Algorithm For Flow Shop Scheduling Research Articles

A novel particle swarm optimization algorithm for permutation flow-shop scheduling to minimize makespan

It is well known that the flow-shop scheduling problem (FSSP) is a branch of production scheduling and is NP-hard. Now, many different approaches have been applied for permutation flow-shop scheduling to minimize makespan, but current algorithms even for moderate size problems cannot be solved to guarantee optimality. Some literatures searching PSO for continuous optimization problems are reported, but papers searching PSO for discrete scheduling problems are few. In this paper, according to the discrete characteristic of FSSP, a novel particle swarm optimization (NPSO) algorithm is presented and successfully applied to permutation flow-shop scheduling to minimize makespan. Computation experiments of seven representative instances (Taillard) based on practical data were made, and comparing the NPSO with standard GA, we obtain that the NPSO is clearly more efficacious than standard GA for FSSP to minimize makespan.

Lagrangian relaxation algorithms for real-time hybrid flowshop scheduling with finite intermediate buffers

We investigate the problem of scheduling N jobs on parallel identical machines in J successive stages with finite buffer capacities between consecutive stages in a real-time environment. The objective is to find a schedule that minimizes the sum of weighted completion time of jobs. This problem has proven strongly NP-hard. In this paper, the scheduling problem is formulated as an integer programming model considering buffers as machines with zero processing time. Lagrangian relaxation algorithms are developed combined with a speed-up dynamic programming approach. The complication and time consumption of solving all the subproblems at each iteration in subgradient optimization motivate the development of the surrogate subgradient method, where only one subproblem is minimized at each iteration and an adaptive multiplier update scheme of Lagrangian multipliers is designed. Computational experiments with up to 100 jobs show that the designed surrogate subgradient algorithm provides a better performance as compared to the subgradient algorithm.

Complexity and algorithms for two-stage flexible flowshop scheduling with availability constraints

This paper considers the two-stage flexible flowshop scheduling problem with availability constraints. We discuss the complexity and the approximability of the problem, and provide some approximation algorithms with finite and tight worst case performance bounds for some special cases of the problem.

A similar particle swarm optimization algorithm for permutation flowshop scheduling to minimize makespan

The flow-shop scheduling problem (FSSP) is a branch of production scheduling, which is among the hardest combinatorial optimization problems. It is well known that this problem with current algorithms even moderately sized problems cannot be solved to guaranteed optimality. Many different approaches have been applied for permutation flowshop scheduling to minimize makespan, but these methods are not satisfying. Particle swarm optimization (PSO) has been developing rapidly and has been applied widely since it was introduced, as it is easily understood and realized. This paper through the improvement of the option modes of gBest and pBest of PSO algorithm, a similar particle swarm optimization algorithm (SPSOA) applied for permutation flowshop scheduling to minimize makespan is firstly presented. The comparisons are made with SPSOAs and the standard GAs, in which we obtained that the SPSOAs are more clearly efficacious than standard GAs for FSSP to minimize makespan. Computational experiments show the efficiency of the proposed (SPSOA) solving approaches.

A new Lagrangian relaxation algorithm for hybrid flowshop scheduling to minimize total weighted completion time

We investigate the problem of scheduling n jobs in s-stage hybrid flowshops with parallel identical machines at each stage. The objective is to find a schedule that minimizes the sum of weighted completion times of the jobs. This problem has been proven to be NP-hard. In this paper, an integer programming formulation is constructed for the problem. A new Lagrangian relaxation algorithm is presented in which precedence constraints are relaxed to the objective function by introducing Lagrangian multipliers, unlike the commonly used method of relaxing capacity constraints. In this way the relaxed problem can be decomposed into machine type subproblems, each of which corresponds to a specific stage. A dynamic programming algorithm is designed for solving parallel identical machine subproblems where jobs may have negative weights. The multipliers are then iteratively updated along a subgradient direction. The new algorithm is computationally compared with the commonly used Lagrangian relaxation algorithms which, after capacity constraints are relaxed, decompose the relaxed problem into job level subproblems and solve the subproblems by using the regular and speed-up dynamic programming algorithms, respectively. Numerical results show that the new Lagrangian relaxation method produces better schedules in much shorter computation time, especially for large-scale problems. Scope and purpose Traditional research on the resolution of hybrid flowshop scheduling has focused on branch and bound algorithms or heuristics to minimize makespan, maximum completion time or maximum lateness, etc. However, little research has been done on minimizing the sum of weighted completion time of all jobs. Further, in many practical scheduling environments, the schedulers expect to obtain a good schedule with acceptable quality in a short computation time. Although the commonly used Lagrangian relaxation method that decomposes the problem into job level subproblems and uses regular dynamic programming to solve the subproblems, has been used to solve similar scheduling problems, it is time-consuming to solve the problem in this paper, even with a small number of jobs. For this reason, this paper considers an alternative Lagrangian decomposition method for hybrid flowshop scheduling. In addition, we combine and generalize the existing approach for parallel identical machine subproblems in the new approach.

