Algorithms for bicriteria minimization in the permutation flow shop scheduling problem

Previous Article
JIMO Home
This Issue
Next Article
New heuristics for solving the economic lot scheduling problem with reworks

January 2011, 7(1): 253-282. doi: 10.3934/jimo.2011.7.253

Algorithms for bicriteria minimization in the permutation flow shop scheduling problem

Ethel Mokotoff ^1,

1.	Departamento de Fundamentos de Economía, Universidad de Alcalá, Alcalá de Henares, Madrid, 28802, Spain

Received August 2009 Revised November 2010 Published January 2011

Abstract
Related Papers

This paper presents two bi-objective simulated annealing procedures to deal with the classical permutation flow shop scheduling problem considering the makespan and the total completion time as criteria. The proposed methods are based on multi-objective simulated annealing techniques combined with constructive and heuristic algorithms. A computational experiment has been carried out and different metrics have been computed to check various attributes of each method. For all the tested instances a net set of potentially efficient schedules has been obtained and compared with previously published results. Results indicate that the proposed algorithms provide efficient solutions with little computational effort which can serve as input for interactive procedures.

Keywords: Multi-Objective Optimization, Heuristics., Management Decision Making, Deterministic Scheduling Theory, Flow-shop.

Mathematics Subject Classification: Primary: 90B35; 90B50; 90C29; Secondary: 90C5.

Citation: Ethel Mokotoff. Algorithms for bicriteria minimization in the permutation flow shop scheduling problem. Journal of Industrial and Management Optimization, 2011, 7 (1) : 253-282. doi: 10.3934/jimo.2011.7.253

References:

