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Solution for flow shop scheduling problems using chaotic hybrid firefly and particle swarm optimization algorithm with improved local search

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Abstract

Scheduling is important for the efficient use of resources in the production and service sectors. Depending on the sector and production environment, scheduling problems can vary greatly. Flow Shop production environments are a common feature of industrial activity. In these production environments, m individual machines are used to process n jobs. As the number of jobs and number of machines employed increases, so does the difficulty of finding an accurate solution to scheduling problems. For this reason, a variety of heuristic and metaheuristic solution methods have been developed for this type of problems. In this study, chaotic hybrid firefly and particle swarm optimization are used with a developed version of local search for scheduling of flow shop production environments. Maximum completion time was taken as the objective function. In order to develop the solutions reached, the initial solution was adapted with NEH method. The proposed method was applied to the problem sets in the literature and the results obtained compared with other methods. The experimental results produced by the proposed algorithm were found to be more reliable than those of other algorithms in the literature.

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References

  • Ahmadizar F (2012) A new ant colony algorithm for makespan minimization in permutation ow shops. Comput Ind Eng 63(2):355–361

    Google Scholar 

  • Andreas C (2004) Nearchou. The effect of various operators on the genetic search for large scheduling problems. Int J Prod Econ 88(2):191–203

    Google Scholar 

  • Aydilek İ, Tenekeci E, Karaçizmeli İ, Kaya S, Gümüşçü A (2019) Hibrit Ateşböceği ve Parçacık Sürü Algoritmasının Kaotik Haritalar ile İyileştirilmesi. Harran Üniversitesi Mühendislik Dergisi 4(2):69–78 Retrieved from https://dergipark.org.tr/tr/pub/humder/issue/47643/560803

  • Benavides Alexander J, Marcus R (2018) Fast heuristics for minimizing the makespan in non- permutation ow shops. Comput Oper Res 100:230–243. https://doi.org/10.1016/j.cor.2018.07.017

    Article  MathSciNet  MATH  Google Scholar 

  • Campbell HG, Dudek RA, Smith BL (1970) A heuristic algorithm for the N-job, mmachine sequencing problem. Manage Sci 16:16

    Google Scholar 

  • Chakravarthi KK, Shyamala L, Vaidehi V (2020) Cost-effective workflow scheduling approach on cloud under deadline constraint using firefly algorithm. Appl Intell. https://doi.org/10.1007/s10489-020-01875-1

    Article  Google Scholar 

  • Chang P-C, Huang W-H, Wu J-L, Cheng T (2013) A block mining and re-com- bination enhanced genetic algorithm for the permutation owshop scheduling problem. Int J Prod Econ 141(1):45–55

    Google Scholar 

  • Chen Y-M, Chen M-C, Chang P-C, Chen S-H (2012) Extended articial chromo- somes genetic algorithm for permutation owshop scheduling problems. Comput Ind Eng 62(2):536–545

    Google Scholar 

  • Dong X, Huang H, Chen P (2008) An improved NEH-based heuristic for the permutation owshop problem. Comput Oper Res 35(12):3962–3968

    MATH  Google Scholar 

  • Dong L, Yang Y, Sun S (2019) QCs scheduling scheme of genetic algorithm (GA) and improved firefly algorithm (FA). Cluster Comput 22:4331–4348. https://doi.org/10.1007/s10586-018-1873-0

    Article  Google Scholar 

  • Dudek Richard A, Foy TO (1964) Development of M-stage decision rule for scheduling N jobs through m machines. Oper Res 12(3):471–497. https://doi.org/10.1287/opre.12.3.471

    Article  MATH  Google Scholar 

  • Durkota K (2011) Implementation of a discrete firefly algorithm for the QAP problem within the sage framework. BSc thesis. Czech Technical University

  • Ekşioğlu B, Ekşioğlu SD, Jain P (2008) A tabu search algorithm for the owshop scheduling problem with changing neighborhoods. Comput Ind Eng 54(1):1–11

    Google Scholar 

  • Eliana M, González-Neiraa B, Jairo R, Montoya T, David B (2017) Flow-shop scheduling problem under uncertainties: review and trends. Int J Ind Eng Comput 8:399–426. https://doi.org/10.5267/j.ijiec.2017.2.001