An effective hybrid genetic algorithm for flow shop scheduling with limited buffers

As a typical manufacturing and scheduling problem with strong industrial background, flow shop scheduling with limited buffers has gained wide attention both in academic and engineering fields. With the objective to minimize the total completion time (or makespan), such an issue is very hard to solve effectively due to the NP-hardness and the constraint on the intermediate buffer. In this paper, an effective hybrid genetic algorithm (HGA) is proposed for permutation flow shop scheduling with limited buffers. In the HGA, not only multiple genetic operators based on evolutionary mechanism are used simultaneously in hybrid sense, but also a neighborhood structure based on graph model is employed to enhance the local search, so that the exploration and exploitation abilities can be well balanced. Moreover, a decision probability is used to control the utilization of genetic mutation operation and local search based on problem-specific information so as to prevent the premature convergence and concentrate computing effort on promising neighbor solutions. Simulation results and comparisons based on benchmarks demonstrate the effectiveness of the HGA. Meanwhile, the effects of buffer size and decision probability on optimization performances are discussed.

Two ant-colony algorithms for minimizing total flowtime in permutation flowshops

The problem of scheduling in flowshops with the objective of minimizing total flowtime is studied. For solving the problem two ant-colony algorithms are proposed and analyzed. The first algorithm refers to some extent to ideas by Stuetzle [Stuetzle, T. (1998). An ant approach for the flow shop problem. In: Proceedings of the sixth European Congress on intelligent techniques and soft computing (EUFIT '98) (Vol. 3) (pp. 1560-1564). Aachen: Verlag Mainz] and Merkle and Middendorf [Merkle, D., & Middendorf, M. (2000). An ant algorithm with a new pheromone evaluation rule for total tardiness problems. In: Proceedings of the EvoWorkshops 2000, lecture notes in computer science 1803 (pp. 287-296). Berlin: Springer]. The second algorithm is newly developed. The proposed ant-colony algorithms have been applied to 90 benchmark problems taken from Taillard [Taillard, E. (1993). Benchmarks for basic scheduling problems. European Journal of Operational Research, 64, 278-285]. A comparison of the solutions yielded by the ant-colony algorithms with the best heuristic solutions known for the benchmark problems up to now, as published in extensive studies by Liu and Reeves [Liu, J., & Reeves, C.R. (2001). Constructive and composite heuristic solutions to the P//ΣCi scheduling problem. European Journal of Operational Research, 132,439-452, and Rajendran and Ziegler [Rajendran, C., & Ziegler, H. (2004). Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs. European Journal of Operational Research, 155, 426-438], shows that the presented ant-colony algorithms are better, on an average, than the heuristics analyzed by Liu and Reeves and Rajendran and Ziegler.

A class of hypothesis-test-based genetic algorithms for flow shop scheduling with stochastic processing time

As an important optimisation problem with a strong engineering background, stochastic flow shop scheduling with uncertain processing time is difficult because of inaccurate objective estimation, huge search space, and multiple local minima, especially NP-hardness. As an effective meta-heuristic, genetic algorithms (GAs) have been widely studied and applied in scheduling fields, but so far seldom for stochastic cases. In this paper, a hypothesis-test method, an effective methodology in statistics, is employed and incorporated into a GA to solve the stochastic flow shop scheduling problem and to avoid premature convergence of the GA. The proposed approach is based on statistical performance and a hypothesis test. It not only preserves the global search ability of a GA, but it can also reduce repeated searches for those solutions with similar performance in a statistical sense so as to enhance population diversity and achieve better results. Simulation results based on some benchmarks demonstrate the feasibility and effectiveness of the proposed method by comparison with traditional GAs. The effects of some parameters on the performance of the proposed algorithms are also discussed .

A multi-objective genetic algorithm for scheduling in flow shops to minimize the makespan and total flow time of jobs

In this paper the problem of permutation flow shop scheduling with the objectives of minimizing the makespan and total flow time of jobs is considered. A Pareto-ranking based multi-objective genetic algorithm, called a Pareto genetic algorithm (GA) with an archive of non-dominated solutions subjected to a local search (PGA-ALS) is proposed. The proposed algorithm makes use of the principle of non-dominated sorting, coupled with the use of a metric for crowding distance being used as a secondary criterion. This approach is intended to alleviate the problem of genetic drift in GA methodology. In addition, the proposed genetic algorithm maintains an archive of non-dominated solutions that are being updated and improved through the implementation of local search techniques at the end of every generation. A relative evaluation of the proposed genetic algorithm and the existing best multi-objective algorithms for flow shop scheduling is carried by considering the benchmark flow shop scheduling problems. The non-dominated sets obtained from each of the existing algorithms and the proposed PGA-ALS algorithm are compared, and subsequently combined to obtain a net non-dominated front. It is found that most of the solutions in the net non-dominated front are yielded by the proposed PGA-ALS.