[1]	J. Arroyo and V. Armentano, Genetic local search for multi-objective flowshop scheduling problems, Eur. J. Oper. Res., 167 (2005), 717-38. doi: 10.1016/j.ejor.2004.07.017.
[2]	T. P. Bagchi, "Multiobjective Scheduling by Genetic Algorithms," Kluwer Academic Publishers, Dordrecht, 1999.
[3]	P. C. Chang, S. H. Chen and C. H. Liu, Sub-population genetic algorithm with mining gene structures for multiobjective flowshop scheduling problems, Expert. Syst. Appl., 33 (2007), 762-77. doi: 10.1016/j.eswa.2006.06.019.
[4]	P. C. Chang, J. C. Hsieh and S. G. Lin, The development of gradual priority weighting approach for the multi-objective flowshop scheduling problem, Int. J. Prod. Econ., 79 (2002), 171-83. doi: 10.1016/S0925-5273(02)00141-X.
[5]	P. Czyzak and A. Jaszkiewicz, Pareto Simulated Annealing-a metaheuristic technique for multiple objective combinatorial optimization, J. Multicriteria Dec. Anal., 7 (1998), 34-47. doi: 10.1002/(SICI)1099-1360(199801)7:1<34::AID-MCDA161>3.0.CO;2-6.
[6]	R. L. Daniels and R. J. Chambers, Multiobjective flow-shop scheduling, Nav. Res. Log., 37 (1990), 981-995. doi: 10.1002/1520-6750(199012)37:6<981::AID-NAV3220370617>3.0.CO;2-H.
[7]	J. Dorn, M. Girsch, G. Skele and W. Slany, Comparison of iterative improvement techniques for schedule optimization, Eur. J. Oper. Res., 94 (1996), 349-361. doi: 10.1016/0377-2217(95)00162-X.
[8]	M. Ehrgott and X. Gandibleux, Multiobjective Combinatorial Optimization: Theory, Methodology, and Applications, in "Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys" (eds. M. Ehrgott and X. Gandibleux), Kluwer Academic Publishers, Boston, (2002), 369-444.
[9]	V. A. Emelichev and V. A. Perepelista, On cardinality of the set of alternatives in discrete many-criterion problems, Discrete Math. Appl., 2 (1992), 461-471. doi: 10.1515/dma.1992.2.5.461.
[10]	J. M. Framinan, R. Leisten and R. Ruiz-Usano, Efficient heuristics for flowshop sequencing with the objectives of makespan and flowtime minimisation, Eur. J. Oper. Res., 141 (2002), 559-569. doi: 10.1016/S0377-2217(01)00278-8.
[11]	M. R. Garey and D. S. Johnson, "Computers and Intractability: A Guide to the Theory of NP-Completeness," Freeman, San Francisco, 1979.
[12]	M. Geiger, On operators and search space topology in multi-objective flow shop scheduling, Eur. J. Oper. Res., 181 (2007), 195-206. doi: 10.1016/j.ejor.2006.06.010.
[13]	R. L. Graham, E. L. Lawler, J. K. Lenstra and A. H. G. Rinnooy Kan, Optimization and approximation in deterministic sequencing and scheduling: A survey, Ann. Discrete Math., 5 (1979), 287-326. doi: 10.1016/S0167-5060(08)70356-X.
[14]	J. N. D. Gupta, V. R. Neppalli and F. Werner, Minimizing total flow time in a two-machine flowshop problem with minimum makespan, Int. J. Prod. Econ., 69 (2001), 323-338. doi: 10.1016/S0925-5273(00)00039-6.
[15]	J. C. Ho and Y. L. Chang, A new heuristic for the n-job, m-machine flowshop problem, Eur. J. Oper. Res., 52 (1991), 194-202. doi: 10.1016/0377-2217(91)90080-F.
[16]	J. A. Hoogeveen, "Single-Machine Bicriteria Scheduling," Ph.D thesis, The Netherlands Technology University in Amsterdam, 1992.
[17]	G. Huang and A. Lim, Fragmental optimization on the 2-machine bicriteria flowshop scheduling problem, in "Proceedings of 15th IEEE International Conference on Tools with Artificial Intelligence," (1992), 33-75.
