An improved NEH-based heuristic for the permutation flowshop problem

NEH is an effective heuristic for solving the permutation flowshop problem with the objective of makespan. It includes two phases: generate an initial sequence and then construct a solution. The initial sequence is studied and a strategy is proposed to solve job insertion ties which may arise in the construct process. The initial sequence which is generated by combining the average processing time of jobs and their standard deviations shows better performance. The proposed strategy is based on the idea of balancing the utilization among all machines. Experiments show that using this strategy can improve the performance of NEH significantly. Based on the above ideas, a heuristic NEH-D (NEH based on Deviation) is proposed, whose time complexity is O(mn²), the same as that of NEH. Computational results on benchmarks show that the NEH-D is significantly better than the original NEH.     

An efficient stochastic hybrid heuristic for flowshop scheduling

The paper addresses the problem of flowshop scheduling in order to minimize the makespan objective. Three probabilistic hybrid heuristics are presented for solving permutation flowshop scheduling problem. The proposed methodology combines elements from both constructive heuristic search and a stochastic improvement technique. The stochastic method used in this paper is simulated annealing (SA). Experiments have been run on a large number of randomly generated test problems of varying jobs and machine sizes. Our approach is shown to outperform best-known existing heuristics, including the classical NEH technique (OMEGA, 1983) and the SA based on (OMEGA, 1989) of Osman and Potts . Statistical tests of significance are performed to substantiate the claims of improvement.     

An improved NEH heuristic to minimize makespan in permutation flow shops

For over 20 years the NEH heuristic of Nawaz, Enscore, and Ham [A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem. Omega, The International Journal of Management Science 1983;11:91–5] has been commonly regarded as the best heuristic for solving the NP-hard problem of minimizing the makespan in permutation flow shops. The strength of NEH lies mainly in its priority order according to which jobs are selected to be scheduled during the insertion phase. Framinan et al. [Different initial sequences for the heuristic of Nawaz, Enscore and Ham to minimize makespan, idle time or flowtime in the static permutation flowshop problem. International Journal of Production Research 2003;41:121–48] presented the results of an extensive study to conclude that the NEH priority order is superior to 136 different orders examined. Based upon the concept of Johnson's algorithm, we propose a new priority order combined with a simple tie-breaking method that leads to a heuristic that outperforms NEH for all problem sizes.     

A Constructive Genetic Algorithm for permutation flowshop scheduling

The general flowshop scheduling problem is a production problem where a set of n jobs have to be processed with identical flow pattern on m machines. In permutation flowshops the sequence of jobs is the same on all machines. A significant research effort has been devoted for sequencing jobs in a flowshop minimizing the makespan. This paper describes the application of a Constructive Genetic Algorithm (CGA) to makespan minimization on flowshop scheduling. The CGA was proposed recently as an alternative to traditional GA approaches, particularly, for evaluating schemata directly. The population initially formed only by schemata, evolves controlled by recombination to a population of well-adapted structures (schemata instantiation). The CGA implemented is based on the NEH classic heuristic and a local search heuristic used to define the fitness functions. The parameters of the CGA are calibrated using a Design of Experiments (DOE) approach. The computational results are compared against some other successful algorithms from the literature on Taillard’s well-known standard benchmark. The computational experience shows that this innovative CGA approach provides competitive results for flowshop scheduling problems.     

Constraint satisfaction adaptive neural network and heuristicscombined approaches for generalized job-shop scheduling

This paper presents a constraint satisfaction adaptive neural network, together with several heuristics, to solve the generalized job-shop scheduling problem, one of NP-complete constraint satisfaction problems. The proposed neural network can be easily constructed and can adaptively adjust its weights of connections and biases of units based on the sequence and resource constraints of the job-shop scheduling problem during its processing. Several heuristics that can be combined with the neural network are also presented. In the combined approaches, the neural network is used to obtain feasible solutions, the heuristic algorithms are used to improve the performance of the neural network and the quality of the obtained solutions. Simulations have shown that the proposed neural network and its combined approaches are efficient with respect to the quality of solutions and the solving speed.     

