Abstract
Dispatching rules are often a method of choice for solving various scheduling problems. Most often, they are designed by human experts in order to optimise a certain criterion. However, it is seldom the case that a schedule should optimise a single criterion all alone. More common is the case where several criteria need to be optimised at the same time. This paper deals with the problem of automatic design of dispatching rules (DRs) by the use of genetic programming, for many-objective scheduling problems. Four multi-objective and many-objective algorithms, including nondominated sorting genetic algorithm II, nondominated sorting genetic algorithm III, harmonic distance based multi-objective evolutionary algorithm and multi-objective evolutionary algorithm based on decomposition, have been used in order to obtain sets of Pareto optimal solutions for various many-objective scheduling problems. Through experiments it was shown that automatically generated multi-objective DRs not only achieve good performance when compared to standard DRs, but can also outperform automatically generated single objective DRs for most criteria combinations.
Similar content being viewed by others
References
A. Allahverdi, J.N.D. Gupta, T. Aldowaisan, A review of scheduling research involving setup considerations. Omega 27(2), 219–239 (1999). doi:10.1016/S0305-0483(98)00042-5
A. Allahverdi, C.T. Ng, T.C.E. Cheng, M.Y. Kovalyov, A survey of scheduling problems with setup times or costs. Eur. J. Oper. Res. 187(3), 985–1032 (2008). doi:10.1016/j.ejor.2006.06.060
S.F. Attar, M. Mohammadi, R. Tavakkoli-Moghaddam, Hybrid flexible flowshop scheduling problem with unrelated parallel machines and limited waiting times. Int. J. Adv. Manuf. Technol. 68(5–8), 1583–1599 (2013). doi:10.1007/s00170-013-4956-3
A. Baykasoğlu, L. Özbakır, Discovering task assignment rules for assembly line balancing via genetic programming. Int. J. Adv. Manuf. Technol. 76(1), 417–434 (2015)
J. Branke, C.W. Pickardt, Evolutionary search for difficult problem instances to support the design of job shop dispatching rules. Eur. J. Oper. Res. 212(1), 22–32 (2011). doi:10.1016/j.ejor.2011.01.044
J. Branke, S. Nguyen, C.W. Pickardt, M. Zhang, Automated design of production scheduling heuristics: a review. IEEE Trans. Evol. Comput. 20(1), 110–124 (2016). doi:10.1109/TEVC.2015.2429314
T.D. Braun, H.J. Siegel, N. Beck, L.L. Bölöni, M. Maheswaran, A.I. Reuther, J.P. Robertson, M.D. Theys, B. Yao, D. Hensgen, R.F. Freund, L.L. Boloni, A comparison of eleven static heuristics for mapping a class of independent tasks onto heterogeneous distributed computing systems. J. Parallel Distrib. Comput. 61(6), 810–837 (2001). doi:10.1006/jpdc.2000.1714
T.D. Braun, H.J. Siegel, N. Beck, L.L. Bölöni, M. Maheswaran, A.I. Reuther, J.P. Robertson, M.D. Theys, B. Yao, D. Hensgen et al., A comparison of eleven static heuristics for mapping a class of independent tasks onto heterogeneous distributed computing systems. J. Parallel Distrib. Comput. 61(6), 810–837 (2001)
E.K. Burke, M.R. Hyde, G. Kendall, G. Ochoa, E. Ozcan, J.R. Woodward, Exploring hyper-heuristic methodologies with genetic programming. Comput. Intell. 1, 177–201 (2009). doi:10.1007/978-3-642-01799-5_6
E.K. Burke, M. Hyde, G. Kendall, G. Ochoa, E. Ozcan, J.R. Woodward, A classification of hyper-heuristics approaches. Handb. Metaheuristics 57, 449–468 (2010). doi:10.1007/978-1-4419-1665-5_15
B. Cardoen, E. Demeulemeester, J. Beliën, Optimizing a multiple objective surgical case sequencing problem. Int. J. Prod. Econ. 119(2), 354–366 (2009)
V.H.L. Cheng, L.S. Crawford, P.K. Menon, Air traffic control using genetic search techniques, in Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No. 99CH36328), vol 1. (1999), pp. 249–254. doi:10.1109/CCA.1999.806209
A. Costa, F. Cappadonna, S. Fichera, 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), 2799–2817 (2013). doi:10.1007/s00170-013-5221-5
E. Davis, J.M. Jaffe, Algorithms for scheduling tasks on unrelated processors. J. ACM (JACM) 28(4), 721–736 (1981)