[18]	E. Ignall and L. E. Schrage, Application of the branch-and-bound technique to some flow-shop scheduling problems, Oper. Res., 13 (1965), 400-412. doi: 10.1287/opre.13.3.400.
[19]	H. Ishibuchi and T. Murata, A multi-objective genetic local search algorithm and its application to flowshop scheduling, IEEE T. Syst. Man. Cy. C., 28 (1998), 392-403. doi: 10.1109/5326.704576.
[20]	A. Jaszkiewicz, A comparative study of multiple-objective metaheuristics on the bi-objective set covering problem and the pareto memetic algorithm, Annals of Operations Research, 13 (2004), 135-158. doi: 10.1023/B:ANOR.0000039516.50069.5b.
[21]	S. M. Johnson, Optimal two- and three-stage production schedules with setup times included, Nav. Res. Log., 1 (1954), 61-68. doi: 10.1002/nav.3800010110.
[22]	D. F. Jones, S. K. Mirrazavi and M. Tamiz, Multi-objective meta-heuristics: An overview of the current state of the art, Eur. J. Oper. Res., 137 (2002), 1-9. doi: 10.1016/S0377-2217(01)00123-0.
[23]	S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi, Optimization by simulated annealing, Science, 220 (1983), 671-680. doi: 10.1126/science.220.4598.671.
[24]	J. Knowles and D. Corne, On Metrics Comparing Nondominated Sets, in "Proceedings of the 2002 Congress on Evolutionary Computation Conference," IEEE Press, (2002), 711-716.
[25]	J. D. Landa-Silva, E. K. Burke and S. Petrovic, An introduction to multiobjective metaheuristics for scheduling and timetabling, Lect. Notes Econ. Math., 535 (2004), 91-129. doi: 10.1007/978-3-642-17144-4_4.
[26]	C. J. Liao, W. C. Yu and C. B. Joe, Bicriterion scheduling in the two-machine flowshop, J. Oper. Res. Soc., 48 (1997), 929-935.
[27]	G. B. McMahon, Optimal production schedules for flow shop, Can. Oper. Res. Soc. J., 7 (1969), 141-151.
[28]	G. Minella, R. Ruiz and M. Ciavotta, A review and evaluation of multi-objective algorithms for the flowshop scheduling problem, Informs. Journal on Computing, 20 (2007), 451-471. doi: 10.1287/ijoc.1070.0258.
[29]	E. Mokotoff, Multi-objective simulated annealing for permutation flow shop problems, in "Computational Intelligence in Flow Shop and Job Shop Scheduling" (ed. U. Chakraborty), Springer Verlag, (2009), 101-150. doi: 10.1007/978-3-642-02836-6_4.
[30]	T. Murata, H. Ishibuchi and H. Tanaka, Multi-objective genetic algorithm and its applications to flowshop scheduling, Comp. Ind. Eng., 30 (1996), 957-968. doi: 10.1016/0360-8352(96)00045-9.
[31]	A. Nagar, S. S. Heragu and J. Haddock, A branch and bound approach for a two machine flowshop scheduling problem, J. Oper. Res. Soc., 46 (1995), 721-734.
[32]	M. Nawaz, E. E. Jr Enscore and I. Ham, A heuristic algorithm for the m machine, n job flowshop sequencing problem, OMEGA-Int J. Manage S., 11 (1983), 91-95. doi: 10.1016/0305-0483(83)90088-9.
[33]	V. L. Neppalli, C. L. Chen and J. N. D. Gupta, Genetic algorithms for the two-stage bicriteria flowshop problem, Eur. J. Oper. Res., 95 (1996), 356-373. doi: 10.1016/0377-2217(95)00275-8.
[34]	S. Parthasarathy and C. Rajendran, An experimental evaluation of heuristics for scheduling in a real-life flowshop with sequence-dependent setup times of jobs, Int. J. Prod. Econ., 49 (1997), 255-263. doi: 10.1016/S0925-5273(97)00017-0.
