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International Conference on Evolutionary Multi-Criterion Optimization

EMO 2011: Evolutionary Multi-Criterion Optimization pp 520–534Cite as

Lorenz versus Pareto Dominance in a Single Machine Scheduling Problem with Rejection

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6576))

Abstract

Scheduling problems have been studied from many years ago. Most of the papers which were published in this domain are different in one or many of issues as following: objective functions, machine environment, constraints and methodology for solving the problems. In this paper we address the problem of single machine scheduling in which due to some constraints like capacity, rejection of a set of jobs is accepted. The problem is considered as bi-objective one: minimization of the sum of weighted completion times for the accepted jobs and minimization of the sum of penalties for the rejected jobs. We find that in this problem, the solutions are not handled in a satisfactory way by general Pareto-dominance rule, so we suggest the application of Lorenz-dominance to an adapted bi-objective simulated annealing algorithm. Finally we justify the use of Lorenz-dominance as a useful refinement of Pareto-dominance by comparing the results.

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References

  1. Bartal, Y., Leonardi, S., Marchetti-Spaccamela, A., Sgall, J., Stougie, L.: Multiprocessor scheduling with rejection. SIAM Journal on Discrete Mathematics 13, 64–78 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  2. Seiden, S.: Preemptive multiprocessor scheduling with rejection. Theoretical Computer Science 262, 437–458 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. Hoogeveen, H., Skutella, M., Woeginger, G.J.: Preemptive scheduling with rejection. Mathematical Programming 94, 361–374 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Lu, L., Zhang, L., Yuan, J.: The unbounded parallel batch machine scheduling with release dates and rejection to minimize makespan. Theoretical Computer Science 396, 283–289 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Zhang, L., Lu, L., Yuan, J.: Single machine scheduling with release dates and rejection. European Journal of Operational Research 198, 975–978 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cheng, Y., Sun, S.: Scheduling linear deteriorating jobs with rejection on a single machine. European Journal of Operational Research 194, 18–27 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lu, L., Cheng, T.C.E., Yuan, J., Zhang, L.: Bounded single-machine parallel-batch scheduling with release dates and rejection. Computers and Operations Research 36, 2748–2751 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Cao, Z., Yang, X.: A PTAS for parallel batch scheduling with rejection and dynamic job arrivals. Theoretical Computer Science 410, 2732–2745 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Dósa, G., He, Y.: Scheduling with machine cost and rejection. Journal of Combinatorial Optimization 12, 337–350 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Nagy-György, J., Imreh, Cs.: Online scheduling with machine cost and rejection. Discrete Applied Mathematics 155, 2546–2554 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. Bansal, N., Blum, A., Chawla, S., Dhamdhere, K.: Scheduling for flow-time with admission control. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 43–54. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  12. Engels, D.W., Karger, D.R., Kolliopoulos, S.G., Sengupta, S., Uma, R.N., Wein, J.: Techniques for scheduling with rejection. Journal of Algorithms 49, 175–191 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. Moghaddam, A., Yalaoui, F., Amodeo, L., Karimi, B., Jolai, F.: Developing a Technique for a Bi-objective Scheduling Model with Rejection by Simulated Annealing. In: MOSIM 2010, Hammamet, Tunisia (2010)

    Google Scholar 

  14. Jolai, F., Sangari, M.S., Babaie, M.: Pareto simulated annealing and colonial competitive algorithm to solve an offline scheduling problem with rejection. In: Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, doi: 10.1243/09544054JEM1746

    Google Scholar 

  15. Moghaddam, A., Yalaoui, F., Amodeo, L.: Single Machine Scheduling with Rejection: Minimizing total Weighted Completion Time and Rejection Cost. In: EURO XXIV, Lisbon, Portugal (2010)

    Google Scholar 

  16. Ulungu, E.L., Teghem, J.: The two phases method: An efficient procedure to solve bi-objective combinatorial optimization problems. Foundation of Computing and Decision Sciences 20(2), 149–165 (1995)

    MathSciNet  MATH  Google Scholar 

  17. Moghaddam, A., Amodeo, L., Yalaoui, F.: Simulated annealing for a bi-objective scheduling problem with rejection: comparative study. In: META 2010, Djerba, Tunisia (2010)

