# A hybrid NSGA-II and VNS for solving a bi-objective no-wait flexible flowshop scheduling problem

## Abstract

We address the no-wait k-stage flexible flowshop scheduling problem where there are *m* identical machines at each stage. The objectives are to schedule the available *n* jobs so that makespan and mean tardiness of *n* jobs are minimized. Sequence-dependent setup times are treated in this problem as one of the prominent practical assumptions. This problem is NP-hard, and therefore we present a new multiobjective approach for solving the mentioned problem. The proposed meta-heuristic is evaluated based on randomly generated data in comparison with two well-known multiobjective algorithm including NSGA-II and SPEA-II. Due to sensitivity of our proposed algorithm to parameter values, a new approach for tackling of this issue was designed. Our proposed method includes Taguchi method (TM) and multiobjective decision making (MODM). We have chosen six measures into two groups. Qualitative metrics including number of Pareto solutions (NPS), diversity metric (DM) as well as the spread of non-dominance solution (SNS) and quantitative metrics including the rate of achievement to two objectives simultaneously (RAS), mean ideal distance (MID) and quality metric (QM) to evaluate the performance of our proposed algorithms. Computational experiments and comparisons show that the proposed NSGA-II + VNS algorithm generates better or competitive results than the existing NSGA-II and SPEA-II for the no-wait flexible flow shop scheduling problem with sequence-dependent setup times to simultaneous minimizing the makespan and mean tardiness criterion.

## Keywords

NSGA-II VNS Hybrid meta-heuristic No-wait flexible flowshop Taguchi method Sequence-dependent setup time## Preview

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## References

- 1.Ahmadizar F, Farahani MH (2012) A novel hybrid genetic algorithm for the open shop scheduling problem. Int J Adv Manuf Technol 62(5–8):775–787CrossRefGoogle Scholar
- 2.Kayvanfar V, Zandieh M (2012) The economic lot scheduling problem with deteriorating items and shortage: an imperialist competitive algorithm. Int J Adv Manuf Technol 62(5–8):759–773CrossRefGoogle Scholar
- 3.Rudek A, Rudek R (2012) On flowshop scheduling problems with the aging effect and resource allocation. Int J Adv Manuf Technol 62(1–4):135–145CrossRefGoogle Scholar
- 4.Huang B, Shi XX, Xu N (2012) Scheduling FMS with alternative routings using Petri nets and near admissible heuristic search. Int J Adv Manuf Technol 63(9–12):1131–1136CrossRefGoogle Scholar
- 5.Liao W, Wang Y, Pan E (2012) Single-machine-based predictive maintenance model considering intelligent machinery prognostics. Int J Adv Manuf Technol 63(1–4):51–63CrossRefGoogle Scholar
- 6.Golmakani HR, Namazi A (2012) An artificial immune algorithm for multiple-route job shop scheduling problem. Int J Adv Manuf Technol 63(1–4):77–86CrossRefGoogle Scholar
- 7.Gokhale R, Mathirajan M (2013) Minimizing total weighted tardiness on heterogeneous batch processors with incompatible job families. Int J Adv Manuf Technol 1–16Google Scholar
- 8.Mirabedini SN, Iranmanesh H (2013) A scheduling model for serial jobs on parallel machines with different preventive maintenance (PM). Int J Adv Manuf Technol 1–11Google Scholar
- 9.Gohareh MM, Karimi B, Khademian M (2014) A simulation-optimization approach for open-shop scheduling problem with random process times. Int J Adv Manuf Technol 70(5–8):821–831CrossRefGoogle Scholar