A bottleneck-based heuristic for minimizing makespan in a flexible flow line with unrelated parallel machines

This study developed a bottleneck-based heuristic (BBFFL) to solve a flexible flow line problem with a bottleneck stage, where unrelated parallel machines exist in all the stages, with the objective of minimizing the makespan. The essential idea of BBFFL is that scheduling jobs at the bottleneck stage may affect the performance of a heuristic for scheduling jobs in all the stages. Therefore, in BBFFL, a variant of Johnson's rule is used to develop a bottleneck-based initial sequence generator (BBISG). Then, a bottleneck-based multiple insertion procedure (BBMIP) is applied to the initial sequence to control the order by which jobs enter the bottleneck stage to be the same as that at the first stage. Five experimental factors were used to design 243 different production scenarios and 10 test problems were randomly generated in each scenario. These test problems were used to compare the performance of BBFFL with several well-known heuristics. Computational results show that the BBFFL significantly outperforms all the well-known heuristics.     

On insertion tie-breaking rules in heuristics for the permutation flowshop scheduling problem

The most efficient approximate procedures so far for the flowshop scheduling problem with makespan objective – i.e. the NEH heuristic and the iterated greedy algorithm – are based on constructing a sequence by iteratively inserting, one by one, the non-scheduled jobs into all positions of an existing subsequence, and then, among the so obtained subsequences, selecting the one yielding the lowest (partial) makespan. This procedure usually causes a high number of ties (different subsequences with the same best partial makespan) that must be broken via a tie-breaking mechanism. The particular tie-breaking mechanism employed is known to have a great influence in the performance of the NEH, therefore different procedures have been proposed in the literature. However, to the best of our knowledge, no tie-breaking mechanism has been proposed for the iterated greedy. In our paper, we present a new tie-breaking mechanism based on an estimation of the idle times of the different subsequences in order to pick the one with the lowest value of the estimation. The computational experiments carried out show that this mechanism outperforms the existing ones both for the NEH and the iterated greedy for different CPU times. Furthermore, embedding the proposed tie-breaking mechanism into the iterated greedy provides the most efficient heuristic for the problem so far.     

A generalized constructive algorithm using insertion-based heuristics

In this paper, a generalized constructive algorithm referred to as GCA is presented which makes it possible to select a wide variety of heuristics just by the selection of its arguments values. A general framework for generating permutations of integers is presented. This framework, referred to as PERMGEN, forms a link between the numbering of permutations and steps in the insertion-based heuristics. A number of arguments controlling the operation of GCA are identified. Features and benefits of the generalized algorithm are presented through the extension of the NEH heuristic, a successful heuristic solution approach of Nawaz, Enscore, and Ham for the permutation flowshop problem (PFSP). The goal of the experimental study is to improve the performance of the NEH heuristic on the PFSP. To achieve this goal, the space of algorithmic control arguments is searched for a combination of values that define an algorithm providing lower makespan solutions than NEH, in a linear increase of CPU time. Computational experiments on a set of 120 benchmark problem instances, originally proposed by Taillard, are performed to establish a more robust version of the original NEH constructive heuristic. The proposed procedures outperform NEH, preserving its efficiency and simplicity.     

An effective hybrid multi-objective genetic algorithm for bi-criteria scheduling on a single batch processing machine with non-identical job sizes

This paper addresses the problem of scheduling jobs with non-identical sizes on a single batch processing machine. A batch processing machine is one which can process multiple jobs simultaneously as a batch as long as the total size of jobs being processed does not exceed the machine capacity. The batch processing time is equal to the longest processing time among all jobs in the batch. For the simultaneous minimization of the bi-criteria of makespan and maximum tardiness, we propose two different multi-objective genetic algorithms based on different representation schemes. While the first algorithm do search via generating sequences of jobs using genetic operators and then batching jobs keeping their order in the sequence, the second algorithm uses the idea of generating batches of jobs directly using genetic operators and ensures feasibility through using heuristic procedures. The type of representation used in the second algorithm allows introducing heuristics with the ability of biasing the search towards each objective and also allows hybridization with a local search heuristic that gives the ability of finding Pareto-optimal or locally efficient Pareto-solutions. Computational results show that the non-dominated solutions obtained by the latter algorithm are very superior in closeness to the true Pareto-optimal solutions and to keep diversity in the obtained Pareto-set, as the problem size increases.     

A neural network to enhance local search in the permutation flowshop

This paper considers the n-job, m-machine permutation flowshop with the objective of minimizing the mean flowtime. Initial sequences that are structured to enhance the performance of local search techniques are constructed from job rankings delivered by a trained neural network. The network's training is done by using data collected from optimal sequences obtained from solved examples of flowshop problems. Once trained, the neural network provides rankable measures that can be used to construct a sequence in which jobs are located as close as possible to the positions they would occupy in an optimal sequence. The contribution of these ‘neural’ sequences in improving the performance of some common local search techniques, such as adjacent pairwise interchange and tabu search, is examined. Tests using initial sequences generated by different heuristics show that the sequences suggested by the neural networks are more effective in directing neighborhood search methods to lower local optima.     