[35]	T. Pasupathy, C. Rajendran and R. K. Suresh, A multi-objective genetic algorithm for scheduling in flow shops to minimize the makespan and total flow time of jobs, Int. J. Adv. Manuf. Technol., 27 (2006), 804-815. doi: 10.1007/s00170-004-2249-6.
[36]	C. Rajendran, Two-stage flowshop scheduling problem with bicriteria, J. Oper. Res. Soc., 43 (1992), 879-884.
[37]	C. Rajendran, Heuristic algorithm for scheduling in a flowshop to minimize total flowtime, Int. J. Prod. Econ., 29 (1993), 65-73. doi: 10.1016/0925-5273(93)90024-F.
[38]	C. Rajendran, Heuristics for scheduling in flowshop with multiple objectives, Eur. J. Oper. Res., 82 (1995), 540-555. doi: 10.1016/0377-2217(93)E0212-G.
[39]	A. H. G. Rinnooy Kan, "Machine Scheduling problems: Classification, Complexity and Computations," Martinus Nijhoff, The Hague, 1976.
[40]	S. Sayin and S. Karabati, A bicriteria approach to the two-machine flow shop scheduling problem, Eur. J. Oper. Res., 113 (1999), 435-449. doi: 10.1016/S0377-2217(98)00009-5.
[41]	W. J. Selen and D. D. Hott, A mixed-integer goal-programming formulation of the standard flow-shop scheduling problem, J. Oper. Res. Soc., 12 (1986), 1121-1128.
[42]	P. Serafini, Simulated annealing for multiple objective optimization problems, in "Proceedings of the Tenth International Conference on Multiple Criteria Decision Making," Taipei, (1992), 87-96.
[43]	F. S. Sivrikaya-Serifoglu and G. Ulusoy, A bicriteria two machine permutation flowshop problem, Eur. J. Oper. Res., 107 (1998), 414-430. doi: 10.1016/S0377-2217(97)00338-X.
[44]	N. Srinivas and K. Deb, Multiobjective function optimization using nondominated sorting genetic algorithms, Evol. Comp., 2 (1995), 221-248. doi: 10.1162/evco.1994.2.3.221.
[45]	V. T'kindt and J. C. Billaut, "Multicriteria scheduling: Theory, Models and Algorithms," 2nd edition, Springer, Berlin, 2006.
[46]	V. T'kindt, J. N. D. Gupta and J. C. Billaut, Two machine flowshop scheduling problem with a secondary criterion, Comp. Oper. Res., 30 (2003), 505-526. doi: 10.1016/S0305-0548(02)00021-7.
[47]	V. T'kindt, N. Monmarche and F et al. Tercinet, An ant colony optimization algorithm to solve a 2-machine bicriteria flowshop scheduling problem, Eur. J. Oper. Res., 142 (2002), 250-257. doi: 10.1016/S0377-2217(02)00265-5.
[48]	E. Taillard, Some efficient heuristic methods for the flow shop sequencing problem, Eur. J. Oper. Res., 47 (1990), 67-74. doi: 10.1016/0377-2217(90)90090-X.
[49]	E. Taillard, Benchmark for basic scheduling problems, Eur. J. Oper. Res., 64 (1993), 278-285. doi: 10.1016/0377-2217(93)90182-M.
[50]	T. K. Varadharajan and C. Rajendran, A multi-objective simulated-annealing algorithm for scheduling in flowshops to minimize the makespan and total flowtime of jobs, Eur. J. Oper. Res., 167 (2005), 772-795. doi: 10.1016/j.ejor.2004.07.020.
[51]	J. M. Wilson, Alternative formulation of a flow shop scheduling problem, J. Oper. Res. Soc., 40 (1989), 395-399.
[52]	B. Yagmahan and M. M. Yenisey, Ant colony optimization for multi-objective flow shop scheduling problem, Comp. Ind. Eng., 54 (2008), 411-420. doi: 10.1016/j.cie.2007.08.003.
[53]	E. Zitzler, "Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications," Ph.D thesis, Swiss Federal Institute of Technology in Zurich, 1999.