K. Deb, H. Jain, An Evolutionary many-objective optimization algorithm using reference-point based non-dominated sorting approach, part I: solving problems with box constraints. IEEE Trans. Evolut. Comput. 18(4), 577–601 (2014). doi:10.1109/TEVC.2013.2281535
K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002). doi:10.1109/4235.996017
C. Dimopoulos, A.M.S. Zalzala, A genetic programming heuristic for the one-machine total tardiness problem, in Proceedings of the 1999 Congress on Evolutionary Computation, CEC 1999, vol 3, no 1 (1999), pp. 2207–2214. doi:10.1109/CEC.1999.785549
C. Dimopoulos, A. Zalzala, Investigating the use of genetic programming for a classic one-machine scheduling problem. Adv. Eng. Softw. 32(6), 489–498 (2001)
M. Đurasević, D. Jakobović, Comparison of solution representations for scheduling in the unrelated machines environment
M. Đurasević, D. Jakobović, K. Knežević, Adaptive scheduling on unrelated machines with genetic programming. Appl. Soft Comput. 48, 419–430 (2016). doi:10.1016/j.asoc.2016.07.025
C. Ferreira, Gene expression programming: a new adaptive algorithm for solving problems. Complex Syst. 13(2), 87–129 (2001)
L. Fowler, M. Pfund, L. Yu, J.W. Fowler, W.M. Carlyle, Development of a robust scheduling rule for a printed wiring board drilling operation with multiple scheduling objectives and fixed order release/pickup times
R.H. Gomez, C.A.C. Coello, MOMBI: A new metaheuristic for many-objective optimization based on the R2 indicator, in 2013 IEEE Congress on Evolutionary Computation, CEC 2013, vol 1 (2013), pp. 2488–2495. doi:10.1109/CEC.2013.6557868
J.V. Hansen, Genetic search methods in air traffic control. Comput. Oper. Res. 31(3), 445–459 (2004). doi:10.1016/S0305-0548(02)00228-9
E. Hart, P. Ross, D. Corne, Evolutionary scheduling: a review. Genet. Program. Evolvable Mach. 6(2), 191–220 (2005). doi:10.1007/s10710-005-7580-7
D. Hensgen, R.F. Freund, Dynamic mapping of a class of independent tasks onto heterogeneous computing systems. J. Distrib. Comput. 59(2), 107–131 (1999)
R. Hern, C.C. Coello, MOMBI : a new metaheuristic for many-objective optimization based on the R2 indicator. Science 1, 2488–2495 (2013). doi:10.1109/CEC.2013.6557868
T. Hildebrandt, J. Heger, B. Scholz-Reiter, Towards improved dispatching rules for complex shop floor scenarios: a genetic programming approach, in GECCO ’10: Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation (2010), pp. 257–264. doi:10.1145/1830483.1830530
R. Hunt, M. Johnston, R. Hunt, M. Johnston, Evolving “Less-myopic” scheduling rules for dynamic job shop scheduling with genetic programming, in GECCO ’14: Proceedings of the 2014 Conference on Genetic and Evolutionary Computation (2014), pp. 927–934. doi:10.1145/2576768.2598224
R. Hunt, M. Johnston, M. Zhang, Evolving machine-specific dispatching rules for a two-machine job shop using genetic programming, in 2014 IEEE Congress on Evolutionary Computation (CEC) (2014), pp. 618–625. doi:10.1109/CEC.2014.6900655
H. Ishibuchi, R. Imada, Y. Setoguchi, Y. Nojima, Performance comparison of NSGA-II and NSGA-III on various many-objective test problems, in 2016 IEEE Congress on Evolutionary Computation (CEC), (2016), pp. 3045–3052. doi:10.1109/CEC.2016.7744174
H. Ishibuchi, Y. Setoguchi, H. Masuda, Y. Nojima, Performance of decomposition-based many-objective algorithms strongly depends on pareto front shapes. IEEE Trans. Evol. Comput. PP(99), 1–1 (2016). doi:10.1109/TEVC.2016.2587749
H. Izakian, A. Abraham, V. Snasel, Comparison of heuristics for scheduling independent tasks on heterogeneous distributed environments, in International Joint Conference on Computational Sciences and Optimization. CSO 2009., vol 1 (IEEE, 2009), pp. 8–12
D. Jakobović, Evolutionary computation framework. http://gp.zemris.fer.hr/ecf
D. Jakobović, Project site. http://gp.zemris.fer.hr/scheduling/
D. Jakobović, L. Budin, Dynamic scheduling with genetic programming, in Proceedings of the 10th European Conference on Genetic Programming, vol. 3905 (2006), pp. 73–86. doi:10.1007/11729976_7
D. Jakobović, L. Jelenković, L. Budin, Genetic programming heuristics for multiple machine scheduling, in Proceedings of the 10th European Conference on Genetic Programming, vol 4445 (2007), pp. 321–330. doi:10.1007/978-3-540-71605-1_30