- 10.Babaei M, Mohammadi M, Ghomi SF (2014) A genetic algorithm for the simultaneous lot sizing and scheduling problem in capacitated flow shop with complex setups and backlogging. Int J Adv Manuf Technol 70(1–4):125–134CrossRefGoogle Scholar
- 11.Su S, Yu H, Wu Z, Tian W (2014) A distributed coevolutionary algorithm for multiobjective hybrid flowshop scheduling problems. Int J Adv Manuf Technol 1–18Google Scholar
- 12.Nejati M, Mahdavi I, Hassanzadeh R, Mahdavi-Amiri N, Mojarad M (2014) Multi-job lot streaming to minimize the weighted completion time in a hybrid flow shop scheduling problem with work shift constraint. Int J Adv Manuf Technol 70(1–4):501–514CrossRefGoogle Scholar
- 13.Gholami O, Sotskov YN (2014) A fast heuristic algorithm for solving parallel-machine job-shop scheduling problems. Int J Adv Manuf Technol 70(1–4):531–546CrossRefGoogle Scholar
- 14.Lee JH, Yu JM, Lee DH (2013) A tabu search algorithm for unrelated parallel machine scheduling with sequence-and machine-dependent setups: minimizing total tardiness. Int J Adv Manuf Technol 69(9–12):2081–2089CrossRefGoogle Scholar
- 15.Navaei J, Ghomi SF, Jolai F, Shiraqai ME, Hidaji H (2013) Two-stage flow-shop scheduling problem with non-identical second stage assembly machines. Int J Adv Manuf Technol 69(9–12):2215–2226CrossRefGoogle Scholar
- 16.Dou J, Li J, Su C (2013) A novel feasible task sequence-oriented discrete particle swarm algorithm for simple assembly line balancing problem of type 1. Int J Adv Manuf Technol 69(9–12):2445–2457CrossRefGoogle Scholar
- 17.Costa A, Cappadonna FA, Fichera S (2013) A hybrid genetic algorithm for job sequencing and worker allocation in parallel unrelated machines with sequence-dependent setup times. Int J Adv Manuf Technol 69(9–12):2799–2817CrossRefGoogle Scholar
- 18.Kalayci CB, Gupta SM (2013) A particle swarm optimization algorithm with neighborhood-based mutation for sequence-dependent disassembly line balancing problem. Int J Adv Manuf Technol 69(1–4):197–209CrossRefGoogle Scholar
- 19.Kayvanfar V, Mahdavi I, Komaki GM (2013) A drastic hybrid heuristic algorithm to approach to JIT policy considering controllable processing times. Int J Adv Manuf Technol 69(1–4):257–267CrossRefGoogle Scholar
- 20.Raaymakers WHM, Hoogeveen JA (2000) Scheduling multipurpose batch process industries with no-wait restrictions by simulated annealing. Eur J Oper Res 126(1):131–151zbMATHCrossRefGoogle Scholar
- 21.Hall NG, Sriskandarajah C (1996) A survey of machine scheduling problems with blocking and no-wait in process. Oper Res 44(3):510–525MathSciNetzbMATHCrossRefGoogle Scholar
- 22.Rajendran C (1994) A no-wait flowshop scheduling heuristic to minimize makespan. J Oper Res Soc 45(4):472–478zbMATHCrossRefGoogle Scholar
- 23.Nagano MS, Da Silva AA, Lorena LAN (2012) A new evolutionary clustering search for a no-wait flow shop problem with set-up times. Eng Appl Artif Intell 25(6):1114–1120CrossRefGoogle Scholar
- 24.Araújo DC, Nagano MS (2010) An effective heuristic for the no-wait flowshop with sequence-dependent setup times problem. In: Advances in artificial intelligence. Springer, Berlin, pp 187–196CrossRefGoogle Scholar
- 25.Ara DC, Seido Nagano M (2011) A new effective heuristic method for the no-wait flowshop with sequence-dependent setup times problem. Int J Ind Eng Comput 2(1):155–166Google Scholar
