Fuzzy greedy search heuristic for combinatorial optimization with specific application to machine scheduling

References

• Baker, K. R. (1974). Introduction to sequencing and scheduling. New York, NY: John Wiley & Sons.
   Google Scholar
• Bang-Jensen, J., Gutin, G., & Yeo, A. (2004). When the greedy algorithm fails. Discrete Optimization, 1, 121–127. 10.1016/j.disopt.2004.03.007
   Google Scholar
• Beasley, J. E. (1990). An algorithm for set covering problems. European Journal of Operational Research, 31, 85–93.
   Web of Science ®Google Scholar
• Boschetti, M., & Maniezzo, V. (2015). A set covering based matheuristic for a real-world city logistics problem. International Transactions in Operational Research, 22, 169–195. 10.1111/itor.12110
   Web of Science ®Google Scholar
• Brucker, P. (2001). Scheduling algorithms (3rd ed.). Berlin, Heidelberg: Springer-Verlag. 10.1007/978-3-662-04550-3
   Google Scholar
• Cela, E., Deineko, V. G., & Woeginger, G. J. (2014). Linearizable special cases of the QAP. Journal of Combinatorial Optimization, 1–11.
   Web of Science ®Google Scholar
• Coelho, L. C., & Laporte, G. (2015). Classification, models and exact algorithms for multi-compartment delivery problems. European Journal of Operational Research, 242, 854–864. 10.1016/j.ejor.2014.10.059
   Web of Science ®Google Scholar
• Cook, S. A. (1971). The complexity of theorem-proving procedures. In Michael A. Harrison, Ranan B. Banerji and Jeffrey D. Ullman (Eds). Proceedings of the 3rd Annual ACM symposium on theory of computing (pp. 151–158). Ohio: Shaker Heights.
   Google Scholar
• Cook, W. J., Cunningham, W. H., Pulleyblank, W. R., & Schrijver, A. (1998). Combinatorial optimization. New York, NY: John Wiley & Sons.
   Google Scholar
• Cormen, T., Leiserson, C. E., & Rivest, R. L. (1990). Introduction to algorithms. Cambridge, Massachusetts: The MIT Press.
   Google Scholar
• Curtis, S. A. (2003). The classification of greedy algorithms. Science of Computer Programming, 49, 125–157. 10.1016/j.scico.2003.09.001
   Web of Science ®Google Scholar
• Dijkstra, E. W. (1959). A note on two problems in connexion with graphs. Numerische Mathematik, 1, 269–271. 10.1007/BF01386390
   Web of Science ®Google Scholar
• Du, D. Z., & Pardalos, P. M. (Eds.). (2005). Handbook of combinatorial optimization. Berlin: Springer-Verlag.
   Google Scholar
• Edmonds, J. (1971). Matroids and the greedy algorithm. Math Programming, 1, 126–136.
   Google Scholar
• Framinan, J. M., Leisten, R., & Ruiz-Usano, R. (2002). Efficient heuristics for flowshop sequencing with the objectives of makespan and flowtime minimisation. European Journal of Operational Research, 141, 559–569. 10.1016/S0377-2217(01)00278-8
   Web of Science ®Google Scholar
• Framinan, J. M., Leisten, R., & Ruiz, R. (2005). Comparison of heuristics for flowtime minimisation in permutation flowshops. Computers & Operations Research, 32, 1237–1254.
   Web of Science ®Google Scholar
• Framinan, J. M., Leisten, R., & Rajendran, C. (2003). Different initial sequences for the heuristic of Nawaz, Enscore and Ham to minimize makespan, idletime or flowtime in the static permutation flowshop sequencing problem. International Journal of Production Research, 41, 121–148. 10.1080/00207540210161650
   Web of Science ®Google Scholar
• French, S. (1982). Sequencing and scheduling: An introduction to the mathematics of the job-shop. England: Ellis Horwood.
