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Swarm lexicographic goal programming for fuzzy open shop scheduling

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Abstract

In this work we consider a multiobjective open shop scheduling problem with uncertain processing times and flexible due dates, both modelled using fuzzy sets. We adopt a goal programming model based on lexicographic multiobjective optimisation of both makespan and due-date satisfaction and propose a particle swarm algorithm to solve the resulting problem. We present experimental results which show that this multiobjective approach achieves as good results as single-objective algorithms for the objective with the highest priority, while greatly improving on the second objective.

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References

  • Alcaide, D., Rodriguez-Gonzalez, A., & Sicilia, J. (2006). A heuristic approach to minimize expected makespan in open shops subject to stochastic processing times and failures. International Journal of Flexible Manufacturing Systems, 17, 201–226.

    Article  MATH  Google Scholar 

  • Andresen, M., Bräsel, H., Mörig, M., Tusch, J., Werner, F., & Willenius, P. (2008). Simulated annealing and genetic algorithms for minimizing mean flow time in an open shop. Mathematical and Computer Modelling, 48, 1279–1293.

    Article  MathSciNet  MATH  Google Scholar 

  • Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management Science, 17(4), 141–164.

    Article  MathSciNet  Google Scholar 

  • Belmecheri, F., Prins, C., & Yalaoui, F. L. A. (2013). Particle swarm optimization algorithm for a vehicle routing problem with heterogeneous fleet, mixed backhauls, and time windows. Journal of Intelligent Manufacturing, 24(4), 775–789.

    Article  Google Scholar 

  • Blum, C. (2005). Beam-ACO—hybridizing ant colony optimization with beam search: An application to open shop scheduling. Computers & Operations Research, 32(6), 1565–1591.

    Article  Google Scholar 

  • Bouveret, S., & Lemaître, M. (2009). Computing leximin-optimal solutions in constraint networks. Artificial Intelligence, 173, 343–364.

    Google Scholar 

  • Brucker, P., Hunrink, J., Jurisch, B., & Wöstmann, B. (1997). A branch & bound algorithm for the open-shop problem. Discrete Applied Mathematics, 76, 43–59.

    Article  MathSciNet  MATH  Google Scholar 

  • Celano, G., Costa, A., & Fichera, S. (2003). An evolutionary algorithm for pure fuzzy flowshop scheduling problems. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 11, 655–669.

    Article  MathSciNet  MATH  Google Scholar 

  • Chen, S. M., & Chang, T. H. (2001). Finding multiple possible critical paths using fuzzy PERT. IEEE Transactions on Systems, Man, and Cybernetics-Part B, 31(6), 930–937.

    Article  CAS  Google Scholar 

  • Coshall, J. T., & Charlesworth, R. (2011). A management orientated approach to combination forecasting of tourism demand. Tourism Management, 32, 759–769.

    Article  Google Scholar 

  • Diaz-Balteiro, L., & Romero, C. (2008). Making forestry decisions with multiple criteria: A review and an assessment. Forest Ecology and Management, 255, 3222–3241.

    Article  Google Scholar 

  • Dubois, D. (2011). The role of fuzzy sets in decision sciences: Old techniques and new directions. Fuzzy Sets and Systems, 184, 3–28.

    Google Scholar 

  • Dubois, D., & Prade, H. (1986). Possibility theory: An approach to computerized processing of uncertainty. New York, NY, USA: Plenum Press.

    Google Scholar 

  • Dubois, D., Fargier, H., & Prade, H. (1995). Fuzzy constraints in job-shop scheduling. Journal of Intelligent Manufacturing, 6, 215–234.

    Google Scholar 

  • Dubois, D., Fargier, H., & Fortemps, P. (2003). Fuzzy scheduling: Modelling flexible constraints vs. coping with incomplete knowledge. European Journal of Operational Research, 147, 231–252.

    Article  MathSciNet  MATH  Google Scholar 

  • Ehrgott, M. (2005). Multicriteria optimization (2nd ed.). Berlin: Springer.

    MATH  Google Scholar 

  • Ehrgott, M., & Gandibleux, X. (2000). A survey and annotated bibliography of multiobjective combinatorial optimization. OR Spektrum, 22, 425–460.

    Article  MathSciNet  MATH  Google Scholar 

  • Farahani, R. Z., SteadieSeifi, M., & Asgari, N. (2010). Multiple criteria facility location problems: A survey. Applied Mathematical Modelling, 34, 1689–1709.

    Article  MathSciNet  MATH  Google Scholar 

  • Fortemps, P. (1997). Jobshop scheduling with imprecise durations: A fuzzy approach. IEEE Transactions of Fuzzy Systems, 7, 557–569.

    Article  Google Scholar 

  • Giffler, B., & Thompson, G. L. (1960). Algorithms for solving production scheduling problems. Operations Research, 8, 487–503.

    Article  MathSciNet  MATH  Google Scholar 

  • Gonçalves, J., Magalhaes Mendes, J. J., & Resende, M. G. C. (2005). A hybrid genetic algorithm for the job shop scheduling problem. European Journal of Operational Research, 167, 77–95.