show all references

References:

[1]	J. Arroyo and V. Armentano, Genetic local search for multi-objective flowshop scheduling problems, Eur. J. Oper. Res., 167 (2005), 717-38. doi: 10.1016/j.ejor.2004.07.017.
[2]	T. P. Bagchi, "Multiobjective Scheduling by Genetic Algorithms," Kluwer Academic Publishers, Dordrecht, 1999.
[3]	P. C. Chang, S. H. Chen and C. H. Liu, Sub-population genetic algorithm with mining gene structures for multiobjective flowshop scheduling problems, Expert. Syst. Appl., 33 (2007), 762-77. doi: 10.1016/j.eswa.2006.06.019.
[4]	P. C. Chang, J. C. Hsieh and S. G. Lin, The development of gradual priority weighting approach for the multi-objective flowshop scheduling problem, Int. J. Prod. Econ., 79 (2002), 171-83. doi: 10.1016/S0925-5273(02)00141-X.
[5]	P. Czyzak and A. Jaszkiewicz, Pareto Simulated Annealing-a metaheuristic technique for multiple objective combinatorial optimization, J. Multicriteria Dec. Anal., 7 (1998), 34-47. doi: 10.1002/(SICI)1099-1360(199801)7:1<34::AID-MCDA161>3.0.CO;2-6.
[6]	R. L. Daniels and R. J. Chambers, Multiobjective flow-shop scheduling, Nav. Res. Log., 37 (1990), 981-995. doi: 10.1002/1520-6750(199012)37:6<981::AID-NAV3220370617>3.0.CO;2-H.
[7]	J. Dorn, M. Girsch, G. Skele and W. Slany, Comparison of iterative improvement techniques for schedule optimization, Eur. J. Oper. Res., 94 (1996), 349-361. doi: 10.1016/0377-2217(95)00162-X.
[8]	M. Ehrgott and X. Gandibleux, Multiobjective Combinatorial Optimization: Theory, Methodology, and Applications, in "Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys" (eds. M. Ehrgott and X. Gandibleux), Kluwer Academic Publishers, Boston, (2002), 369-444.
[9]	V. A. Emelichev and V. A. Perepelista, On cardinality of the set of alternatives in discrete many-criterion problems, Discrete Math. Appl., 2 (1992), 461-471. doi: 10.1515/dma.1992.2.5.461.
[10]	J. M. Framinan, R. Leisten and R. Ruiz-Usano, Efficient heuristics for flowshop sequencing with the objectives of makespan and flowtime minimisation, Eur. J. Oper. Res., 141 (2002), 559-569. doi: 10.1016/S0377-2217(01)00278-8.
[11]	M. R. Garey and D. S. Johnson, "Computers and Intractability: A Guide to the Theory of NP-Completeness," Freeman, San Francisco, 1979.
[12]	M. Geiger, On operators and search space topology in multi-objective flow shop scheduling, Eur. J. Oper. Res., 181 (2007), 195-206. doi: 10.1016/j.ejor.2006.06.010.
[13]	R. L. Graham, E. L. Lawler, J. K. Lenstra and A. H. G. Rinnooy Kan, Optimization and approximation in deterministic sequencing and scheduling: A survey, Ann. Discrete Math., 5 (1979), 287-326. doi: 10.1016/S0167-5060(08)70356-X.
[14]	J. N. D. Gupta, V. R. Neppalli and F. Werner, Minimizing total flow time in a two-machine flowshop problem with minimum makespan, Int. J. Prod. Econ., 69 (2001), 323-338. doi: 10.1016/S0925-5273(00)00039-6.
[15]	J. C. Ho and Y. L. Chang, A new heuristic for the n-job, m-machine flowshop problem, Eur. J. Oper. Res., 52 (1991), 194-202. doi: 10.1016/0377-2217(91)90080-F.
[16]	J. A. Hoogeveen, "Single-Machine Bicriteria Scheduling," Ph.D thesis, The Netherlands Technology University in Amsterdam, 1992.
[17]	G. Huang and A. Lim, Fragmental optimization on the 2-machine bicriteria flowshop scheduling problem, in "Proceedings of 15th IEEE International Conference on Tools with Artificial Intelligence," (1992), 33-75.