- 26.Framinan JM, Nagano MS (2008) Evaluating the performance for makespan minimisation in no-wait flowshop sequencing. J Mater Process Technol 197(1):1–9CrossRefGoogle Scholar
- 27.Ribeiro Filho G, Nagano MS, Lorena LAN (2007) Hybrid evolutionary algorithm for flowtime minimisation in no-wait flowshop scheduling. In: MICAI 2007: advances in artificial Intelligence. Springer, Berlin, pp 1099–1109Google Scholar
- 28.Ruiz R, Allahverdi A (2009) New heuristics for no-wait flow shops with a linear combination of makespan and maximum lateness. Int J Prod Res 47(20):5717–5738zbMATHCrossRefGoogle Scholar
- 29.Jolai F, Sheikh S, Rabbani M, Karimi B (2009) A genetic algorithm for solving no-wait flexible flow lines with due window and job rejection. Int J Adv Manuf Technol 42(5–6):523–532CrossRefGoogle Scholar
- 30.Moradinasab N, Shafaei R, Rabiee M, Ramezani P (2013) No-wait two stage hybrid flow shop scheduling with genetic and adaptive imperialist competitive algorithms. J Exp Theor Artif Intell 25(2):207–225CrossRefGoogle Scholar
- 31.Rabiee M, Zandieh M, Jafarian A (2012) Scheduling of a no-wait two-machine flow shop with sequence-dependent setup times and probable rework using robust meta-heuristics. Int J Prod Res 50(24):7428–7446CrossRefGoogle Scholar
- 32.Jolai F, Rabiee M, Asefi H (2012) A novel hybrid meta-heuristic algorithm for a no-wait flexible flow shop scheduling problem with sequence dependent setup times. Int J Prod Res 50(24):7447–7466CrossRefGoogle Scholar
- 33.Akrout H, Jarboui B, Rebai A, Siarry P (2013) New Greedy Randomized Adaptive Search Procedure based on differential evolution algorithm for solving no-wait flowshop scheduling problem. In Advanced Logistics and Transport (ICALT), 2013 International Conference on (pp. 327–334). IEEEGoogle Scholar
- 34.Naderi B, Khalili M, Khamseh AA (2014) Mathematical models and a hunting search algorithm for the no-wait flowshop scheduling with parallel machines. Int J Prod Res (ahead-of-print) 1–15Google Scholar
- 35.Pang KW (2013) A genetic algorithm based heuristic for two machine no-wait flowshop scheduling problems with class setup times that minimizes maximum lateness. Int J Prod Econ 141(1):127–136CrossRefGoogle Scholar
- 36.Liu G, Song S, Wu C (2013) Some heuristics for no-wait flowshops with total tardiness criterion. Comput Oper Res 40(2):521–525MathSciNetCrossRefGoogle Scholar
- 37.Davendra D, Zelinka I, Bialic-Davendra M, Senkerik R, Jasek R (2013) Discrete self-organising migrating algorithm for flow-shop scheduling with no-wait makespan. Math Comput Model 57(1):100–110MathSciNetCrossRefGoogle Scholar
- 38.Nagano MS, da Silva AA, Nogueira Lorena LA (2014) An evolutionary clustering search for the no-wait flow shop problem with sequence dependent setup times. Expert Syst Appl 41(8):3628–3633CrossRefGoogle Scholar
- 39.Jin Z, Yang Z, Ito T (2006) Metaheuristic algorithms for the multistage hybrid flowshop scheduling problem. Int J Prod Econ 100(2):322–334CrossRefGoogle Scholar
- 40.Ruiz R, Maroto C (2006) A genetic algorithm for hybrid flowshops with sequence dependent setup times and machine eligibility. Eur J Oper Res 169(3):781–800MathSciNetzbMATHCrossRefGoogle Scholar
- 41.Zandieh M, Fatemi Ghomi SMT, Moattar Husseini SM (2006) An immune algorithm approach to hybrid flow shops scheduling with sequence-dependent setup times. Appl Math Comput 180(1):111–127MathSciNetzbMATHCrossRefGoogle Scholar
- 42.Janiak A, Kozan E, Lichtenstein M, Oğuz C (2007) Metaheuristic approaches to the hybrid flow shop scheduling problem with a cost-related criterion. Int J Prod Econ 105(2):407–424CrossRefGoogle Scholar
