Iterated Local Search and Other Algorithms for Buffered Two-Machine Permutation Flow Shops with Constant Processing Times on One Machine

Abstract The two-machine permutation flow shop scheduling problem with buffer is studied for the special case that all processing times on one of the two machines are equal to a constant c. This case is interesting because it occurs in various applications, for example, when one machine is a packing machine or when materials have to be transported. Different types of buffers and buffer usage are considered. It is shown that all considered buffer flow shop problems remain NP-hard for the makespan criterion even with the restriction to equal processing times on one machine. However, the special case where the constant c is larger or smaller than all processing times on the other machine is shown to be polynomially solvable by presenting an algorithm (2BF-OPT) that calculates optimal schedules in O(nlogn) steps. Two heuristics for solving the NP-hard flow shop problems are proposed: (i) a modification of the commonly used NEH heuristic (mNEH) and (ii) an Iterated Local Search heuristic (2BF-ILS) that uses the mNEH heuristic for computing its initial solution. It is shown experimentally that the proposed 2BF-ILS heuristic obtains better results than two state-of-the-art algorithms for buffered flow shop problems from the literature and an Ant Colony Optimization algorithm. In addition, it is shown experimentally that 2BF-ILS obtains the same solution quality as the standard NEH heuristic, however, with a smaller number of function evaluations.

[1]  Iie Amar Dev Amar Senior Member,et al.  Simulated Versus Real Life Data in Testing the Efficiency of Scheduling Algorithms , 1986 .

[2]  Inyong Ham,et al.  A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem , 1983 .

[3]  Quan-Ke Pan,et al.  Solving the large-scale hybrid flow shop scheduling problem with limited buffers by a hybrid artificial bee colony algorithm , 2015, Inf. Sci..

[4]  P. A. Kononova,et al.  The variable neighborhood search for the two machine flow shop problem with a passive prefetch , 2013 .

[5]  Colin R. Reeves,et al.  A genetic algorithm for flowshop sequencing , 1995, Comput. Oper. Res..

[6]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[7]  Erhan Kozan,et al.  Scheduling a flow-shop with combined buffer conditions , 2009 .

[8]  Gaurav Singh,et al.  Flexible Flow Shop with Storage: Complexity and Optimisation Methods , 2016 .

[9]  Andreas T. Ernst,et al.  Flexible flow shop with dedicated buffers , 2019, Discret. Appl. Math..

[10]  Byung-Cheon Choi,et al.  Two-machine flow shops with an optimal permutation schedule under a storage constraint , 2020, J. Sched..

[11]  Chelliah Sriskandarajah,et al.  A Survey of Machine Scheduling Problems with Blocking and No-Wait in Process , 1996, Oper. Res..

[12]  Alessandro Agnetis,et al.  An exact algorithm for the batch sequencing problem in a two‐machine flow shop with limited buffer , 1998 .

[13]  Ling Wang,et al.  An effective hybrid PSO-based algorithm for flow shop scheduling with limited buffers , 2008, Comput. Oper. Res..

[14]  Yakov Zinder,et al.  Permutation schedules for a two-machine flow shop with storage , 2016, Oper. Res. Lett..

[15]  Yan Jin,et al.  A new improved NEH heuristic for permutation flowshop scheduling problems , 2017 .

[16]  Ravi Sethi,et al.  The Complexity of Flowshop and Jobshop Scheduling , 1976, Math. Oper. Res..

[17]  Marco Pranzo,et al.  Batch scheduling in a two-machine flow shop with limited buffer and sequence independent setup times and removal times , 2004, Eur. J. Oper. Res..

[18]  Victor Fernandez-Viagas,et al.  NEH-based heuristics for the permutation flowshop scheduling problem to minimise total tardiness , 2015, Comput. Oper. Res..

[19]  Lixin Tang,et al.  A tabu search algorithm based on new block properties and speed-up method for permutation flow-shop with finite intermediate storage , 2005, J. Intell. Manuf..

[20]  Jing J. Liang,et al.  Multi-objective flow shop scheduling with limited buffers using hybrid self-adaptive differential evolution , 2019, Memetic Computing.

[21]  Liang Zhang,et al.  An effective hybrid genetic algorithm for flow shop scheduling with limited buffers , 2006, Comput. Oper. Res..

[22]  Liang Gao,et al.  An effective hybrid discrete differential evolution algorithm for the flow shop scheduling with intermediate buffers , 2011, Inf. Sci..