[18]	E. Ignall and L. E. Schrage, Application of the branch-and-bound technique to some flow-shop scheduling problems, Oper. Res., 13 (1965), 400-412. doi: 10.1287/opre.13.3.400.
[19]	H. Ishibuchi and T. Murata, A multi-objective genetic local search algorithm and its application to flowshop scheduling, IEEE T. Syst. Man. Cy. C., 28 (1998), 392-403. doi: 10.1109/5326.704576.
[20]	A. Jaszkiewicz, A comparative study of multiple-objective metaheuristics on the bi-objective set covering problem and the pareto memetic algorithm, Annals of Operations Research, 13 (2004), 135-158. doi: 10.1023/B:ANOR.0000039516.50069.5b.
[21]	S. M. Johnson, Optimal two- and three-stage production schedules with setup times included, Nav. Res. Log., 1 (1954), 61-68. doi: 10.1002/nav.3800010110.
[22]	D. F. Jones, S. K. Mirrazavi and M. Tamiz, Multi-objective meta-heuristics: An overview of the current state of the art, Eur. J. Oper. Res., 137 (2002), 1-9. doi: 10.1016/S0377-2217(01)00123-0.
[23]	S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi, Optimization by simulated annealing, Science, 220 (1983), 671-680. doi: 10.1126/science.220.4598.671.
[24]	J. Knowles and D. Corne, On Metrics Comparing Nondominated Sets, in "Proceedings of the 2002 Congress on Evolutionary Computation Conference," IEEE Press, (2002), 711-716.
[25]	J. D. Landa-Silva, E. K. Burke and S. Petrovic, An introduction to multiobjective metaheuristics for scheduling and timetabling, Lect. Notes Econ. Math., 535 (2004), 91-129. doi: 10.1007/978-3-642-17144-4_4.
[26]	C. J. Liao, W. C. Yu and C. B. Joe, Bicriterion scheduling in the two-machine flowshop, J. Oper. Res. Soc., 48 (1997), 929-935.
[27]	G. B. McMahon, Optimal production schedules for flow shop, Can. Oper. Res. Soc. J., 7 (1969), 141-151.
[28]	G. Minella, R. Ruiz and M. Ciavotta, A review and evaluation of multi-objective algorithms for the flowshop scheduling problem, Informs. Journal on Computing, 20 (2007), 451-471. doi: 10.1287/ijoc.1070.0258.
[29]	E. Mokotoff, Multi-objective simulated annealing for permutation flow shop problems, in "Computational Intelligence in Flow Shop and Job Shop Scheduling" (ed. U. Chakraborty), Springer Verlag, (2009), 101-150. doi: 10.1007/978-3-642-02836-6_4.
[30]	T. Murata, H. Ishibuchi and H. Tanaka, Multi-objective genetic algorithm and its applications to flowshop scheduling, Comp. Ind. Eng., 30 (1996), 957-968. doi: 10.1016/0360-8352(96)00045-9.
[31]	A. Nagar, S. S. Heragu and J. Haddock, A branch and bound approach for a two machine flowshop scheduling problem, J. Oper. Res. Soc., 46 (1995), 721-734.
[32]	M. Nawaz, E. E. Jr Enscore and I. Ham, A heuristic algorithm for the m machine, n job flowshop sequencing problem, OMEGA-Int J. Manage S., 11 (1983), 91-95. doi: 10.1016/0305-0483(83)90088-9.
[33]	V. L. Neppalli, C. L. Chen and J. N. D. Gupta, Genetic algorithms for the two-stage bicriteria flowshop problem, Eur. J. Oper. Res., 95 (1996), 356-373. doi: 10.1016/0377-2217(95)00275-8.
[34]	S. Parthasarathy and C. Rajendran, An experimental evaluation of heuristics for scheduling in a real-life flowshop with sequence-dependent setup times of jobs, Int. J. Prod. Econ., 49 (1997), 255-263. doi: 10.1016/S0925-5273(97)00017-0.