- 43.Haouari M, Hidri L (2008) On the hybrid flowshop scheduling problem. Int J Prod Econ 113(1):495–497CrossRefGoogle Scholar
- 44.Pargar F, Zandieh M (2012) Bi-criteria SDST hybrid flow shop scheduling with learning effect of setup times: water flow-like algorithm approach. Int J Prod Res 50(10):2609–2623CrossRefGoogle Scholar
- 45.Shiau DF, Huang YM (2012) A hybrid two-phase encoding particle swarm optimization for total weighted completion time minimization in proportionate flexible flow shop scheduling. Int J Adv Manuf Technol 58(1–4):339–357CrossRefGoogle Scholar
- 46.Mohammadi M, Jafari N (2011) A new mathematical model for integrating lot sizing, loading, and scheduling decisions in flexible flow shops. Int J Adv Manuf Technol 55(5–8):709–721CrossRefGoogle Scholar
- 47.Defersha FM, Chen M (2012) Mathematical model and parallel genetic algorithm for hybrid flexible flowshop lot streaming problem. Int J Adv Manuf Technol 62(1–4):249–265CrossRefGoogle Scholar
- 48.Singh MR, Mahapatra SS (2012) A swarm optimization approach for flexible flow shop scheduling with multiprocessor tasks. Int J Adv Manuf Technol 62(1–4):267–277CrossRefGoogle Scholar
- 49.Reddi SS, Ramamoorthy CV (1972) On the flow-shop sequencing problem with no wait in process. Oper Res Q 23(3):323–331zbMATHCrossRefGoogle Scholar
- 50.Aldowaisan T, Allahverdi A (1998) Total flow time in no-wait flow shops with separated setup times. Comput Oper Res 25(9):757–765zbMATHCrossRefGoogle Scholar
- 51.Allahverdi A, Aldowaisan T (2000) No-wait and separate setup three-machine flowshop with total completion time criterion. Int Trans Oper Res 7(3):245–264MathSciNetCrossRefGoogle Scholar
- 52.Shyu SJ, Lin BMT, Yin PY (2004) Application of ant colony optimization for no-wait flowshop scheduling problem to minimize the total completion time. Comput Ind Eng 47(2):181–193CrossRefGoogle Scholar
- 53.Brown SI, McGarvey RG, Ventura JA (2004) Total flowtime and makespan for a no-wait m-machine flowshop with set-up times separated. J Oper Res Soc 55(6):614–621zbMATHCrossRefGoogle Scholar
- 54.Tseng LY, Lin YT (2010) A hybrid genetic algorithm for no-wait flowshop scheduling problem. Int J Prod Econ 128(1):144–152CrossRefGoogle Scholar
- 55.Huang RH, Yang CL, Huang YC (2009) No-wait two-stage multiprocessor flow shop scheduling with unit setup. Int J Adv Manuf Technol 44(9–10):921–927CrossRefGoogle Scholar
- 56.Wang S, Liu M (2013) A genetic algorithm for two-stage no-wait hybrid flow shop scheduling problem. Comput Oper Res 40(4):1064–1075MathSciNetCrossRefGoogle Scholar
- 57.Rabiee M, Rad RS, Mazinani M, Shafaei R (2014) An intelligent hybrid meta-heuristic for solving a case of no-wait two-stage flexible flow shop scheduling problem with unrelated parallel machines. Int J Adv Manuf Technol 1–17Google Scholar
- 58.Ramezani P, Rabiee M, Jolai F (2013) No-wait flexible flowshop with uniform parallel machines and sequence-dependent setup time: a hybrid meta-heuristic approach. J Int Manuf 1–14Google Scholar
- 59.Khalili M (2012) Multi-objective no-wait hybrid flowshop scheduling problem with transportation times. Int J Comput Sci Eng 7(2):147–154CrossRefGoogle Scholar
- 60.Khalili M (2013) A multi-objective electromagnetism algorithm for a bi-objective hybrid no-wait flowshop scheduling problem. Int J Adv Manuf Technol 1–11Google Scholar