D. Jakobović, K. Marasović, Evolving priority scheduling heuristics with genetic programming. Appl. Soft Comput. J. 12(9), 2781–2789 (2012). doi:10.1016/j.asoc.2012.03.065
S. Jiang, Y.S. Ong, J. Zhang, L. Feng, Consistencies and contradictions of performance metrics in multiobjective optimization. IEEE Trans. Cybern. 44(12), 2391–2404 (2014). doi:10.1109/TCYB.2014.2307319
M. Johnston, T. Liddle, M. Zhang, A Relaxed Approach to Simplification in Genetic Programming (Springer, Berlin, 2010), pp. 110–121
K. Kaban, Z. Othman, D.S. Rohmah, Comparison of dispatching rules in job-shop scheduling problem using simulation: a case study. Int. J. Simul. Model. 11(3), 129–140 (2012). doi:10.2507/IJSIMM11(3)2.201
M. Keijzer, V. Babovic, Dimensionally aware genetic programming. Proc. Genet. Evol. Comput. Conf. 2, 1069–1076 (1999)
D. Kinzett, M. Johnston, M. Zhang, Numerical simplification for bloat control and analysis of building blocks in genetic programming. Evol. Intel. 2(4), 151 (2009). doi:10.1007/s12065-009-0029-9
F. Kolahan, V. Kayvanfar, A heuristic algorithm approach for scheduling of multi-criteria unrelated parallel machines. Inter. J. Mech. Aero. Indus. Mechatronic Manuf. Eng. 3(11), 1406–1409 (2009)
J.R. Koza, Human-competitive results produced by genetic programming. Genet. Program Evolvable Mach. 11(3–4), 251–284 (2010). doi:10.1007/s10710-010-9112-3
Y.H. Lee, K. Bhaskaran, M. Pinedo, A heuristic to minimize the total weighted tardiness with sequence-dependent setups. IIE Trans. 29(1), 45–52 (1997). doi:10.1080/07408179708966311
Y.K. Lin, J.W. Fowler, M.E. Pfund, Multiple-objective heuristics for scheduling unrelated parallel machines. Eur. J. Oper. Res. 227(2), 239–253 (2013)
M. Maheswaran, S. Ali, H. Siegal, D. Hensgen, R. Freund, Dynamic matching and scheduling of a class of independent tasks onto heterogeneous computing systems, in Proceedings of Eighth Heterogeneous Computing Workshop (HCW’99), (June 1999). doi:10.1109/HCW.1999.765094
A. Masood, Y. Mei, G. Chen, M. Zhang, Many-objective genetic programming for job-shop scheduling, in 2016 IEEE Congress on Evolutionary Computation (CEC), (2016), pp. 209–216
K. Miyashita, Job-shop scheduling with genetic programming, in Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2000), (2000), pp. 505–512
S. Nguyen, M. Zhang, M. Johnston, A sequential genetic programming method to learn forward construction heuristics for order acceptance and scheduling, in 2014 IEEE Congress on Evolutionary Computation (CEC), (2014), pp. 1824–1831. doi:10.1109/CEC.2014.6900347
S. Nguyen, M. Zhang, M. Johnston, K.C Tan, A coevolution genetic programming method to evolve scheduling policies for dynamic multi-objective job shop scheduling problems, in 2012 IEEE Congress on Evolutionary Computation, CEC 2012, vol i (2012), pp. 10–15. doi:10.1109/CEC.2012.6252968
S. Nguyen, M. Zhang, K.C. Tan, A dispatching rule based genetic algorithm for order acceptance and scheduling, in Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation, GECCO ’15, ACM, New York, NY, USA (2015), pp. 433–440. doi:10.1145/2739480.2754821
S. Nguyen, M. Zhang, K.C. Tan, Enhancing genetic programming based hyper-heuristics for dynamic multi-objective job shop scheduling problems, in 2015 IEEE Congress on Evolutionary Computation (CEC), (2015), pp. 2781–2788. doi:10.1109/CEC.2015.7257234
S. Nguyen, M. Zhang, M. Johnston, K.C. Tan, A computational study of representations in genetic programming to evolve dispatching rules for the job shop scheduling problem. IEEE Trans. Evol. Comput. 17(5), 621–639 (2013). doi:10.1109/TEVC.2012.2227326
S. Nguyen, M. Zhang, M. Johnston, K.C. Tan, Dynamic multi-objective job shop scheduling: a genetic programming approach, in Automated Scheduling and Planning, Studies in Computational Intelligence, vol. 505, ed. by A.S. Uyar, E. Ozcan, N. Urquhart (Springer, Berlin, 2013), pp. 251–282
S. Nguyen, M. Zhang, M. Johnston, K.C. Tan, Learning iterative dispatching rules for job shop scheduling with genetic programming. Int. J. Adv. Manuf. Technol. 67(1–4), 85–100 (2013). doi:10.1007/s00170-013-4756-9
