A self-adaptive differential evolution heuristic for two-stage assembly scheduling problem to minimize maximum lateness with setup times

The two-stage assembly flowshop scheduling problem has been addressed with respect to different criteria in the literature where setup times are ignored. For some applications, setup times are essential to be explicitly considered since they may take considerable amount of time. We address the two-stage assembly flowshop scheduling problem with respect to maximum lateness criterion where setup times are treated as separate from processing times. We formulate the problem and obtain a dominance relation. Moreover, we propose a self-adaptive differential evolution heuristic. To the best of our knowledge, this is the first attempt to use a self-adaptive differential evolution heuristic to a scheduling problem. We conduct extensive computational experiments to compare the performance of the proposed heuristic with those of particle swarm optimization (PSO), tabu search, and EDD heuristics. The computational analysis indicates that PSO performs much better than tabu and EDD. Moreover, the analysis indicates that the proposed self-adaptive differential evolution heuristic performs as good as PSO in terms of the average error while only taking one-third of CPU time of PSO.     

An efficient heuristic for scheduling in a flowshop to minimize total weighted flowtime of jobs

The problem of scheduling in a flowshop is considered with the objective of minimizing the total weighted flowtime of jobs. A heuristic algorithm is developed by the introduction of lower bounds on the completion times of jobs and the development of heuristic preference relations for the scheduling problem under study. An improvement scheme is incorporated in the heuristic to enhance the quality of its solution. The proposed heuristic, with and without the improvement scheme, and the existing heuristics are evaluated by a large number of randomly generated problems. The results of an extensive computational investigation for various problem sizes are presented. It has been observed that both versions of the proposed heuristic perform better than the existing heuristics in giving a superior solution quality and that the proposed heuristic without the improvement scheme yields a good solution by requiring a negligible CPU time. In addition, an experimental investigation is carried out to evaluate the effectiveness of the improvement scheme when implemented in the proposed heuristic and the existing heuristics, as well as the effectiveness of a variant of the scheme. The results are also discussed.     

Using a Hybrid Evolutionary Algorithm to Minimize Variance in Response Time for Multimedia Object Requests

This research addresses the scheduling problem of multimedia object requests, which is an important problem in information systems, in particular, for World Wide Web applications. The performance measure considered is the variance of response time which is crucial as end users expect fair treatment to their service requests. This problem is known to be NP-hard. The literature survey indicates that two heuristics have been proposed to solve the problem. In this paper, we present a new heuristic, a hybrid evolutionary heuristic, which is shown to perform much better than the two existing ones, e.g., the overall average errors of the existing ones are 1.012 and 2.042 while the error of the proposed hybrid evolutionary heuristic is 0.154.     

Minimizing the total completion time in a two-machine flowshop with sequence-independent setup times

We consider the problem of minimizing the sum of completion times in a two-machine permutation flowshop subject to setup times. We propose a new priority rule, several constructive heuristics, local search procedures, as well as an effective multiple crossover genetic algorithm. Computational experiments carried out on a large set of randomly generated instances provide evidence that a constructive heuristic based on newly derived priority rule dominates all the proposed constructive heuristics. More specifically, we show that one of our proposed constructive heuristics outperforms the best constructive heuristic in the literature in terms of both error and computational time. Furthermore, we show that one of our proposed local search-based heuristics outperforms the best local search heuristic in the literature in terms of again both error and computational time. We also show that, in terms of quality-to-CPU time ratio, the multiple crossover genetic algorithm performs consistently well.     

No-wait flowshops with bicriteria of makespan and total completion time

We consider the m-machine no-wait flowshop scheduling problem with the objective of minimizing a weighted sum of makespan and total completion time. For the two-machine problem, we develop a dominance relation and embed it within a proposed branch-and-bound algorithm. For the m-machine problem, we propose a heuristic. Computational experiments show that the proposed heuristic outperforms the best existing multi-criteria heuristics and the best single criterion heuristics for makespan and total completion time. The efficiency of the dominance relation and branch-and-bound algorithm is also investigated and shown to be effective.     

Heuristics for the flow line problem with setup costs

This paper presents two new heuristics for the flowshop scheduling problem with sequence-dependent setup times (SDSTs) and makespan minimization objective. The first is an extension of a procedure that has been very successful for the general flowshop scheduling problem. The other is a greedy randomized adaptive search procedure (GRASP) which is a technique that has achieved good results on a variety of combinatorial optimization problems. Both heuristics are compared to a previously proposed algorithm based on the traveling salesman problem (TSP). In addition, local search procedures are developed and adapted to each of the heuristics. A two-phase lower bounding scheme is presented as well. The first phase finds a lower bound based on the assignment relaxation for the asymmetric TSP. In phase two, attempts are made to improve the bound by inserting idle time. All procedures are compared for two different classes of randomly generated instances. In the first case where setup times are an order of magnitude smaller than the processing times, the new approaches prove superior to the TSP-based heuristic; for the case where both processing and setup times are identically distributed, the TSP-based heuristic outperforms the proposed procedures.     