    Google Scholar 

  • González Rodríguez, I., Puente, J., Vela, C. R., & Varela, R. (2008). Semantics of schedules for the fuzzy job shop problem. IEEE Transactions on Systems, Man and Cybernetics, Part A, 38(3), 655–666.

    Article  Google Scholar 

  • González-Rodríguez, I., Palacios, J.J., Vela, C.R., & Puente, J. (2010). Heuristic local search for fuzzy open shop scheduling. In: Proceedings IEEE international conference on fuzzy systems, FUZZ-IEEE2010 (pp. 1858–1865). IEEE.

  • González Rodríguez, I., Vela, C. R., & Puente, J. (2010). A genetic solution based on lexicographical goal programming for a multiobjective job shop with uncertainty. Journal of Intelligent Manufacturing, 21, 65–73.

    Article  Google Scholar 

  • Graham, R., Lawler, E., & Lenstra, J. (1979). Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Mathematics, 4, 287–326.

    Article  MathSciNet  Google Scholar 

  • Guéret, C., & Prins, C. (1998). Classical and new heuristics for the open-shop problem: A computational evaluation. European Journal of Operational Research, 107, 306–314.

    Article  MATH  Google Scholar 

  • Guiffrida, A. L., & Nagi, R. (1998). Fuzzy set theory applications in production management research: A literature survey. Journal of Intelligent Manufacturing, 9, 39–56.

    Article  Google Scholar 

  • Herroelen, W., & Leus, R. (2005). Project scheduling under uncertainty: Survey and research potentials. European Journal of Operational Research, 165, 289–306.

    Article  MATH  Google Scholar 

  • Hu, X., Eberhart, R.C., & Shi, Y. (2003). Swarm intelligence for permutation optimization: A case study of n-queens problem. In: Swarm intelligence symposium, 2003. SIS’03. Proceedings of the 2003 IEEE (pp. 243–246). IEEE.

  • Jia, Q., & Seo, Y. (2013). An improved particle swarm optimization for the resource-constrained project scheduling problem. International Journal of Advanced Manufacturing Technology , 67(9–12), 2627–2638.

    Google Scholar 

  • Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. IEEE international conference on neural networks (pp. 1942–1948). New Jersey: IEEE Press.

    Google Scholar 

  • Kim, B. I., & Son, S. J. (2012). A probability matrix based particle swarm optimization for the capacitated vehicle routing problem. Journal of Intelligent Manufacturing, 23, 1119–1126.

    Article  Google Scholar 

  • Lei, D. (2008). Pareto archive particle swarm optimization for multi-objective fuzzy job shop scheduling problems. International Journal of Advanced Manufacturing Technology, 37, 157–165.

    Article  Google Scholar 

  • Liaw, C. F. (1999). A tabu search algorithm for the open shop scheduling problem. Computers and Operations Research, 26, 109–126.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Liaw, C. F. (2000). A hybrid genetic algorithm for the open shop scheduling problem. European Journal of Operational Research, 124, 28–42.

    Article  MathSciNet  MATH  Google Scholar 

  • Liberatore, F., Ortuño, M.T., Tirado, G., Vitoriano, B., & Scaparra, M. P. (2014). A hierarchical compromise model for the joint optimization of recovery operations and distribution of emergency goods in humanitarian logistics. Computers & Operations Research, 42, 3–13.

    Google Scholar 

  • Liu, B., & Liu, Y. K. (2002). Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems, 10, 445–450.

    Article  Google Scholar 

  • Marinakis, Y., & Marinaki, M. (2013). Particle swarm optimization with expanding neighborhood topology for the permutation flowshop scheduling problem. Soft Computing, 17(7), 1159–1173.

    Article  Google Scholar 

  • Naderi, B., Fatemi Ghomi, S. M. T., Aminnayeri, M., & Zandieh, M. (2011). A study on open shop scheduling to minimise total tardiness. International Journal of Production Research, 49(15), 4657–4678.

  • Niu, Q., Jiao, B., & Gu, X. (2008). Particle swarm optimization combined with genetic operators for job shop scheduling problem with fuzzy processing time. Applied Mathematics and Computation, 205, 148–158.

    Article  MathSciNet  MATH  Google Scholar 

  • Noori-Darvish, S., Mahdavi, I., & Mahdavi-Amiri, N. (2012). A bi-objective possibilistic programming model for open shop scheduling problems with sequence-dependent setup times, fuzzy processing times, and fuzzy due-dates. Applied Soft Computing, 12, 1399–1416.

    Article  Google Scholar 

  • Palacios, J.J., González-Rodríguez, I., Vela, C.R., & Puente, J. (2011). Particle swarm optimisation for open shop problems with fuzzy durations. In: Proceedings of IWINAC 2011, Part I, Springer, Lecture Notes in Computer Science (Vol. 6686, pp. 362–371).