Fuzzy Gupta Scheduling for Flow Shops with More than two Machines

In past work the authors demonstrated how fuzzy concepts can easily be used in the Johnson algorithm for managing uncertain scheduling on two-machine flow shops. This article extends these concepts to fuzzy flow shops with more than two machines. A new fuzzy heuristic flow-shop scheduling algorithm (the fuzzy Gupta algorithm) is then designed, as optimal solutions seem unnecessary for uncertain environments. Also, the conventional Gupta algorithm is shown as a special case of the fuzzy Gupta algorithm with special membership functions being assigned.

Fuzzy Gupta Scheduling for Flow Shops with more than Two Machines

In past work the authors demonstrated how fuzzy concepts can easily be used in the Johnson algorithm for managing uncertain scheduling on two-machine flow shops. This article extends these concepts to fuzzy flow shops with more than two machines. A new fuzzy heuristic flow-shop scheduling algorithm (the fuzzy Gupta algorithm) is then designed, as optimal solutions seem unnecessary for uncertain environments. Also, the conventional Gupta algorithm is shown as a special case of the fuzzy Gupta algorithm with special membership functions being assigned.

Fuzzy branch-and-bound algorithm for flow shop scheduling

Scheduling is the allocation of resources over time to perform a collection of task. It is an important subject of production and operations management area. For most of scheduling problems made so far, the processing times of each job on each machine and due dates have been assigned as a real number. However in the real world, information is often ambiguous or imprecise. In this paper fuzzy concept are applied to the flow shop scheduling problems. The branch-and-bound algorithm of Ignall and Schrage was modified and rewritten for three-machine flow shop problems with fuzzy processing time. Fuzzy arithmetic on fuzzy numbers is used to determine the minimum completion time (C max). Proposed algorithm gets a scheduling result with a membership function for the final completion time. With this membership function determined, a wider point of view is provided for the manager about the optimal schedule.

Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs

The problem of scheduling in permutation flowshops is considered with the objective of minimizing the makespan, followed by the consideration of minimization of total flowtime of jobs. Two ant-colony optimization algorithms are proposed and analyzed for solving the permutation flowshop scheduling problem. The first algorithm extends the ideas of the ant-colony algorithm by Stuetzle [Proceedings of the 6th European Congress on Intelligent Techniques and Soft Computing (EUFIT ’98), vol. 3, Verlag Mainz, Aachen, Germany, 1998, p. 1560], called max–min ant system (MMAS), by incorporating the summation rule suggested by Merkle and Middendorf [Proceedings of the EvoWorkshops 2000, Lecture Notes in Computer Science No. 1803, Springer-Verlag, Berlin, 2000, p. 287] and a newly proposed local search technique. The second ant-colony algorithm is newly developed. The proposed ant-colony algorithms have been applied to 90 benchmark problems taken from Taillard [European Journal of Operational Research 64 (1993) 278]. First, a comparison of the solutions yielded by the MMAS and the two ant-colony algorithms developed in this paper, with the heuristic solutions given by Taillard [European Journal of Operational Research 64 (1993) 278] is undertaken with respect to the minimization of makespan. The comparison shows that the two proposed ant-colony algorithms perform better, on an average, than the MMAS. Subsequently, by considering the objective of minimizing the total flowtime of jobs, a comparison of solutions yielded by the proposed ant-colony algorithms with the best heuristic solutions known for the benchmark problems, as published in an extensive study by Liu and Reeves [European Journal of Operational Research 132 (2001) 439], is carried out. The comparison shows that the proposed ant-colony algorithms are clearly superior to the heuristics analyzed by Liu and Reeves. For 83 out of 90 problems considered, better solutions have been found by the two proposed ant-colony algorithms, as compared to the solutions reported by Liu and Reeves.

An improved approximation algorithm for two-machine flow shop scheduling with an availability constraint

We study the problem of scheduling n jobs in a two-machine flow shop where the second machine is not available for processing during a given time interval. A resumable scenario is assumed, i.e., if a job cannot be finished before the down period it is continued after the machine becomes available again. The objective is to minimize the makespan. The best fast approximation algorithm for this problem guarantees a relative worst-case error bound of 4/3. We present an improved algorithm with a relative worst-case error bound of 5/4.