A No-Wait Flowshop Scheduling Heuristic to Minimize Makespan

The scheduling problem in the no-wait or constrained flowshop, with the makespan objective, is considered in this article. A simple heuristic algorithm is proposed on the basis of heuristic preference relations and job insertion. When evaluated over a large number of problems of various sizes, the solutions given by the proposed heuristic are found to be fairly accurate and much superior to those given by the two existing heuristics.     

A polynomial time heuristic for the two-machine flowshop scheduling problem with setup times and random processing times

The two-machine flowshop scheduling problem to minimize makespan is addressed. Jobs have random processing times which are bounded within certain intervals. The distributions of job processing times are not known. This problem has been addressed in the literature with the assumption that setup times are included in processing times or are zero. In this paper, we relax this assumption and treat setup times as separate from processing times. We propose a polynomial time heuristic algorithm. Both Johnson algorithm and Yoshida and Hitomi algorithm, both of which developed for the deterministic problem, are special cases of the proposed algorithm. The heuristic algorithm uses a weighted average of lower and upper bounds for processing times. For different weights, the results of the proposed algorithm are compared based on randomly generated data. The computational analysis has shown that the proposed algorithm, with equal weights given to the lower and upper bounds, performs considerably well with an overall average error of 0.36%. The analysis has also shown that the proposed algorithm can safely be used regardless of processing time distributions and the range between lower and upper bounds.     

A Savings Index Heuristic Algorithm for Flowshop Scheduling with Sequence Dependent Set-up Times

This paper considers the permutation flowshop scheduling problem with significant sequence dependent set-up times and develops a savings index heuristic algorithm to find an approximately minimum makespan schedule. The proposed algorithm determines the savings in time associated with a particular sequence and selects the sequence with the maximum time savings as the best heuristic solution. Computational experience indicating the effectiveness and efficiency of the proposed savings index heuristic algorithm are reported and discussed.     

A penalty-based heuristic algorithm for the permutation flowshop scheduling problem with sequence-dependent set-up times

This paper considers the permutation flowshop scheduling problem with sequence-dependent set-up times and develops a penalty-based heuristic algorithm to find an approximately minimum makespan schedule. The proposed algorithm determines the penalty in time associated with a particular sequence and selects the sequence with the minimum time penalty as the best heuristic solution. Computational results comparing the effectiveness and efficiency of the proposed penalty-based heuristic algorithm with an existing savings index heuristic algorithm are reported and discussed.     

A bicriteria m-machine flowshop scheduling with sequence-dependent setup times

In this study, a bicriteria m-machine flowshop scheduling with sequence-dependent setup times is considered. The objective function of the problem is minimization of the weighted sum of total completion time and makespan. Only small size problems with up to 6 machines and 18 jobs can be solved by the proposed integer programming model. Also the model is tested on an example. We also proposed three heuristic approaches for solving large jobs problems. To solve the large sizes problems up to 100 jobs and 10 machines, special heuristics methods is used. Results of computational tests show that the proposed model is effective in solving problems.     

Two-Machine Flowshop Batching and Scheduling

We consider in this paper a two-machine flowshop scheduling problem in which the first machine processes jobs individually while the second machine processes jobs in batches. The forming of each batch on the second machine incurs a constant setup time. The objective is to minimize the makespan. This problem was previously shown to be NP-hard in the ordinary sense. In this paper, we first present a strong NP-hardness result of the problem. We also identify a polynomially solvable case with either anticipatory or non-anticipatory setups. We then establish a property that an optimal solution for the special case is a lower bound for the general problem. To obtain near-optimal solutions for the general problem, we devise some heuristics. The lower bound is used to evaluate the quality of the heuristic solutions. Results of computational experiments reveal that the heuristics produce solutions with small error ratios. They also suggest that the lower bound is close to the optimal solution.     

Minimizing total tardiness on a two-machine re-entrant flowshop

We present a branch and bound algorithm for a two-machine re-entrant flowshop scheduling problem with the objective of minimizing total tardiness. In the re-entrant flowshop considered here, all jobs must be processed twice on each machine, that is, each job should be processed on machine 1, machine 2 and then machine 1 and machine 2. By regarding a job as a pair of sub-jobs, each of which represents a pass through the two machines, we develop dominance properties, a lower bound and heuristic algorithms for the problem, and use these to develop a branch and bound algorithm. For evaluation of the performance of the algorithms, computational experiments are performed on randomly generated test problems and results are reported. Results of the experiments show that the suggested branch and bound algorithm can solve problems with up to 20 sub-jobs in a reasonable amount of CPU time, and the average percentage gap of the heuristic solutions is about 13%.     

