![](bg8.png)
It is proposed for future works that AIV will be
tested on the entire set of test problems available in
(de Optimizaci´on Aplicada, 2011). An improvement
that will be studied is an incorporation of a Mixed
Integer Programming(MIP) model to AIV for solving
related sub problems.
ACKNOWLEDGEMENTS
The authors thank the Brazilian agencies FAPEMIG
and CNPq, and the Universidade Federal de Ouro
Preto (UFOP) for the financial support on the devel-
opment of this work.
REFERENCES
Al-Salem, A. (2004). Scheduling to minimize makespan on
unrelated parallel machines with sequence dependent
setup times. Engineering Journal of the University of
Qatar, 17(1):177–187.
Arnaout, J., Rabadi, G., and Musa, R. (2010). A two-
stage ant colony optimization algorithm to minimize
the makespan on unrelated parallel machines with
sequence-dependent setup times. Journal of Intelli-
gent Manufacturing, 21(6):693–701.
Baker, K. R. (1974). Introduction to Sequencing and
Scheduling. John Wiley & Sons.
Chang, P. and Chen, S. (2011). Integrating dominance prop-
erties with genetic algorithms for parallel machine
scheduling problems with setup times. Applied Soft
Computing, 11(1):1263–1274.
de Optimizaci´on Aplicada, S. (2011). A web site
that includes benchmark problem data sets and
solutions for scheduling problems. Available at
http://soa.iti.es/problem-instances.
Fleszar, K., Charalambous, C., and Hindi, K. (2011).
A variable neighborhood descent heuristic for
the problem of makespan minimisation on unre-
lated parallel machines with setup times. Jour-
nal of Intelligent Manufacturing, 23(5):1949–1958.
doi:10.1007/s10845-011-0522-8.
Garey, M. and Johnson, D. (1979). Computers and in-
tractability: A guide to the theory of np-completeness.
WH Freeman & Co., San Francisco, 174.
Graham, R., Lawler, E., Lenstra, J., and Kan, A. (1979).
Optimization and approximation in deterministic se-
quencing and scheduling: a survey. Annals of discrete
Mathematics, 5(2):287–326.
Helal, M., Rabadi, G., and Al-Salem, A. (2006). A tabu
search algorithm to minimize the makespan for the
unrelated parallel machines scheduling problem with
setup times. International Journal of Operations Re-
search, 3(3):182–192.
Karp, R. M. (1972). Reducibility among combinatorial
problems. Complexity of Computer Computations,
40(4):85–103.
Kim, D. W., Na, D. G., and Frank Chen, F. (2003). Un-
related parallel machine scheduling with setup times
and a total weighted tardiness objective. Robotics and
Computer-Integrated Manufacturing, 19:173–181.
Logendran, R., McDonell, B., and Smucker, B. (2007).
Scheduling unrelated parallel machines with
sequence-dependent setups. Computers & Oper-
ations research, 34(11):3420–3438.
Lourenc¸o, H. R., Martin, O., and St¨utzle, T. (2003). Iter-
ated local search. In Glover, F. and Kochenberger, G.,
editors, Handbook of Metaheuristics, volume 57 of In-
ternational Series in Operations Research & Manage-
ment Science, pages 321–353. Kluwer Academic Pub-
lishers, Norwell, MA.
Mladenovic, N. and Hansen, P. (1997). Variable neighbor-
hood search. Computers and Operations Research,
24(11):1097–1100.
Montgomery, D. (2007). Design and Analysis of Experi-
ments. John Wiley & Sons, New York, NY, fifth edi-
tion.
Pereira Lopes, M. J. and de Carvalho, J. M. (2007). A
branch-and-price algorithm for scheduling parallel
machines with sequence dependent setup times. Eu-
ropean Journal of Operational Research, 176:1508–
1527.
Rabadi, G., Moraga, R. J., and Al-Salem, A. (2006). Heuris-
tics for the unrelated parallel machine scheduling
problem with setup times. Journal of Intelligent Man-
ufacturing, 17(1):85–97.
Souza, M., Coelho, I., Ribas, S., Santos, H., and Mer-
schmann, L. (2010). A hybrid heuristic algorithm
for the open-pit-mining operational planning prob-
lem. European Journal of Operational Research,
207(2):1041–1051.
Subramanian, A., Drummond, L., Bentes, C., Ochi, L., and
Farias, R. (2010). A parallel heuristic for the vehicle
routing problem with simultaneous pickup and deliv-
ery. Computers & Operations Research, 37(11):1899–
1911.
Vallada, E. and Ruiz, R. (2011). A genetic algorithm for the
unrelated parallel machine scheduling problem with
sequence dependent setup times. European Journal of
Operational Research, 211(3):612–622.
Weng, M. X., Lu, J., and Ren, H. (2001). Unrelated parallel
machine scheduling with setup consideration and a to-
tal weighted completion time objective. International
Journal of Production Economics, 70:215–226.
Ying, K.-C., Lee, Z.-J., and Lin, S.-W. (2012). Makespan
minimisation for scheduling unrelated parallel ma-
chines with setup times. Journal of Intelligent Manu-
facturing, 23(5):1795–1803.
AIV:AHeuristicAlgorithmbasedonIteratedLocalSearchandVariableNeighborhoodDescentforSolvingtheUnrelated
ParallelMachineSchedulingProblemwithSetupTimes
383