S. Nguyen, M. Zhang, M. Johnston, K.C. Tan, Automatic design of scheduling policies for dynamic multi-objective job shop scheduling via cooperative coevolution genetic programming. IEEE Trans. Evol. Comput. 18(2), 193–208 (2014). doi:10.1109/TEVC.2013.2248159
L. Nie, L. Gao, P. Li, L. Zhang, Application of gene expression programming on dynamic job shop scheduling problem, in Proceedings of the 2011 15th International Conference on Computer Supported Cooperative Work in Design (CSCWD), (2011), pp. 291–295. doi:10.1109/CSCWD.2011.5960088
L. Nie, X. Shao, L. Gao, W. Li, Evolving scheduling rules with gene expression programming for dynamic single-machine scheduling problems. Int. J. Adv. Manuf. Technol. 50(5–8), 729–747 (2010). doi:10.1007/s00170-010-2518-5
J. Park, S. Nguyen, M. Zhang, M. Johnston, Genetic programming for order acceptance and scheduling, in 2013 IEEE Congress on Evolutionary Computation, CEC 2013, vol 3 (2013), pp. 1005–1012. doi:10.1109/CEC.2013.6557677
S. Petrovic, E. Castro, A genetic algorithm for radiotherapy pre-treatment scheduling. Appl. Evol. Comput. 6025(August 2015), 462–471 (2010). doi:10.1007/978-3-642-12242-2
M. Pfund, J.W. Fowler, J.N.D. Gupta, A survey of algorithms for single and multi-objective unrelated parallel-machine deterministic scheduling problems. J. Chin. Inst. Ind. Eng. 21(3), 230–241 (2004). doi:10.1080/10170660409509404
C.W. Pickardt, T. Hildebrandt, J. Branke, J. Heger, B. Scholz-Reiter, Evolutionary generation of dispatching rule sets for complex dynamic scheduling problems. Int. J. Prod. Econ. 145(1), 67–77 (2013). doi:10.1016/j.ijpe.2012.10.016
M. Pinedo, Scheduling Therory, Algorithms and Systems (Springer US, Boston, MA, 2012)
R. Poli, W.B. Langdon, N.F. McPhee, A field guide to genetic programming. Published via http://lulu.com and freely available at http://www.gp-field-guide.org.uk (2008). (With contributions by J. R. Koza)
H. Seada, K. Deb, U-NSGA-III: a unified evolutionary algorithm for single, multiple, and many-objective optimization, in International Conference on Evolutionary Multi-Criterion Optimization (2014), pp. 1–30. doi:10.1007/978-3-319-15892-1_3
J.C. Tay, N.B. Ho, Evolving dispatching rules using genetic programming for solving multi-objective flexible job-shop problems. Comput. Ind. Eng. 54(3), 453–473 (2008). doi:10.1016/j.cie.2007.08.008
Z. Wang, K. Tang, X. Yao, Multi-objective approaches to optimal testing resource allocation in modular software systems. IEEE Trans. Reliab. 59(3), 563–575 (2010). doi:10.1109/TR.2010.2057310
L. Yu, H.M. Shih, M. Pfund, W.M. Carlyle, J.W. Fowler, Scheduling of unrelated parallel machines: an application to pwb manufacturing. IIE Trans. 34(11), 921–931 (2002). doi:10.1023/A:1016185412209
M. Zhang, W. Smart, Learning weights in genetic programs using gradient descent for object recognition, in Proceedings of the 3rd European Conference on Applications of Evolutionary Computing, EC’05, (Springer, Berlin, 2005), pp. 417–427
Q. Zhang, H. Li, MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evolut. Comput. 11(6), 712–731 (2007). doi:10.1109/TEVC.2007.892759
M. Zhang, P. Wong, Genetic programming for medical classification: a program simplification approach. Genet. Program Evolvable Mach. 9(3), 229–255 (2008). doi:10.1007/s10710-008-9059-9
A. Zhou, B.Y. Qu, H. Li, S.Z. Zhao, P.N. Suganthan, Q. Zhang, Multiobjective evolutionary algorithms: a survey of the state of the art. Swarm Evolut. Comput. 1(1), 32–49 (2011)
E. Zitzler, M. Laumanns, L. Thiele, SPEA2: improving the strength pareto evolutionary algorithm (2005), pp. 95–100. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.112.5073
E. Zitzler, L. Thiele, Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans. Evolut. Comput. 3(4), 257–271 (1999). doi:10.1109/4235.797969
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ɖurasević, M., Jakobović, D. Evolving dispatching rules for optimising many-objective criteria in the unrelated machines environment. Genet Program Evolvable Mach 19, 9–51 (2018). https://doi.org/10.1007/s10710-017-9310-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10710-017-9310-3