[35]	T. Pasupathy, C. Rajendran and R. K. Suresh, A multi-objective genetic algorithm for scheduling in flow shops to minimize the makespan and total flow time of jobs, Int. J. Adv. Manuf. Technol., 27 (2006), 804-815. doi: 10.1007/s00170-004-2249-6.
[36]	C. Rajendran, Two-stage flowshop scheduling problem with bicriteria, J. Oper. Res. Soc., 43 (1992), 879-884.
[37]	C. Rajendran, Heuristic algorithm for scheduling in a flowshop to minimize total flowtime, Int. J. Prod. Econ., 29 (1993), 65-73. doi: 10.1016/0925-5273(93)90024-F.
[38]	C. Rajendran, Heuristics for scheduling in flowshop with multiple objectives, Eur. J. Oper. Res., 82 (1995), 540-555. doi: 10.1016/0377-2217(93)E0212-G.
[39]	A. H. G. Rinnooy Kan, "Machine Scheduling problems: Classification, Complexity and Computations," Martinus Nijhoff, The Hague, 1976.
[40]	S. Sayin and S. Karabati, A bicriteria approach to the two-machine flow shop scheduling problem, Eur. J. Oper. Res., 113 (1999), 435-449. doi: 10.1016/S0377-2217(98)00009-5.
[41]	W. J. Selen and D. D. Hott, A mixed-integer goal-programming formulation of the standard flow-shop scheduling problem, J. Oper. Res. Soc., 12 (1986), 1121-1128.
[42]	P. Serafini, Simulated annealing for multiple objective optimization problems, in "Proceedings of the Tenth International Conference on Multiple Criteria Decision Making," Taipei, (1992), 87-96.
[43]	F. S. Sivrikaya-Serifoglu and G. Ulusoy, A bicriteria two machine permutation flowshop problem, Eur. J. Oper. Res., 107 (1998), 414-430. doi: 10.1016/S0377-2217(97)00338-X.
[44]	N. Srinivas and K. Deb, Multiobjective function optimization using nondominated sorting genetic algorithms, Evol. Comp., 2 (1995), 221-248. doi: 10.1162/evco.1994.2.3.221.
[45]	V. T'kindt and J. C. Billaut, "Multicriteria scheduling: Theory, Models and Algorithms," 2nd edition, Springer, Berlin, 2006.
[46]	V. T'kindt, J. N. D. Gupta and J. C. Billaut, Two machine flowshop scheduling problem with a secondary criterion, Comp. Oper. Res., 30 (2003), 505-526. doi: 10.1016/S0305-0548(02)00021-7.
[47]	V. T'kindt, N. Monmarche and F et al. Tercinet, An ant colony optimization algorithm to solve a 2-machine bicriteria flowshop scheduling problem, Eur. J. Oper. Res., 142 (2002), 250-257. doi: 10.1016/S0377-2217(02)00265-5.
[48]	E. Taillard, Some efficient heuristic methods for the flow shop sequencing problem, Eur. J. Oper. Res., 47 (1990), 67-74. doi: 10.1016/0377-2217(90)90090-X.
[49]	E. Taillard, Benchmark for basic scheduling problems, Eur. J. Oper. Res., 64 (1993), 278-285. doi: 10.1016/0377-2217(93)90182-M.
[50]	T. K. Varadharajan and C. Rajendran, A multi-objective simulated-annealing algorithm for scheduling in flowshops to minimize the makespan and total flowtime of jobs, Eur. J. Oper. Res., 167 (2005), 772-795. doi: 10.1016/j.ejor.2004.07.020.
[51]	J. M. Wilson, Alternative formulation of a flow shop scheduling problem, J. Oper. Res. Soc., 40 (1989), 395-399.
[52]	B. Yagmahan and M. M. Yenisey, Ant colony optimization for multi-objective flow shop scheduling problem, Comp. Ind. Eng., 54 (2008), 411-420. doi: 10.1016/j.cie.2007.08.003.
[53]	E. Zitzler, "Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications," Ph.D thesis, Swiss Federal Institute of Technology in Zurich, 1999.

