A discrete particle swarm optimization algorithm with self-adaptive diversity control for the permutation flowshop problem with blocking

doi:10.1016/j.asoc.2011.09.021

Applied Soft Computing

Volume 12, Issue 2, February 2012, Pages 652-662

https://doi.org/10.1016/j.asoc.2011.09.021 Get rights and content

Abstract

This paper proposes a discrete particle swarm optimization (DPSO) algorithm for the m-machine permutation flowshop scheduling problem with blocking to minimize the makespan, which has a strong industrial background, e.g., many production processes of chemicals and pharmaceuticals in chemical industry can be reduced to this problem. To prevent the DPSO from premature convergence, a self-adaptive diversity control strategy is adopted to diversify the population when necessary by adding a random perturbation to the velocity of each particle according to a probability controlled by the diversity of the current population. In addition, a stochastic variable neighborhood search is used as the local search to improve the search intensification. Computational results using benchmark problems show that the proposed DPSO algorithm outperforms previous algorithms proposed in the literature and that it can obtain 111 new best known upper bounds for the 120 benchmark problems.

Graphical abstract

Highlights

► ► Several operators are proposed to construct the update mechanism of particles in the proposed discrete particle swarm optimization algorithm. ► A self-adaptive diversity control strategy is adopted to prevent the DPSO from premature convergence. ► A stochastic variable neighborhood search is used as the local search to improve the search intensification. ► Computational results show that the proposed DPSO algorithm can obtain 111 new best known upper bounds for the 120 benchmark problems.

Introduction

The classical permutation flowshop scheduling problem (PFSP) is one of the best known production scheduling problems due to its strong industrial background [1]. In the classical PFSP, it is assumed that intermediate buffers have infinite capacity and that the partially processed jobs can be stored in buffers for unlimited amount of time. However, in practice there may be no buffers between consecutive machines [2]. Therefore, in recent years the PFSP with blocking (F_m/blocking/C_max) has drawn a considerable amount of interest.

In the F_m/blocking/C_max problem, there are no buffers between machines and hence a job, which has completed processing on a machine, must remain in this machine and block it until the immediate downstream machine becomes available. Hall and Sriskandarajah [3] gave a detailed survey on the flowshop scheduling problems with blocking and no-wait in process, as well as their real-life applications in industries, and showed that the F_m/blocking/C_max problem with m ≥ 3 is strongly NP-complete based on the result of Papadimitriou and Kanellakis [4]. Exact method such as the branch-and-bound (B&B) can solve this problem only for small size and consequently the soft computing approaches such as heuristics and metaheuristics become the only choice. Among the solution methods for the F_m/blocking/C_max problem, the tabu search proposed by Grabowski and Pempera [5] is the state-of-the-art. To improve the performance of the proposed tabu search algorithm, the authors developed two properties of the problem associated with the blocks of jobs and several other improvement strategies such as the multi-moves and the dynamical tabu list.

Recently, the particle swarm optimization (PSO) algorithm has demonstrated a very promising performance for the classical PFSP and many other kinds of optimization problems [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24]; however, most of them are continuous PSO and thus a decoding procedure is needed to transform the continuous solution into the job permutation. Though there have been some discrete PSO (DPSO) proposed for the PFSP, the velocity they used was a list of moves to transform a particle into a new one. Our experimental results reveal that this representation is not very effective for the F_m/blocking/C_max problem. Therefore, this paper aims to propose a novel and effective DPSO for this problem by introducing a new velocity and particle update model to generate new population, a self-adaptively diversify control strategy to avoid premature convergence, and a stochastic variable neighborhood search (SVNS) to strengthen the search intensification.

The rest of this paper is organized as follows. Section 2 is devoted to briefly describe the F_m/blocking/C_max problem, and Section 3 presents the proposed DPSO algorithm. The computational results on benchmark problems are presented in Section 4. Finally, Section 5 concludes the paper.

Section snippets

Problem description

The F_m/blocking/C_max can be briefly described as follows. In this problem, there is a set of jobs J = {1, 2, …, n} and a set of machines M = {1, 2, …, m}. Each job i ∈ J must be processed on these m machines in the same machine order of 1, 2, …, m. That is, the processing of each job should start from machine 1, then machine 2, and at last finish on machine m. The processing time of job i ∈ J on machine j ∈ M is denoted as p_ij, which is fixed and nonnegative. It is assumed that the jobs are available at

Brief introduction of PSO

PSO is an evolutionary metaheuristic proposed by Kennedy and Eberhart [33], [34]. Its basic principle is to simulate the social behavior of bird flocking or fish schooling, as well as the means of information exchange between individuals, to solve optimization problems. In the PSO algorithm, a swarm consists of m individuals (called particles) that fly around in an n-dimensional search space. The position of the ith particle at the tth iteration is used to evaluate the particle and represent

Experimental design

To test the performance of the proposed DPSO algorithm, computational experiments were carried out on the well-known benchmark set of Taillard [46], which is composed of 120 instances ranging from 20 jobs and 5 machines to 500 jobs and 20 machines, except that the blocking constraint is taken into account. In this benchmark set there are 10 instances for each problem size. Our proposed DPSO algorithm was implemented in C++, and tested on a personal PC with Intel 2.33 GHz CPU and 2 GB memory. In

Conclusions

This paper proposed a novel DPSO algorithm for the permutation flowshop scheduling problem with blocking. Different from previous DPSO algorithms, our DPSO adopts a new velocity and particle update model to evolve the population, a self-adaptive diversity control strategy to improve the population diversity, and a local search named SVNS to improve the search intensification. The Taillard's benchmark instances were used to evaluate our DPSO algorithm. The computational results demonstrated the

Acknowledgements

The authors are very grateful to the anonymous reviewers for their insightful comments and helpful suggestions.

This research is supported by the Key Program of National Natural Science Foundation of China (71032004), the National Natural Science Foundation of China (70902065), the National Science Foundation for Post-doctoral Scientists of China (20100481197), and the Fundamental Research Funds for the Central Universities (N090404018).

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A discrete particle swarm optimization algorithm with self-adaptive diversity control for the permutation flowshop problem with blocking

Abstract

Graphical abstract

Highlights

Introduction

Section snippets

Problem description

Brief introduction of PSO

Experimental design

Conclusions

Acknowledgements

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Eur. J. Oper. Res.

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Appl. Soft Comput.

Appl. Soft Comput.

Appl. Soft Comput.

Inf. Process. Lett.

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Appl. Soft Comput.

Appl. Soft Comput.

Appl. Soft Comput.

Appl. Soft Comput.

Omega – Int. J. Manage. Sci.

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Microprocess. Microsyst.

Appl. Soft Comput.

Appl. Soft Comput.

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Comput. Oper. Res.

Eur. J. Oper. Res.