   Google Scholar
• Garey, M. R., Johnson, D. S., & Sethi, R. (1976). The complexity of flowshop and jobshop scheduling. Mathematics of Operations Research, 1, 117–129. 10.1287/moor.1.2.117
   Google Scholar
• Garey, M. R., & Johnson, D. S. (1979). Computers and intractability a guide to the theory of NP-completeness. W.H. Freeman and Company, San Francisco
   Google Scholar
• Gonzalez, T., & Sahni, S. (1978). Flowshop and Jobshop Schedules: Complexity and Approximation. Operations Research, 26, 36–52.10.1287/opre.26.1.36
   Web of Science ®Google Scholar
• Grimaldi, R. P. (1989). Discrete and combinatorial mathematics. New York, NY: Addison-Wesley.
   Google Scholar
• Gutin, G., & Punnen, A. P. (Eds.). (2002). The traveling salesman problem and its variations. Dordrecht: Kluwer Academic Publishers.
   Google Scholar
• Gutin, G., & Yeo, A. (2002). Anti-matroids. Operations research letters, 30, 97–99. 10.1016/S0167-6377(02)00117-7
   Web of Science ®Google Scholar
• Gutin, G., Yeo, A., & Zverovich, A. (2002). Traveling salesman should not be greedy: domination analysis of greedy-type heuristics for the TSP. Discrete Applied Mathematics, 117, 81–86. 10.1016/S0166-218X(01)00195-0
   Web of Science ®Google Scholar
• Gutin G. (2013). Section 4.6 traveling salesman problems. Jonathan L. Gross, Jay Yellen and Ping Zhang (eds). Handbook of Graph Theory, 336–359.
   Google Scholar
• Ho, J. C. (1995). Flowshop sequencing with mean flowtime objective. European Journal of Operational Research, 81, 571–578. 10.1016/0377-2217(93)E0353-Y
   Web of Science ®Google Scholar
• Horowitz, E., & Sahni, S. (1978). Fundamentals of computer algorithms. Maryland: Computer Science Press.
   Google Scholar
• Johnson, S. M. (1954). Optimal two- and three-stage production schedules with setup times included. Naval Research Logistics Quarterly, 1, 61–68. 10.1002/(ISSN)1931-9193
   Google Scholar
• Klir, G. J., & Yuan, B. (1995). Fuzzy sets and fuzzy logic: Theory and applications. Englewood Cliffs, NJ: Prentice Hall.
   Google Scholar
• Korte B, Lovász L. (1981). Mathematical structures underlying greedy algorithms. In Gecseg F. (ed.) Fundamentals of computation theory. Lecture notes in computer science, Springer-Verlag 117: 205–209.
   Google Scholar
• Korte, B., & Lovász, L. (1983). Structural properties of greedoids. Combinatorica, 3, 359–374. 10.1007/BF02579192
   Web of Science ®Google Scholar
• Korte, B., Schrader, Rainer, & Lovász, László (1991). Greedoids. Berlin: Springer-Verlag. 10.1007/978-3-642-58191-5
   Google Scholar
• Korte B, Vygen J (2012). Combinatorial optimization: Theory and algorithms. Algorithms and combinatorics, Vol. 21, Springer-Verlag Berlin Heidelberg.
   Google Scholar
• Kruskal, J. B. (1956). On the shortest spanning subtree of a graph and the traveling salesman problem. Proceedings of the American Mathematical Society, 7, 48–48. 10.1090/S0002-9939-1956-0078686-7
   Google Scholar
• Lawler, E. L. (1985). The traveling salesman problem: A guided tour of combinatorial optimization. New York, NY: John Wiley & Sons.
   Google Scholar
• Li, X., Wang, Q., & Wu, C. (2009). Efficient composite heuristics for total flowtime minimization in permutation flow shops. Omega the International Journal of Management Science, 37, 155–164. 10.1016/j.omega.2006.11.003
   Web of Science ®Google Scholar
• Liu, J., & Reeves, C. R. (2001). Constructive and composite heuristic solutions to the P//∑Ci scheduling problem. European Journal of Operational Research, 132, 439–452. 10.1016/S0377-2217(00)00137-5
   Web of Science ®Google Scholar
• Martello S and Ries B. (2015). Advances in combinatorial optimization. Discrete Applied Mathematics, 196( C), 1–3. 10.1016/j.dam.2015.08.011
   Web of Science ®Google Scholar
• Nawaz, M., Enscore, E. E., Jr, & Ham, I. (1983). A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem. Omega, 11, 91–95.10.1016/0305-0483(83)90088-9
   Web of Science ®Google Scholar
• Neapolitan, R. E., & Naimipour, K. (2003). Foundations of algorithms using C++ pseudo-code. Boston, MA: Jones & Bartlett Publishers.