[23]  Christos H. Papadimitriou,et al.  Flowshop scheduling with limited temporary storage , 1980, JACM.

[24]  Dexian Huang,et al.  An effective hybrid DE-based algorithm for multi-objective flow shop scheduling with limited buffers , 2009, Comput. Oper. Res..

[25]  Appa Iyer Sivakumar,et al.  Optimisation of flow-shop scheduling with batch processor and limited buffer , 2012 .

[26]  Hanyu Gu,et al.  Efficient Lagrangian Heuristics for the Two-Stage Flow Shop with Job Dependent Buffer Requirements , 2017, IWOCA.

[27]  Y.-C. Hsieh,et al.  A note of using effective immune based approach for the flow shop scheduling with buffers , 2009, Appl. Math. Comput..

[28]  Le Thi Hoai An,et al.  Optimization of Complex Systems: Theory, Models, Algorithms and Applications, WCGO 2019, World Congress on Global Optimization, Metz, France, 8-10 July, 2019 , 2020, WCGO.

[29]  Leslie Pérez Cáceres,et al.  The irace package: Iterated racing for automatic algorithm configuration , 2016 .

[30]  Xing-sheng Gu,et al.  An effective discrete artificial bee colony algorithm for flow shop scheduling problem with intermediate buffers , 2015 .

[31]  Zbigniew Michalewicz,et al.  Benchmarking Optimization Algorithms: An Open Source Framework for the Traveling Salesman Problem , 2014, IEEE Computational Intelligence Magazine.

[32]  Joanna Berlinska,et al.  Two-Machine Flow Shop with a Dynamic Storage Space and UET Operations , 2019, WCGO.

[33]  Éric D. Taillard,et al.  Benchmarks for basic scheduling problems , 1993 .

[34]  Gabriela Ochoa,et al.  On the automatic discovery of variants of the NEH procedure for flow shop scheduling using genetic programming , 2011, J. Oper. Res. Soc..

[35]  S. M. Johnson,et al.  Optimal two- and three-stage production schedules with setup times included , 1954 .

[36]  Bertrand M. T. Lin,et al.  A two-machine flowshop problem with processing time-dependent buffer constraints - An application in multimedia presentations , 2009, Comput. Oper. Res..

[37]  Rainer Leisten,et al.  Flowshop sequencing problems with limited buffer storage , 1990 .

[38]  L. Darrell Whitley,et al.  Contrasting Structured and Random Permutation Flow-Shop Scheduling Problems: Search-Space Topology and Algorithm Performance , 2002, INFORMS J. Comput..

[39]  Ghasem Moslehi,et al.  A hybrid variable neighborhood search algorithm for solving the limited-buffer permutation flow shop scheduling problem with the makespan criterion , 2014, Comput. Oper. Res..

[40]  Jose M. Framiñan,et al.  New hard benchmark for flowshop scheduling problems minimising makespan , 2015, Eur. J. Oper. Res..

[41]  Quan-ke Pan,et al.  An effective invasive weed optimization algorithm for the flow shop scheduling with intermediate buffers , 2013, 2013 25th Chinese Control and Decision Conference (CCDC).

[42]  Julia Memar,et al.  Flow Shop with Job-Dependent Buffer Requirements - a Polynomial-Time Algorithm and Efficient Heuristics , 2019, MOTOR.

[43]  Peter Brucker,et al.  Flow-shop problems with intermediate buffers , 2003, OR Spectr..

[44]  Bertrand M. T. Lin,et al.  Sequence optimization for media objects with due date constraints in multimedia presentations from digital libraries , 2013, Inf. Syst..

[45]  Keyi Xing,et al.  Differential evolution metaheuristics for distributed limited-buffer flowshop scheduling with makespan criterion , 2019, Comput. Oper. Res..

[46]  R. Gomory,et al.  Sequencing a One State-Variable Machine: A Solvable Case of the Traveling Salesman Problem , 1964 .

[47]  Yazid Mati,et al.  Complexity of flowshop scheduling problems with a new blocking constraint , 2003, Eur. J. Oper. Res..

[48]  Liang Gao,et al.  A chaotic harmony search algorithm for the flow shop scheduling problem with limited buffers , 2011, Appl. Soft Comput..

[49]  Martin Middendorf,et al.  An Iterated Local Search Algorithm for the Two-Machine Flow Shop Problem with Buffers and Constant Processing Times on One Machine , 2019, EvoCOP.