against two other algorithms from the literature shows good performance.     

A variable neighbourhood search algorithm for the flexible job-shop scheduling problem

The flexible job-shop scheduling problem (FJSP) is a generalisation of the classical job-shop scheduling problem which allows an operation of each job to be executed by any machine out of a set of available machines. FJSP consists of two sub-problems which are assigning each operation to a machine out of a set of capable machines (routing sub-problem) and sequencing the assigned operations on the machines (sequencing sub-problem). This paper proposes a variable neighbourhood search (VNS) algorithm that solves the FJSP to minimise makespan. In the process of the presented algorithm, various neighbourhood structures related to assignment and sequencing problems are used for generating neighbouring solutions. To compare our algorithm with previous ones, an extensive computational study on 181 benchmark problems has been conducted. The results obtained from the presented algorithm are quite comparable to those obtained by the best-known algorithms for FJSP.     

A two-dimensional bin-packing problem with conflict penalties

In this paper, we address the two-dimensional bin-packing (2BP) problem with variable conflict penalties, which incur if conflicting items are loaded into the same bin. Such a problem is observed in applications such as supermarket chains and automobile components transportation. The problem not only focuses on minimisation of number of bins used, but also deals with the conflict penalties at the same time. We propose a heuristic method based on the IMA algorithm and adapt it to solve this problem. A local search procedure is also designed to further improve the solutions. For instances derived from benchmark test data, the computational results indicate that the adapted IMA heuristic algorithm with local search effectively balances the number of bins used and the conflict penalties. The algorithm outperforms several adapted approaches that are well known for the 2BP problems.     

Dynamic job shop scheduling using variable neighbourhood search

In this paper a scheduling method based on variable neighbourhood search (VNS) is introduced to address a dynamic job shop scheduling problem that considers random job arrivals and machine breakdowns. To deal with the dynamic nature of the problem, an event-driven policy is selected. To enhance the efficiency and effectiveness of the scheduling method, an artificial neural network with a back propagation error learning algorithm is used to update parameters of the VNS at any rescheduling point according to the problem condition. The proposed method is compared with some common dispatching rules that have been widely used in the literature for the dynamic job shop scheduling problem. Results illustrate the high efficiency and effectiveness of the proposed method in a variety of shop floor conditions.