- 61.Allahverdi A, Aldowaisan T (2004) No-wait flowshops with bicriteria of makespan and maximum lateness. Eur J Oper Res 152(1):132–147MathSciNetzbMATHCrossRefGoogle Scholar
- 62.Tavakkoli-Moghaddam R, Rahimi-Vahed A, Mirzaei AH (2007) A hybrid multi-objective immune algorithm for a flow shop scheduling problem with bi-objectives: weighted mean completion time and weighted mean tardiness. Inf Sci 177(22):5072–5090MathSciNetzbMATHCrossRefGoogle Scholar
- 63.Rahimi-Vahed AR, Javadi B, Rabbani M, Tavakkoli-Moghaddam R (2008) A multi-objective scatter search for a bi-criteria no-wait flow shop scheduling problem. Eng Optim 40(4):331–346MathSciNetCrossRefGoogle Scholar
- 64.Pan QK, Wang L, Qian B (2009) A novel differential evolution algorithm for bi-criteria no-wait flow shop scheduling problems. Comput Oper Res 36(8):2498–2511MathSciNetzbMATHCrossRefGoogle Scholar
- 65.Qian B, Wang L, Huang DX, Wang WL, Wang X (2009) An effective hybrid DE-based algorithm for multi-objective flow shop scheduling with limited buffers. Comput Oper Res 36(1):209–233MathSciNetzbMATHCrossRefGoogle Scholar
- 66.Naderi B, Aminnayeri M, Piri M, Ha'iri Yazdi MH (2012) Multi-objective no-wait flowshop scheduling problems: models and algorithms. Int J Prod Res 50(10):2592–2608CrossRefGoogle Scholar
- 67.Sriskandarajah C, Ladet P (1986) Some no-wait shops scheduling problems: complexity aspect. Eur J Oper Res 24(3):424–438MathSciNetCrossRefGoogle Scholar
- 68.Ziztler E, Laumanns M, Thiele L (2002) Spea2: improving the strength pareto evolutionary algorithm for multiobjective optimization. Evol Methods Des Optim Control 95–100Google Scholar
- 69.Deb K, Pratap A, Agarwal S, Meyarivan TAMT (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. Evol Comput IEEE Trans 6(2):182–197CrossRefGoogle Scholar
- 70.Hansen P, Mladenović N (2001) Variable neighborhood search: principles and applications. Eur J Oper Res 130(3):449–467zbMATHCrossRefGoogle Scholar
- 71.Adeli H, Cheng NT (1993) Integrated genetic algorithm for optimization of space structures. J Aerosp Eng 6(4):315–328CrossRefGoogle Scholar
- 72.Beasley JE, Chu PC (1996) A genetic algorithm for the set covering problem. Eur J Oper Res 94(2):392–404zbMATHCrossRefGoogle Scholar
- 73.Fleurent C, Ferland JA (1996) Genetic and hybrid algorithms for graph coloring. Ann Oper Res 63(3):437–461zbMATHCrossRefGoogle Scholar
- 74.Baker BM, Ayechew MA (2003) A genetic algorithm for the vehicle routing problem. Comput Oper Res 30(5):787–800MathSciNetzbMATHCrossRefGoogle Scholar
- 75.Herrera F, Lozano M, Sánchez AM (2003) A taxonomy for the crossover operator for real coded genetic algorithms: an experimental study. Int J Intell Syst 18(3):309–338zbMATHCrossRefGoogle Scholar
- 76.Kaya M (2011) The effects of two new crossover operators on genetic algorithm performance. Appl Soft Comput 11(1):881–890CrossRefGoogle Scholar
- 77.Bakırlı G, Birant D, Kut A (2011) An incremental genetic algorithm for classification and sensitivity analysis of its parameters. Expert Syst Appl 38(3):2609–2620CrossRefGoogle Scholar
- 78.Behnamian J, Fatemi Ghomi SMT, Zandieh M (2009) A multi-phase covering Pareto-optimal front method to multi-objective scheduling in a realistic hybrid flowshop using a hybrid metaheuristic. Expert Syst Appl 36(8):11057–11069CrossRefGoogle Scholar
- 79.Karimi N, Zandieh M, Karamooz HR (2010) Bi-objective group scheduling in hybrid flexible flowshop: a multi-phase approach. Expert Syst Appl 37(6):4024–4032CrossRefGoogle Scholar