    Article  Google Scholar 

  • Fan B, Yang W, Zhang Z (2019) Solving the two-stage hybrid flow shop scheduling problem based on mutant firefly algorithm. J Ambient Intell Human Comput 10:979–990. https://doi.org/10.1007/s12652-018-0903-3

    Article  Google Scholar 

  • FarahmandRad S, Ruiz R, Boroojerdian N (2009) New high performing heuristics for minimizing makespan in permutation owshops. Omega 37(2):331–345

    Google Scholar 

  • Fernandez-Viagas V, Framinan JM (2014) On insertion tie-breaking rules in heuris- tics for the permutation owshop scheduling problem. Comput Oper Res 45:60–67

    MathSciNet  MATH  Google Scholar 

  • Fernandez-Viagas V, Framinan JM (2014) On insertion tie-breaking rules in heuristics for the permutation owshop scheduling problem. Comput Oper Res 45:60–67

    MathSciNet  MATH  Google Scholar 

  • Gandomi AH, Yang X-S, Alavi AH (2011) Mixed variable structural optimization using firefly algorithm computers structures. Comput Struct 89(23–24):2325–2336. https://doi.org/10.1016/j.compstruc.2011.08.002

    Article  Google Scholar 

  • Grabowski J, Wodecki M (2004) A very fast tabu search algorithm for the permu- tation ow shop problem with makespan criterion. Comput Oper Res 31(11):1891–1909

    MathSciNet  MATH  Google Scholar 

  • Gupta JN (1971) A functional heuristic algorithm for the flowshop scheduling problem. J Oper Res Soc 22(1):39–47

    MATH  Google Scholar 

  • Haq AN, Saravanan M, Vivekraj AR, Prasad T (2007) A scatter search approach for general owshop scheduling problem. Int J Adv Manuf Technol 31(7–8):731–736

    Google Scholar 

  • Honig U (2010) A firefly algorithm-based approach for scheduling task graphs in homogeneous systems. Proc IASTED Int Conf 724(33):256–263

    Google Scholar 

  • Hsieh YC, You PS, Liou CD (2009) A note of using effective immune based approach for the ow shop scheduling with buffers. Appl Math Comput 215:1984–1989

    MathSciNet  MATH  Google Scholar 

  • Huang KL, Liao CJ (2006) Ant colony optimization combined with tabu search for the job shop scheduling problem. Comput Oper Res 35(4):1030–1046

    MATH  Google Scholar 

  • Hui L, Xiaoteng W, Zongming F, Meikang Q (2014) The effects of using chaotic map on improving the performance of multiobjective evolutionary algorithms. Math Probl Eng. https://doi.org/10.1155/2014/924652

    Article  MathSciNet  MATH  Google Scholar 

  • Hui W, Wenjun W, Hui S, Zhihua C, Shahryar R, Sanyou Z (2017) A new cuckoo search algorithm with hybrid strategies for ow shop scheduling problems. Soft Comput 21:4297–4307. https://doi.org/10.1007/s00500-016-2062-9

    Article  Google Scholar 

  • İbrahim BA (2018) A hybrid firefly and particle swarm optimization algorithm for computationally expensive numerical problems. Appl Soft Comput 66:1568–4946. https://doi.org/10.1016/j.asoc.2018.02.025

    Article  Google Scholar 

  • Johnson SM (1954) Optimal two and three stage production schedules with setup time included. Naval Research Logistics Quarterly, pp 61–68

  • Kalczynski PJ, Kamburowski J (2009) An empirical analysis of the optimality rate of ow shop heuristics. Eur J Oper Res 198(1):93–101

    MATH  Google Scholar 

  • Kashikolaei SMG, Hosseinabadi AAR, Saemi B, Shareh MB et al (2020) An enhancement of task scheduling in cloud computing based on imperialist competitive algorithm and frefy algorithm. J Supercomput 76:6302–6329. https://doi.org/10.1007/s11227-019-02816-7

    Article  Google Scholar 

  • Kaya S, Çelik A, Karaçizmeli İH, Aydilek İB, Gümüşçü A, Tenekeci ME (2019) Mathematical model of flow shop scheduling problems and solution with metaheuristic methods. In: International Conference On Data Science, Machinelearning And Statistics—2019 (Dms-2019)