   Google Scholar
• Papadimitriou, C. D., & Steiglitz, K. (1982). Combinatorial optimization: Algorithms and complexity. Englewood Cliffs, NJ: Prentice-Hall.
   Google Scholar
• Pinedo, M., Zacharias, C., & Zhu, N. (2015). Scheduling in the service industries: An overview. Journal of Systems Science and Systems Engineering, 24(1), 1–48. 10.1007/s11518-015-5266-0
   Web of Science ®Google Scholar
• Prim, R. C. (1957). Shortest connection networks and some generalizations. Bell System Technical Journal, 36, 1389–1401. 10.1002/bltj.1957.36.issue-6
   Google Scholar
• Pulleyblank W. R. (Ed.) (2014). Progress in combinatorial optimization. Academic Press Canada, Don Mills, Ontario.
   Google Scholar
• Rajendran, C. (1995). Heuristics for scheduling in flowshop with multiple objectives. European Journal of Operational Research, 82, 540–555. 10.1016/0377-2217(93)E0212-G
   Web of Science ®Google Scholar
• Rajendran, C., & Ziegler, H. (1997). An efficient heuristic for scheduling in a flowshop to minimize total weighted flowtime of jobs. European Journal of Operational Research, 103, 129–138. 10.1016/S0377-2217(96)00273-1
   Web of Science ®Google Scholar
• Sheibani K. (2005). Fuzzy greedy evaluation in search, optimisation, and learning. PhD thesis, London Metropolitan University, London, UK.
   Google Scholar
• Sheibani, K. (2010). A fuzzy greedy heuristic for permutation flow-shop scheduling. Journal of the Operational Research Society, 61, 813–818. 10.1057/jors.2008.194
   Web of Science ®Google Scholar
• Sheibani, K. (2013). A constructive heuristic for permutation flow-shop scheduling with the makespan criterion: in a particular case where the sum of the processing times of each job is the same on each machine. Lecture Notes in Management Science, 5, 18–24.
   Google Scholar
• Sule, D. R. (1997). Industrial scheduling. Boston, MA: PWS Publishing Company.
   Google Scholar
• Taillard, E. (1993). Benchmarks for basic scheduling problems. European Journal of Operational Research, 64, 278–285. 10.1016/0377-2217(93)90182-M
   Web of Science ®Google Scholar
• Vince, A. (2002). A framework for the greedy algorithm. Discrete Applied Mathematics, 121, 247–260. 10.1016/S0166-218X(01)00362-6
   Web of Science ®Google Scholar
• Wang, C., Chu, C., & Proth, J. M. (1997). Heuristic approaches for n/m/F/ ∑Ci scheduling problems. European Journal of Operational Research, 96, 636–644. 10.1016/0377-2217(95)00347-9
   Web of Science ®Google Scholar
• Wang, Z., & Klir, G. (2013). Fuzzy measure theory. Springer Science & Business Media, New York.
   Google Scholar
• Whitney, H. (1935). On the abstract properties of linear dependence. American Journal of Mathematics, 57, 509–533.10.2307/2371182
   Google Scholar
• Wilson, R. J. (1985). Introduction to graph theory (3rd ed.). New York, NY: Longman.
   Google Scholar
• Woo, D. S., & Yim, D. S. (1998). A heuristic algorithm for mean flowtime objective in flowshop scheduling. Computers & Operations Research, 25, 175–182.
   Web of Science ®Google Scholar
• Zimmermann, H. J. (2001). Fuzzy set theory—and its applications (4th ed.). Berlin: Springer-Verlag. 10.1007/978-94-010-0646-0
   Google Scholar