A TSP-GA multi-objective algorithm for flow-shop scheduling

A multi-objective evolutionary search algorithm using a travelling salesman algorithm and genetic algorithm for flow-shop scheduling is proposed in this paper. The initial sequence is obtained by solving the TSP. The initial population of the genetic algorithm is created with the help of a neighbourhood creation scheme known as a random insertion perturbation scheme, which uses the sequence obtained from TSP. The proposed algorithm uses a weighted sum of multiple objectives as a fitness function. The weights are randomly generated for each generation to enable a multi-directional search. The performance measures considered include minimising makespan, mean flow time and machine idle time. The performance of the proposed algorithm is demonstrated by applying it to benchmark problems available in the OR-Library.

A class of order-based genetic algorithm for flow shop scheduling

A class of order-based genetic algorithm is presented for flow shop scheduling that is a typical NP-hard combinatorial optimisation problem with a strong engineering background. The proposed order-based genetic algorithm borrows from the idea of ordinal optimisation to ensure the quality of the solution found with a reduction in computation effort and applies the evolutionary searching mechanism and learning capability of genetic algorithms to effectively perform exploration and exploitation. Under the guidance of ordinal optimisation and with an emphasis on order-based searching and elitist-based evolution in the proposed approach, a solution that is "good enough" can be guaranteed with a high confidence level and reduced level of computation. The effectiveness of the proposed algorithm is demonstrated by numerical simulation results based on benchmarks, and its optimisation quality is much better than that of the classic genetic algorithm, the well-known NEH heuristic, as well as being better than a pure blind search. Moreover, the effects of some parameters on optimisation performance are discussed.

Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling

This paper shows how the performance of evolutionary multiobjective optimization (EMO) algorithms can be improved by hybridization with local search. The main positive effect of the hybridization is the improvement in the convergence speed to the Pareto front. On the other hand, the main negative effect is the increase in the computation time per generation. Thus, the number of generations is decreased when the available computation time is limited. As a result, the global search ability of EMO algorithms is not fully utilized. These positive and negative effects are examined by computational experiments on multiobjective permutation flowshop scheduling problems. Results of our computational experiments clearly show the importance of striking a balance between genetic search and local search. In this paper, we first modify our former multiobjective genetic local search (MOGLS) algorithm by choosing only good individuals as initial solutions for local search and assigning an appropriate local search direction to each initial solution. Next, we demonstrate the importance of striking a balance between genetic search and local search through computational experiments. Then we compare the modified MOGLS with recently developed EMO algorithms: the strength Pareto evolutionary algorithm and revised nondominated sorting genetic algorithm. Finally, we demonstrate that a local search can be easily combined with those EMO algorithms for designing multiobjective memetic algorithms.

An experimental analysis of the CGPS algorithm for the three-machine flow shop scheduling with minimum makespan criterion

The algorithm developed by Chen, Glass, Potts and Strusevich (CGPS) is by far the best one in terms of the worst-case performance ratio for the three-machine flow shop scheduling (3FSS) with minimum makespan criterion. This paper focuses on the experimental analysis of the CGPS algorithm. Three simulation experiments are conducted to compare and evaluate its performance in terms of six evaluation measures. It is shown that the CGPS algorithm is not empirically preferred for the 3FSS with minimum makespan criterion.

A palmer-based continuous fuzzy flexible flow-shop scheduling algorithm

Flexible flow shops can be thought of as generalizations of simple flow shops. In the past, the processing time for each job was usually assumed to be known exactly, but in many real-world applications, processing times may vary dynamically due to human factors or operating faults. In the past, we demonstrated how discrete fuzzy concepts could easily be used in the Palmer algorithm for managing uncertain flexible-flow-shop scheduling. In this paper, we generalize it to continuous fuzzy domains. We use triangular membership functions for flexible flow shops with more than two machine centers to examine processing-time uncertainties and to make scheduling more suitable for real applications. We first use the triangular fuzzy LPT algorithm to allocate jobs, and then use the triangular fuzzy Palmer algorithm to deal with sequencing the tasks. The proposed method thus provides a more flexible way of scheduling jobs than conventional scheduling methods.

A modification to the CGPS algorithm for three-machine flow shop scheduling

In this paper, the three-machine flow shop schedtlling (3FSS) with the objective of minimizing the makespan is considered. The algorithm developed by Chen, Glass, Potts and Strusevich (CGPS) is by far the best one in terms of the worst-case performance ratio for the 3FSS. This paper analyzes a particular condition in a step of the CGPS algorithm and proposes a modification to the CGPS algorithm by changing this condition. It is shown that this modified algorithm is more general one for the 3FSS.