Hybrid tabu search and a truncated branch-and-bound for the unrelated parallel machine scheduling problem

We consider the problem of scheduling a number of jobs on a number of unrelated parallel machines in order to minimize the makespan. We develop three heuristic approaches, i.e., a genetic algorithm, a tabu search algorithm and a hybridization of these heuristics with a truncated branch-and-bound procedure. This hybridization is made in order to accelerate the search process to near-optimal solutions. The branch-and-bound procedure will check whether the solutions obtained by the meta-heuristics can be scheduled within a tight upper bound. We compare the performances of these heuristics on a standard dataset available in the literature. Moreover, the influence of the different heuristic parameters is examined as well. The computational experiments reveal that the hybrid heuristics are able to compete with the best known results from the literature.     

Production scheduling for blocking flowshop in distributed environment using effective heuristics and iterated greedy algorithm

Production scheduling plays an important role in the intelligent decision support system and intelligent optimization decision technology. In the context of the globalization trend, the current production and management may extend from a single factory to a distributed production network. In this paper, we study the distributed blocking flowshop scheduling problem (DBFSP) that is an important generalization of the traditional blocking flowshop scheduling problem in the distributed environment. Six constructive heuristics and an iterated greedy (IG) algorithm are proposed to minimize the makespan, which provides procedures for obtaining efficient and effective solutions to make decision-making sounder. The first five heuristics are developed based on the well-known NEH2 heuristic [B. Naderi, R. Ruiz, The distributed permutation flowshop scheduling problem, Computers & Operations Research, 37 (4) (2010) 754–768.] and the last heuristic is presented by extending the PW heuristic [Q.K. Pan, L. Wang, Effective heuristics for the blocking flowshop scheduling problem with makespan minimization, Omega, 40 (2) (2012) 218–229.] to DBFSP in an effective way. The composite heuristics that combining constructive heuristics and local searches are also studied. The proposed composite heuristics are chosen to generate an initial solution with a high level of quality. Keeping the simplicity of the IG algorithm, three local search procedures, two destruction procedures, an improved reconstruction procedure, and a simulated annealing-like acceptance criterion are well designed based on the problem-specific knowledge to enhance the IG algorithm. The computational experiments are carried out based on the 720 benchmark instances from the literature. The results show that the proposed heuristics are very effective for solving the problem under consideration and the presented IG algorithm performs significantly better than the other state-of-the-art metaheuristics from the literature.     

基于分支定界和神经网络的实时调度策略

为解决一些对精度和实时性要求较高的调度问题,设计一个基于分枝定界算法和人工神经网络的实时调度算法.策略先使朋分枝定界算法来找到m个作业的最佳排序.在生成足够多的排序以后,将排序作为训练样本来训练一个m维人工神经网络,从而得到一个m维的人工种经网络主矩阵.在实际的乍产环境中,先对实际到达的n(n>m)个作业进行分组,再利用离线生成的人工神经网络主矩阵对每个分组进行初始排序.最后将每个分组看作一个整体,根据Palmer算法得到n个作业的最终排序.仿真表明该策略具有较好的实时性,同时也能达到较高的精确性.     

Integrating the lot-sizing and sequencing decisions for scheduling a capacitated flow line

In this paper we consider a general problem of scheduling a single flow line consisting of multiple machines and producing a given set of jobs. The manufacturing environment is characterized by sequence dependent set-up times, limited intermediate buffer space, and capacity constraints. In addition, jobs are assigned with due dates that have to be met. The objectives of the scheduling are: (1) to meet the due dates without violating the capacity constraints, (2) to minimize the makespan, and (3) to minimize the inventory holding costs. While most of the approaches in the literature treat the problem of scheduling in flow lines as two independent sub-problems of lot-sizing and sequencing, our approach integrates the lot-sizing and sequencing heuristics. The integrated approach uses the Silver-Meal heuristic (modified to include lot-splitting) for lot-sizing and an improvement procedure applied to Palmer's heuristic for sequencing, which takes into account the actual sequence dependent set-up times and the limited intermedite buffer capacity. We evaluate the performance of the integrated approach and demonstrate its efficacy for scheduling a real world SMT manufacturing environment.     