    Google Scholar 

  18. Dugardin, F., Yalaoui, F., Amodeo, L.: New multi-objective method to solve reentrant hybrid flow shop scheduling problem. European Journal of Operational Research 203, 22–31 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  19. Kostreva, M.M., Ogryczak, W., Wierzbicki, A.: Equitable aggregation and multiple criteria analysis. European Journal of Operational Research 158, 362–377 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  20. Golden, B., Perny, P.: Infinite order Lorenz dominance for fair multiagent optimization. In: van der Hoek, W., Kaminka, G.A., Lespérance, Y., Luck, M., Sen, S.: (eds.) Conf. on Autonomous Agents and Multiagent Systems (AAMAS 2010), Toronto, Canada, May 10-14, pp. 383–390 (2010)

    Google Scholar 

  21. Perny, P., Spanjaard, O., Storme, L.-X.: A decision-theoretic approach to robust optimization in multivalued graphs. Annals of Operations Research 147, 317–341 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  22. Moghaddam, A., Amodeo, L., Yalaoui, F.: Single Machine Scheduling with Rejection: Minimizing total Weighted Completion Time and Rejection Cost. Journal of Mathematical Modelling and Algorithms (to be submitted)

    Google Scholar 

  23. McCormick, G.P.: Computability of global solutions to factorable nonconvex programs: Part I - Convex underestimating problems. Mathematical Programming 10, 146–175 (1976)

    Article  MATH  Google Scholar 

  24. Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220, 671–680 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  25. Mansouri, S.A.: A simulated annealing approach to a bi-criteria sequencing problem in a two-stage supply chain. Computers and Industrial Engineering, 1–15 (2006)

    Google Scholar 

  26. Varadharajan, T.K., Rajendran, C.: A multi-objective simulated-annealing algorithm for scheduling in flowshops to minimize the makespan and total flowtime of jobs. European Journal of Operational Research 167, 772–795 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  27. Ulungu, E.L., Teghem, J., Fortemps, P.H., Tuyttens, D.: MOSA method: A tool for solving multiobjective combinatorial optimization problems. Journal of Multi-Criteria Decision Analysis 8, 221–236 (1999)

    Article  MATH  Google Scholar 

  28. Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Fonseca, V.G.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Transactions on Evolutionary Computation 7, 117–132 (2003)

    Article  Google Scholar 

  29. Riise, A.: Comparing genetic algorithms and tabu search for multi-objective optimization. In: IFORS, Proceedings of Abstract Conference, p. 29 (2002)

    Google Scholar 

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Author information

Authors and Affiliations

  1. ICD, LOSI, University of Technology of Troyes, 12 rue Marie Curie, 10010, Troyes, France

    Atefeh Moghaddam, Farouk Yalaoui & Lionel Amodeo

Authors
  1. Atefeh Moghaddam
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  2. Farouk Yalaoui
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  3. Lionel Amodeo
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Federal University of Minas Gerais, Av. Antônio Carlos 6627, 31270-901, Belo Horizonte, MG, Brazil

    Ricardo H. C. Takahashi

  2. Department of Mechanical Engineering, Indian Institute of Technology Kanpur, 208 016, Kanpur, India

    Kalyanmoy Deb

  3. Department of Computer Engineering, Centro Federal de Educaçao Tecnológica de Minas Gerais, Av. Amazonas 5253, 30421-169, Belo Horizonte, MG, Brazil

    Elizabeth F. Wanner

  4. Faculty of Economics, University of Catania, Corso Italia 55, 95129, Catania, Italy

    Salvatore Greco

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© 2011 Springer-Verlag Berlin Heidelberg

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Moghaddam, A., Yalaoui, F., Amodeo, L. (2011). Lorenz versus Pareto Dominance in a Single Machine Scheduling Problem with Rejection. In: Takahashi, R.H.C., Deb, K., Wanner, E.F., Greco, S. (eds) Evolutionary Multi-Criterion Optimization. EMO 2011. Lecture Notes in Computer Science, vol 6576. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19893-9_36

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  • DOI: https://doi.org/10.1007/978-3-642-19893-9_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-19892-2

  • Online ISBN: 978-3-642-19893-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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