  • Kaya S, Karaçizmeli İH, Aydilek İB, Tenekeci ME, Gümüşçü A (2019) The effects of initial populations in the solution of flow shop scheduling problems by hybrid firefly and particle swarm optimization algorithms. Pamukkale Univ J Eng Sci. https://doi.org/10.5505/pajes.2019.94763

  • Khadwilard A, Chansombat S, Thepphakorn T, Chainate W, Pongcharoen P (2012) Application of firefly algorithm and its parameter setting for job shop scheduling. J Ind Technol 8(1):49–58

    Google Scholar 

  • Kumar V, Kumar DA (2020) Systematic review on firefly algorithm: past, present, and future. Arch Comput Methods Eng. https://doi.org/10.1007/s11831-020-09498-y

    Article  Google Scholar 

  • Kwiecień J, Filipowicz B (2012) Firefly algorithm in optimization of queueing systems. Bull Polish Acad Sci Tech Sci 60(2):363–368

    Google Scholar 

  • Lee C-Y, Cheng TCE, Lin BMT (1993) Minimizing the makespan in the 3-machine assembly-type flowshop scheduling problem. Manage Sci 39(5):616–625. https://doi.org/10.1287/mnsc.39.5.616

    Article  MATH  Google Scholar 

  • Li X, Yin M (2012) A discrete articial bee colony algorithm with composite mutation strategies for permutation ow shop scheduling problem. Scientia Iranica 19(6):1921–1935

    Google Scholar 

  • Li X, Yin M (2013) A hybrid cuckoo search via Lévy ights for the permutation ow shop scheduling problem. Int J Prod Res 51(16):4732–4754

    Google Scholar 

  • Li X, Yin M (2013) An opposition-based differential evolution algorithm for permutation ow shop scheduling based on diversity measure. Adv Eng Softw 55:10–31

    Google Scholar 

  • Lian Z, Gu X, Jiao B (2008) A novel particle swarm optimization algorithm for permutation flow-shop scheduling to minimize makespan. Chaos Solitons Fractals 35(5):851–861

    MATH  Google Scholar 

  • Lin Q, Gao L, Li X, Zhang C (2015b) A hybrid backtracking search algorithm for permutation ow-shop scheduling problem. Comput Ind Eng 85:437–446

    Google Scholar 

  • Liu Y-F, Liu S-Y (2013) A hybrid discrete articial bee colony algorithm for per- mutation owshop scheduling problem. Appl Soft Comput 13(3):1459–1463

    Google Scholar 

  • Liu B, Wang L, Jin Y-H (2007) An effective pso-based memetic algorithm for ow shop scheduling. IEEE Trans Sys Man Cybern Part B Cybern 37(1):18–27

    Google Scholar 

  • Liu B, Wang L, Jin YH (2008) An effective hybrid PSO-based algorithm for ow shop scheduling with limited buffers. Comput Oper Res 35:2791–2806

    MATH  Google Scholar 

  • Liu Y, Yin M, Gu W (2014) An effective differential evolution algorithm for permutation ow shop scheduling problem. Appl Math Comput 248:143–159

    MATH  Google Scholar 

  • Łukasik SŻak S (2009) Firefly algorithm for continuous constrained optimization tasks. In: Nguyen NT, Kowalczyk R, Chen SM (eds) Computational collective intelligence. Semantic Web, Social Networks and Multiagent Systems. ICCCI 2009. Lecture Notes in Computer Science, vol 5796. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04441-08

  • Marichelvam MK (2012) An improved hybrid cuckoo search (ihcs) metaheuristics algorithm for permutation ow shop scheduling problems. Int J Bio-Inspired Comput 4(4):200–205

    Google Scholar 

  • Miller-Todd J, Steinhöfel K, Veenstra P (2018) Firefly-inspired algorithm for job shop scheduling. In: Böckenhauer HJ., Komm D., Unger W. (eds) Adventures Between Lower Bounds and Higher Altitudes. Lecture Notes in Computer Science, vol 11011. Springer, Cham. https://doi.org/10.1007/978-3-319-98355-424

  • Nagano MS, Ruiz R, Lorena LAN (2008) A constructive genetic algorithm for permutation owshop scheduling. Comput Ind Eng 55(1):195–207

    Google Scholar 

  • Nagaraj G, Arunachalam M, Vinayagar K, Paramasamy S (2020) Enhancing performance of cell formation problem using hybrid efficient swarm optimization. Soft Comput 24:16679–16690. https://doi.org/10.1007/s00500-020-05059-4

