A discrete artificial bee colony algorithm for the no-idle permutation flowshop scheduling problem with the total tardiness criterion

Abstract In this paper, we present a discrete artificial bee colony algorithm to solve the no-idle permutation flowshop scheduling problem with the total tardiness criterion. The no-idle permutation flowshop problem is a variant of the well-known permutation flowshop scheduling problem where idle time is not allowed on machines. In other words, the start time of processing the first job on a given machine must be delayed in order to satisfy the no-idle constraint. The paper presents the following contributions: First of all, a discrete artificial bee colony algorithm is presented to solve the problem on hand first time in the literature. Secondly, some novel methods of calculating the total tardiness from makespan are introduced for the no-idle permutation flowshop scheduling problem. Finally, the main contribution of the paper is due to the fact that a novel speed-up method for the insertion neighborhood is developed for the total tardiness criterion. The performance of the discrete artificial bee colony algorithm is evaluated against a traditional genetic algorithm. The computational results show its highly competitive performance when compared to the genetic algorithm. Ultimately, we provide the best known solutions for the total tardiness criterion with different due date tightness levels for the first time in the literature for the Taillard’s benchmark suit.

[1]  Ping Chen,et al.  An iterated local search algorithm for the permutation flowshop problem with total flowtime criterion , 2009, Comput. Oper. Res..

[2]  Alain Guinet,et al.  Three stage no-idle flow-shops , 2003 .

[3]  Rubén Ruiz,et al.  Scheduling in Flowshops with No-Idle Machines , 2009 .

[4]  Józef Grabowski,et al.  Some local search algorithms for no-wait flow-shop problem with makespan criterion , 2005, Comput. Oper. Res..

[5]  Thomas Stützle,et al.  A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem , 2007, Eur. J. Oper. Res..

[6]  Alain Guinet,et al.  A travelling salesman approach to solve the F , 2005, Eur. J. Oper. Res..

[7]  Lawrence Davis,et al.  Applying Adaptive Algorithms to Epistatic Domains , 1985, IJCAI.

[8]  Jerzy Kamburowski,et al.  On no-wait and no-idle flow shops with makespan criterion , 2007, Eur. J. Oper. Res..

[9]  D. Pohoryles,et al.  Flowshop/no-idle or no-wait scheduling to minimize the sum of completion times , 1982 .

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

[11]  Quan-Ke Pan,et al.  A novel differential evolution algorithm for no-idle permutation flow-shop scheduling problems , 2008 .

[12]  Gur Mosheiov,et al.  A note on a greedy heuristic for flow-shop makespan minimization with no machine idle-time , 2008, Eur. J. Oper. Res..

[13]  Ling Wang,et al.  No-idle permutation flow shop scheduling based on a hybrid discrete particle swarm optimization algorithm , 2008 .

[14]  D. Karaboga,et al.  On the performance of artificial bee colony (ABC) algorithm , 2008, Appl. Soft Comput..

[15]  Rainer Leisten,et al.  Total tardiness minimization in permutation flow shops: a simple approach based on a variable greedy algorithm , 2008 .

[16]  Porpan Vachajitpan,et al.  Job sequencing with continuous machine operation , 1982 .

[17]  P. C. Bagga,et al.  Flowshop/no-idle scheduling to minimise the mean flowtime , 2005, The ANZIAM Journal.

[18]  Dervis Karaboga,et al.  A comparative study of Artificial Bee Colony algorithm , 2009, Appl. Math. Comput..

[19]  Mehmet Fatih Tasgetiren,et al.  A discrete particle swarm optimization algorithm for the no-wait flowshop scheduling problem , 2008, Comput. Oper. Res..

[20]  Jung Woo Jung,et al.  Flowshop-scheduling problems with makespan criterion: a review , 2005 .

[21]  Rubén Ruiz,et al.  A comprehensive review and evaluation of permutation flowshop heuristics to minimize flowtime , 2013, Comput. Oper. Res..

[22]  Mehmet Fatih Tasgetiren,et al.  A discrete artificial bee colony algorithm for the lot-streaming flow shop scheduling problem , 2011, Inf. Sci..

[23]  Nurhan Karaboga,et al.  A new design method based on artificial bee colony algorithm for digital IIR filters , 2009, J. Frankl. Inst..

[24]  P. C. Bagga,et al.  Flowshop/No-idle Scheduling to Minimize Total Elapsed Time , 2005, J. Glob. Optim..

[25]  Jerzy Kamburowski,et al.  More on three-machine no-idle flow shops , 2004, Comput. Ind. Eng..

[26]  Chandrasekharan Rajendran,et al.  Scheduling in flowshops to minimize total tardiness of jobs , 2004 .

[27]  C. R. Woollam.  Flowshop with no idle machine time allowed , 1986 .

[28]  Mehmet Fatih Tasgetiren,et al.  A discrete artificial bee colony algorithm for the total flowtime minimization in permutation flow shops , 2011, Inf. Sci..

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

[30]  Dervis Karaboga,et al.  AN IDEA BASED ON HONEY BEE SWARM FOR NUMERICAL OPTIMIZATION , 2005 .

[31]  Mehmet Fatih Tasgetiren,et al.  A discrete artificial bee colony algorithm for the permutation flow shop scheduling problem with total flowtime criterion , 2010, IEEE Congress on Evolutionary Computation.

[32]  Milan Vlach,et al.  Note: On the two-machine no-idle flowshop problem , 2000 .

[33]  É. Taillard.  Some efficient heuristic methods for the flow shop sequencing problem , 1990 .

[34]  Dervis Karaboga,et al.  A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm , 2007, J. Glob. Optim..

[35]  K. R. Baker,et al.  An investigation of due-date assignment rules with constrained tightness , 1981 .