  • Panahi, H., Rabbani, M., & Tavakkoli-Moghaddam, R. (2008). Solving an open shop scheduling problem by a novel hybrid multi-objective ant colony optimization. In: Eighth international conference on hybrid intelligent systems (pp. 320–325). IEEE.

  • Pasandideh, S. H. R., Niaki, S. T. A., & Hajipour, V. (2013). A multi-objective facility location model with batch arrivals: two parameter-tuned meta-heuristic algorithms. Journal of Intelligent Manufacturing, 24(2), 331–348.

    Google Scholar 

  • Petrovic, S., Fayad, S., & Petrovic, D. (2008). Sensitivity analysis of a fuzzy multiobjective scheduling problem. International Journal of Production Research, 46(12), 3327–3344.

    Article  MATH  Google Scholar 

  • Pinedo, M. L. (2008). Scheduling, theory, algorithms, and systems (3rd ed.). Berlin: Springer.

    MATH  Google Scholar 

  • Prins, C. (2000). Competitive genetic algorithms for the open-shop scheduling problem. Mathematical Methods of Operations Research, 52, 389–411.

    Article  MathSciNet  MATH  Google Scholar 

  • Puente, J., Vela, C. R., & González-Rodríguez, I. (2010). Fast local search for fuzzy job shop scheduling. In: Proceedings of ECAI 2010 (pp. 739–744). IOS Press.

  • Puente, J., Vela, C. R., González-Rodríguez, I., Rodríguez, L. J., & Palacios, J. J. (2013). GRASPing examination board assignments for university-entrance exams. In: IEA-AIE 2013, Proceedings of, Springer, Lecture notes in computer science (Vol 7906, pp. 171–180).

  • Romero, C. (2001). Extended lexicographic goal programming: a unifying approach. Omega, 29, 63–71.

    Article  Google Scholar 

  • Sakawa, M., & Kubota, R. (2000). Fuzzy programming for multiobjective job shop scheduling with fuzzy processing time and fuzzy duedate through genetic algorithms. European Journal of Operational Research, 120, 393–407.

    Article  MathSciNet  MATH  Google Scholar 

  • Sha, D., Lin, H. H., & Hsu, C. (2010). A modified particle swarm optimization for multi-objective open shop scheduling. In: Proceeding of the international multiconference of engineers and computer scientists, Vol 3.

  • Sha, D. Y., & Cheng-Yu, H. (2008). A new particle swarm optimization for the open shop scheduling problem. Computers & Operations Research, 35, 3243–3261.

    Article  MATH  Google Scholar 

  • Tamiz, M., Jones, D., & Romero, C. (1998). Goal programming for decision making: An overview of the current state-of-the-art. European Journal of Operations Research, 111, 569–581.

    Article  MATH  Google Scholar 

  • Tassopoulos, I. X., & Beligiannis, G. N. (2012). Using particle swarm optimization to solve effectively the school timetabling problem. Soft Computing, 16, 1229–1252.

    Article  Google Scholar 

  • T’kindt, V., & Billaut, J. C. (2006). Multicriteria scheduling. Theory, models and algorithms (2nd ed.). Berlin: Springer.

    MATH  Google Scholar 

  • Vijay Chakaravarthy, G., Marimuthu, S., & Naveen Sait, A. (2013). Performance evaluation of proposed differential evolution and particle swarm optimization algorithms for scheduling m-machine flow shops with lot streaming. Journal of Intelligent Manufacturing, 24, 175–191.

    Article  Google Scholar 

  • Wang, L., Zhou, G., Xu, Y., & Min, L. (2013). A hybrid artificial bee colony algorithm for the fuzzy flexible job-shop scheduling problem. International Journal of Production Research, 51(2), 3593–3608.

    Google Scholar 

  • Zheng, Y., Li, Y., & Lei, D. (2011). Swarm-based neighbourhood search for fuzzy job shop scheduling. International Journal of Innovative Computing and Applications, 3(3), 144–151.

    Article  Google Scholar 

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Acknowledgments

We would like to thank the anonymous referees for their insightful and constructive comments. This research has been supported by the Spanish Government under research grants FEDER TIN2010-20976-C02-02 and MTM2010-16051 and by the Principality of Asturias (Spain) under grant Severo Ochoa BP13106.

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Authors and Affiliations

  1. Department of Computing, University of Oviedo, Campus de Viesques, 33204 , Gijón, Spain

    Juan José Palacios, Camino R. Vela & Jorge Puente

  2. Department of Mathematics, Statistics and Computing, University of Cantabria, Los Castros s/n, 39005 , Santander, Spain

    Inés González-Rodríguez

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  1. Juan José Palacios
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  2. Inés González-Rodríguez
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  3. Camino R. Vela
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  4. Jorge Puente
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Correspondence to Inés González-Rodríguez.

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Palacios, J.J., González-Rodríguez, I., Vela, C.R. et al. Swarm lexicographic goal programming for fuzzy open shop scheduling. J Intell Manuf 26, 1201–1215 (2015). https://doi.org/10.1007/s10845-013-0850-y

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