    Article  Google Scholar 

  • Nawaz M, Enscore E, Ham I (1983) A heuristic algorithm for the m-machine, n-job owshop sequencing problem. OMEGA Int J Manage Sci 11(1):91–95

    Google Scholar 

  • Nowicki E, Smutnicki C (2006) Some aspects of scatter search in the ow-shop problem. Eur J Oper Res 169(2):654–666

    MATH  Google Scholar 

  • NowickiE Smutnicki C (1996) A fast tabu search algorithm for the permutation owshop problem. Eur J Oper Res 91:160–175

    Google Scholar 

  • Onwubolu G, Davendra D (2006) Scheduling ow shops using differential evolution algorithm. Eur J Oper Res 171(2):674–692

    MATH  Google Scholar 

  • Osman I, Potts C (1989) Simulated annealing for permutation ow shop scheduling. Omega 17:551–557

    Google Scholar 

  • Page ES (1961) An approach to the scheduling of jobs on machines. J Royal Stat Soc Ser B Methodol 23(2):484–492

    MathSciNet  Google Scholar 

  • Palmer D (1965) Sequencing jobs through a multi-stage process in the minimum total time—a quick method of obtaining a near optimum. Oper Res Quarterly 16(1):101–107

    Google Scholar 

  • Pan QK, Tasgetiren MF, Liang YC (2008) A discrete differential evolution algorithm for the permutation ow shop scheduling problem. Comput Ind Eng 55:795–816

    Google Scholar 

  • Pan QK, Wang L, Gao L, Li WD (2011) An effective hybrid discrete differential evolution algorithm for the ow shop scheduling with intermediate buffers. Inf Sci 181:668–685

    Google Scholar 

  • Pan Q-K, Wang L, Li J-Q, Duan J-H (2014) A novel discrete articial bee colony algorithm for the hybrid owshop scheduling problem with makespan minimisation. Omega 45:42–56

    Google Scholar 

  • Pinedo ML (2012) Scheduling: Theory, algorithms and systems, 2nd edn. Springer, New York. https://doi.org/10.1007/978-1-4614-2361-4

    Book  MATH  Google Scholar 

  • Rajendran C, Ziegler H (2004) Ant-colony algorithms for permutation owshop scheduling to minimize makespan/total owtime of jobs. Eur J Oper Res 155(2):426–438

    MATH  Google Scholar 

  • Reeves CR (1995) A genetic algorithm for owshop sequencing. Comput Oper Res 22:5–13

    MATH  Google Scholar 

  • Rossi FL, Nagano MS, Neto RFT (2016) Evaluation of high performance con- structive heuristics for the ow shop with makespan minimization. Int J Adv Manuf Technol, pp 1–12

  • Rubén R, Quan-Ke P, Bahman N (2019) Iterated Greedy methods for the distributed permutation flowshop scheduling problem. Omega 83:213–222

    Google Scholar 

  • Ruiz R, Stützle T (2007) A simple and effective iterated greedy algorithm for the permutation owshop scheduling problem. Eur J Oper Res 177(3):2033–2049

    MATH  Google Scholar 

  • Ruiz R, Maroto C, Alcaraz J (2006) Two new robust genetic algorithms for the owshop scheduling problem. Omega 34(5):461–476

    Google Scholar 

  • Sadjadi SJ, Bouquard JL, Ziaee M (2008) An ant colony algorithm for the owshop scheduling problem. J Appl Sci 8:3938–44

    Google Scholar 

  • Sana A, Javad R (2015) Minimizing makespan for ow shop scheduling problem with intermediate buffers by using hybrid approach of articial immune system. Appl Soft Comput 28:44–56. https://doi.org/10.1016/j.asoc.2014.11.022

    Article  Google Scholar 

  • Saremi S, Mirjalili S, Lewis A (2014) Biogeography-based optimisation with chaos. Neural Comput Appl. https://doi.org/10.1007/s00521-014-1597-x

    Article  Google Scholar 

  • Shao W, Pi D (2016) A self-guided differential evolution with neighborhood search for permutation ow shop scheduling. Expert Syst Appl 51:161–176

    Google Scholar 

  • Suyanto Jati GK (2011) Evolutionary discrete firefly algorithm for travelling salesman problem. In: Bouchachia A. (eds) Adaptive and intelligent systems. ICAIS 2011. Lecture Notes in Computer Science, 6943:393–403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23857-438