Some effective heuristics for no-wait flowshops with setup times to minimize total completion time

In this work, we consider a complex flowshop scheduling problem in which both no-wait and separate setup times are considered. The optimisation criterion is the minimisation of the total completion time. We propose an effective dominance rule for the four machine case that can also be used for m machines. Five simple and fast heuristics are proposed along with two easy to code stochastic local search methods, one of them being based on Iterated Local Search (ILS). An extensive computational evaluation is carried out with two sets of 5,400 instances. All seven methods are compared to two recent algorithms. The results, confirmed by thorough statistical analyses, show that the proposed methods are more effective and efficient when compared to the best existing algorithms in the literature for the considered problem.     

New heuristics for total tardiness minimization in a flexible flowshop

This paper analyses the total tardiness minimization in a flowshop with multiple processors at each stage. While there is considerable research to minimize the makespan, very little work is reported on minimizing the total tardiness for this problem. This research focuses on heuristic methods that consider this environment as a series of parallel machine problems. New dispatching rules are introduced. One of the proposed rules is able to deal with jobs that will come afterwards and not only the available jobs at the decision time. Dispatching rules are also associated with classical (forward and backward) and new list scheduling algorithms. A special scheduling algorithm able to deal with idle times is proposed. Computational experiments in a set of 4,320 literature instances show that the developed heuristics are competitive and outperforms their classical counterparts.     

A hybrid three-stage flowshop problem: Efficient heuristics to minimize makespan

We treat a problem of scheduling n jobs on a three stages hybrid flowshop of particular structure (one machine in the first and third stages and two dedicated machines in stage two). The objective is to minimize the makespan. This problem is NP-complete. We propose two heuristic procedures to cope with realistic problems. Extensive experimentation with various problem sizes are conducted and the computational results show excellent performance of the proposed heuristics.     

An empirical study of hyperheuristics for managing very large sets of low level heuristics

Hyperheuristics give us the appealing possibility of abstracting the solution method from the problem, since our hyperheuristic, at each decision point, chooses between different low level heuristics rather than different solutions as is usually the case for metaheuristics. By assembling low level heuristics from parameterised components we may create hundreds or thousands of low level heuristics, and there is increasing evidence that this is effective in dealing with every eventuality that may arise when solving different combinatorial optimisation problem instances since at each iteration the solution landscape is amenable to at least one of the low level heuristics. However, the large number of low level heuristics means that the hyperheuristic has to intelligently select the correct low level heuristic to use, to make best use of available CPU time. This paper empirically investigates several hyperheuristics designed for large collections of low level heuristics and adapts other hyperheuristics from the literature to cope with these large sets of low level heuristics on a difficult real-world workforce scheduling problem. In the process we empirically investigate a wide range of approaches for setting tabu tenure in hyperheuristic methods, for a complex real-world problem. The results show that the hyperheuristic methods described provide a good way to trade off CPU time and solution quality.     

A genetic algorithm for flow shop scheduling problems

Many scheduling problems are NP-hard problems. For such NP-hard combinatorial optimization problems, heuristics play a major role in searching for near-optimal solutions. In this paper we develop a genetic algorithm-based heuristic for the flow shop scheduling problem with makespan as the criterion. The performance of the algorithm is compared with the established NEH algorithm. Computational experience indicates that genetic algorithms can be good techniques for flowshop scheduling problems.     

Efficient heuristics for flowshop sequencing with the objectives of makespan and flowtime minimisation

In this paper we analyse the performance of flowshop sequencing heuristics with respect to the objectives of makespan and flowtime minimisation. For flowtime minimisation, we propose the strategy employed by the NEH heuristic to construct partial solutions. Results show that this approach outperforms the common fast heuristics for flowtime minimisation while performing similarly or slightly worse than others which, on reward, prove to be much more CPU time-consuming. Additionally, the suggested approach is well balanced with respect to makespan and flowtime minimisation. Based on the previous results, two algorithms are proposed for the sequencing problem with multiple objectives – makespan and flowtime minimisation. These algorithms provide the decision maker with a set of heuristically efficient solutions such that he/she may choose the most suitable sequence for a given ratio between costs associated with makespan and those assigned to flowtime. Computational experience shows both algorithms to perform better than the current heuristics designed for the two-criteria problem.     

A Recovering Beam Search algorithm for the one-machine dynamic total completion time scheduling problem

This paper deals with the one-machine dynamic total completion time scheduling problem. This problem is known to be NP-hard in the strong sense. A polynomial time heuristic algorithm is proposed which applies the recently introduced Recovering Beam Search (RBS) approach. The algorithm is based on a beam search procedure with unitary beam width and includes a recovering subroutine that allows to overcome wrong decisions taken at higher levels of the beam search tree. It is shown that the total number of considered nodes is bounded by n where n is the jobsize. The proposed algorithm is able to solve in very short CPU time problems with up to 500 jobs outperforming the best state of the art heuristics.