Comparing three-step heuristics for the permutation flow shop problem

In this paper a three steps heuristic for the permutation flow shop problem is proposed. The objective is to minimize the maximum time for completing the jobs, or the makespan. The first two steps are inspired by the NEH heuristic, to which a new tie breaking strategy has been incorporated in the insertion phase. Furthermore, the reversibility property of the problem dealt with is taken as a tool for improving the obtained solution. The third step consists of an iterated local search procedure with an embedded local search which is a variant of the non exhaustive descent algorithm. The statistical analysis of the results shows the effectiveness of the proposed procedures.     

Heuristic-based neural networks for stochastic dynamic lot sizing problem

Multi-period single-item lot sizing problem under stochastic environment has been tackled by few researchers and remains in need of further studies. It is mathematically intractable due to its complex structure. In this paper, an optimum lot-sizing policy based on minimum total relevant cost under price and demand uncertainties was studied by using various artificial neural networks trained with heuristic-based learning approaches; genetic algorithm (GA) and bee algorithm (BA). These combined approaches have been examined with three domain-specific costing heuristics comprising revised silver meal (RSM), revised least unit cost (RLUC), cost benefit (CB). It is concluded that the feed-forward neural network (FF-NN) model trained with BA outperforms the other models with better prediction results. In addition, RLUC is found the best operating domain-specific heuristic to calculate the total cost incurring of the lot-sizing problem. Hence, the best paired heuristics to help decision makers are suggested as RLUC and FF-NN trained with BA.     

一种基于虚拟截止时间制导的改进的Min-Min元任务调度算法

在网格环境下,资源状况和用户行为相当复杂,是一个异构计算环境,元任务（meta—task）调度比传统并行调度更为复杂。如何映射一组任务到一组机器上被证明是NP问题,其目的一般是最小化任务完成时间（makespan）。为解决这一问题,已经提出一些启发式任务调度算法,例如具有代表性的MinMin元任务调度算法。本文在Min-Min元任务调度算法的基础上,通过虚拟截止时间制导的方法来改进Min-Min算法。实验结果表明,本文提出的算法具有更短的任务完成时间。     

Single machine scheduling with controllable processing times to minimize total tardiness and earliness

In most deterministic scheduling problems job processing times are considered as invariable and known in advance. Single machine scheduling problem with controllable processing times with no inserted idle time is presented in this study. Job processing times are controllable to some extent that they can be reduced or increased, up to a certain limit, at a cost proportional to the reduction or increase. In this study, our objective is determining a set of compression/expansion of processing times in addition to a sequence of jobs simultaneously, so that total tardiness and earliness are minimized. A mathematical model is proposed firstly and afterward a net benefit compression–net benefit expansion (NBC–NBE) heuristic is presented so as to acquire a set of amounts of compression and expansion of jobs processing times in a given sequence. Three heuristic techniques in small problems and in medium-to-large instances two meta-heuristic approaches, as effective local search methods, as well as these heuristics are employed to solve test examples. The single machine total tardiness problem (SMTTP) is already NP-hard, so the considered problem is NP-hard obviously. The computational experiments demonstrate that our proposed heuristic is efficient approach for such just-in-time (JIT) problem, especially equipped with competent heuristics.     

Scheduling two parallel machines with a single server: the general case

This paper considers the problem of scheduling two-operation non-preemptable jobs on two identical semi-automatic machines. A single server is available to carry out the first (or setup) operation. The second operation is executed automatically, without the server. The general problem of makespan minimization is NP-hard in the strong sense. In earlier work, we showed that the equal total length problem is polynomial time and we also provided efficient and effective solutions for the special cases of equal setup and equal processing times. Most of the cases analyzed thus far have fallen into the category of regular problems. In this paper we build on this earlier work to deal with the general case. Various approaches will be considered. One may reduce the problem to a regular one by amalgamating jobs, or we may apply the earlier heuristics to (possibly regular) job clusters. Alternately we may apply a greedy heuristic, a metaheuristic such as a genetic algorithm or the well known Gilmore–Gomory algorithm to solve the general problem. We report on the performance of these various methods.     

Hierarchical minimization of completion time variance and makespan in jobshops

This paper addresses the problem of minimizing makespan for a given set of n jobs to be processed on each of m machines in a static jobshop, subject to the minimum completion time variance (CTV). A lower bound on CTV is developed for the static jobshop problem. A backward scheduling approach is proposed using the observations on the development of lower bound for hierarchical minimization of CTV and makespan. A lower bound on makespan subject to minimum CTV is also presented for this problem. Finally, we present two simulated annealing heuristic approaches using the concepts of forward and backward scheduling. Their performances are compared against each other through the use of the lower bounds established in this work. The simulated annealing heuristic based on backward scheduling is shown to perform well by evaluating the developed heuristics on 82 jobshop problems taken from literature.