  • Taillard E (1993) Benchmarks for basic scheduling problems. Eur J Oper Res 64(2):278–285

    MathSciNet  MATH  Google Scholar 

  • Tasgetiren MF, Liang Y-C, Sevkli M, Gencyilmaz G (2006) Particle swarm optimization and differential evolution for the single machine total weighted tardiness problem. Int J Prod Res 44(22):4737–4754

    MATH  Google Scholar 

  • Tasgetiren MF, Liang Y-C, Sevkli M, Gencyilmaz G (2007) A particle swarm optimization algorithm for makespan and total owtime minimization in the permutation owshop sequencing problem. Eur J Oper Res 177(3):1930–1947

    MATH  Google Scholar 

  • Vallada E, Ruiz R (2009) Cooperative metaheuristics for the permutation owshop scheduling problem. Eur J Oper Res 193(2):365–376

    MATH  Google Scholar 

  • Vasiljevic D, Danilovic M (2015) Handling ties in heuristics for the permutation ow shop scheduling problem. J Manuf Syst 35:1–9

    Google Scholar 

  • Wang L, Zhang L, Zheng DZ (2006) An effective hybrid genetic algorithm for ow shop scheduling with limited buffers. Comput Oper Res 33:2960–2971

    MathSciNet  MATH  Google Scholar 

  • Xin GJ, Hai Chen, Y (2009) A particle swarm optimizer with multi-stagelinearly-decreasing inertia weight. In: Proc. 2009 Int. Jt. Conf. Comput. Sci.Optim., CSO 2009, pp 505–508. https://doi.org/10.1109/CSO.2009.420

  • Yang X-S, Deb S (2009) Cuckoo search via Lévy ights. In: World congress on nature and biologically inspired computing IEEE, pp 210–214

  • Yang XS (2008) Nature-inspired metaheuristic algorithms. Luniver Press, ISBN 978-1-905986-10-1

  • Ying K-C, Lin S-W (2007) Multi-heuristic desirability ant colony system heuristic for non-permutation owshop scheduling problems. Int J Adv Manuf Technol 33:739–802

    Google Scholar 

  • Yousif A, Abdullah AH, Nor SM, Abdelaziz AA (2011) Scheduling jobs on grid computing using firefly algorithm. J Theor Appl Inf Technol 33(2):155–164

    Google Scholar 

  • Zhang CY, Li P, Rao Y, Guan Z (2008) A very fast TS/SA algorithm for the job shop scheduling problem. Comput Oper Res 35(1):282–294

    MathSciNet  MATH  Google Scholar 

  • Zhang C, Ning J, Ouyang D (2010a) A hybrid alternate two phases particle swarm optimization algorithm for ow shop scheduling problem. Comput Ind Eng 58(1):1–11

    Google Scholar 

  • Zhang J, Zhang C, Liang S (2010b) The circular discrete particle swarm optimization algorithm for ow shop scheduling problem. Expert Syst Appl 37(8):5827–5834

    Google Scholar 

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Acknowledgements

This study was funded by The Scientific and Technological Research Council of Turkey (TUBITAK) (Grant Number 118E355) named as “Solving the flow shop scheduling problem with new chaotic metaheuristic optimization algorithms”. The numerical calculations reported in this paper were partially performed at Harran University High Performance Computing Center (Harran HPC resources).

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  1. Department of Industrial Engineering, Harran University, Sanliurfa, Turkey

    Serkan Kaya & İzzettin Hakan Karaçizmeli

  2. Department of Electrical and Electronics Engineering, Harran University, Sanliurfa, Turkey

    Abdülkadir Gümüşçü

  3. Department of Computer Engineering, Harran University, Sanliurfa, Turkey

    İbrahim Berkan Aydilek & Mehmet Emin Tenekeci

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  1. Serkan Kaya
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  2. Abdülkadir Gümüşçü
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Correspondence to Serkan Kaya.

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Kaya, S., Gümüşçü, A., Aydilek, İ.B. et al. Solution for flow shop scheduling problems using chaotic hybrid firefly and particle swarm optimization algorithm with improved local search. Soft Comput 25, 7143–7154 (2021). https://doi.org/10.1007/s00500-021-05673-w

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