[1]	Hamed Fazlollahtabar, Mohammad Saidi-Mehrabad. Optimizing multi-objective decision making having qualitative evaluation. Journal of Industrial and Management Optimization, 2015, 11 (3) : 747-762. doi: 10.3934/jimo.2015.11.747
[2]	Alireza Eydi, Rozhin Saedi. A multi-objective decision-making model for supplier selection considering transport discounts and supplier capacity constraints. Journal of Industrial and Management Optimization, 2021, 17 (6) : 3581-3602. doi: 10.3934/jimo.2020134
[3]	Zhongqiang Wu, Zongkui Xie. A multi-objective lion swarm optimization based on multi-agent. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022001
[4]	Yuan-mei Xia, Xin-min Yang, Ke-quan Zhao. A combined scalarization method for multi-objective optimization problems. Journal of Industrial and Management Optimization, 2021, 17 (5) : 2669-2683. doi: 10.3934/jimo.2020088
[5]	Ankan Bhaumik, Sankar Kumar Roy, Gerhard Wilhelm Weber. Multi-objective linguistic-neutrosophic matrix game and its applications to tourism management. Journal of Dynamics and Games, 2021, 8 (2) : 101-118. doi: 10.3934/jdg.2020031
[6]	Shungen Luo, Xiuping Guo. Multi-objective optimization of multi-microgrid power dispatch under uncertainties using interval optimization. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021208
[7]	Xia Zhao, Jianping Dou. Bi-objective integrated supply chain design with transportation choices: A multi-objective particle swarm optimization. Journal of Industrial and Management Optimization, 2019, 15 (3) : 1263-1288. doi: 10.3934/jimo.2018095
[8]	Han Yang, Jia Yue, Nan-jing Huang. Multi-objective robust cross-market mixed portfolio optimization under hierarchical risk integration. Journal of Industrial and Management Optimization, 2020, 16 (2) : 759-775. doi: 10.3934/jimo.2018177
[9]	Qiang Long, Xue Wu, Changzhi Wu. Non-dominated sorting methods for multi-objective optimization: Review and numerical comparison. Journal of Industrial and Management Optimization, 2021, 17 (2) : 1001-1023. doi: 10.3934/jimo.2020009
[10]	Min Zhang, Gang Li. Multi-objective optimization algorithm based on improved particle swarm in cloud computing environment. Discrete and Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1413-1426. doi: 10.3934/dcdss.2019097
[11]	Liwei Zhang, Jihong Zhang, Yule Zhang. Second-order optimality conditions for cone constrained multi-objective optimization. Journal of Industrial and Management Optimization, 2018, 14 (3) : 1041-1054. doi: 10.3934/jimo.2017089
[12]	Danthai Thongphiew, Vira Chankong, Fang-Fang Yin, Q. Jackie Wu. An on-line adaptive radiation therapy system for intensity modulated radiation therapy: An application of multi-objective optimization. Journal of Industrial and Management Optimization, 2008, 4 (3) : 453-475. doi: 10.3934/jimo.2008.4.453
[13]	Yu Chen, Yonggang Li, Bei Sun, Chunhua Yang, Hongqiu Zhu. Multi-objective chance-constrained blending optimization of zinc smelter under stochastic uncertainty. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021169
[14]	Xiliang Sun, Wanjie Hu, Xiaolong Xue, Jianjun Dong. Multi-objective optimization model for planning metro-based underground logistics system network: Nanjing case study. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021179
[15]	Shoufeng Ji, Jinhuan Tang, Minghe Sun, Rongjuan Luo. Multi-objective optimization for a combined location-routing-inventory system considering carbon-capped differences. Journal of Industrial and Management Optimization, 2022, 18 (3) : 1949-1977. doi: 10.3934/jimo.2021051
[16]	Tone-Yau Huang, Tamaki Tanaka. Optimality and duality for complex multi-objective programming. Numerical Algebra, Control and Optimization, 2022, 12 (1) : 121-134. doi: 10.3934/naco.2021055
[17]	Henri Bonnel, Ngoc Sang Pham. Nonsmooth optimization over the (weakly or properly) Pareto set of a linear-quadratic multi-objective control problem: Explicit optimality conditions. Journal of Industrial and Management Optimization, 2011, 7 (4) : 789-809. doi: 10.3934/jimo.2011.7.789
[18]	Lin Jiang, Song Wang. Robust multi-period and multi-objective portfolio selection. Journal of Industrial and Management Optimization, 2021, 17 (2) : 695-709. doi: 10.3934/jimo.2019130
[19]	Jian Xiong, Zhongbao Zhou, Ke Tian, Tianjun Liao, Jianmai Shi. A multi-objective approach for weapon selection and planning problems in dynamic environments. Journal of Industrial and Management Optimization, 2017, 13 (3) : 1189-1211. doi: 10.3934/jimo.2016068
[20]	Dušan M. Stipanović, Claire J. Tomlin, George Leitmann. A note on monotone approximations of minimum and maximum functions and multi-objective problems. Numerical Algebra, Control and Optimization, 2011, 1 (3) : 487-493. doi: 10.3934/naco.2011.1.487

2020 Impact Factor: 1.801

Tools

Metrics

Other articles
by authors

on AIMS
Ethel Mokotoff
on Google Scholar
Ethel Mokotoff

[Back to Top]