Using Multi-Objective Particle Swarm Optimization for Bi-objective Multi-Mode Resource-Constrained Project Scheduling Problem
In this paper the multi-mode resource-constrained project scheduling problem with discounted cash flows is considered. Minimizing the makespan and maximization the net present value (NPV) are the two common objectives that have been investigated in the literature. We apply one evolutionary algorithm named multiobjective particle swarm optimization (MOPSO) to find Pareto front solutions. We used standard sets of instances from the project scheduling problem library (PSPLIB). The results are computationally compared respect to different metrics taken from the literature on evolutionary multi-objective optimization.
[1] J. Blazewicz, J.K. Lenstra and A.H.G RinnooyKan, "SchedulingSubject
to resource constraints:classification and complexity",Discrete Applied
Mathematics, vol. 5, pp. 11-24, 1983.
[2] P. Bricker, A. Drexl, R. Mohring, K. Neumann and E. Pesch, "Resourceconstrained
project scheduling: Notation, classification, models and
methods", European Journal of Operational Research, vol. 112, pp.3-
41,1999.
[3] S. Hartmann and D. Briskorn, "A Survey of variants and extensions of
the resource-constrained project scheduling problem", European Journal
of Operational Research, to be published.
[4] J. Jozefowska, M. Mika, R. Rozycki, G. Waligora, and J.
welgarez,"Simulated annealing for multi-mode recourse-constrained
project scheduling",Annals of Operational Research,vol. 102, pp.137-
155, 2001.
[5] K. Bouleimen and H. Lecocq, "A new efficient simulated annealing for
the recourse constrained project scheduling problem and its multiple
mode version",European Journal of Operational Research, vol.149,
pp.268-281, 2003.
[6] J. ALcaraz, C. Maroto and R. Ruiz, "Solving the multi-mode recourseconstrained
project scheduling problem with genetic algorithms".
Journal of the Operational Research Society, vol. 54, pp.614-626, 2003.
[7] S. Hartmann and A. Drexl, "Project scheduling with multi modes: A
comparison of exact algorithms",Network, vol. 32, pp. 283-297, 1998.
[8] M. Mori and CC. Tseng, "A genetic algorithm for multi-mode recourseconstrained
project scheduling problem". European Journal of
Operational Research, vol. 100, pp.134-141, 1997.
[9] B. Jarboui, N. Damak, P. siarry and A. Rebai, "A combinatorial particle
swarm optimization for solving multi-mode resource-constrained project
scheduling problem",Applied Mathematics and Computation,vol. 115,
pp.195-299, 2008.
[10] R. Kolisch and S. Hartmann, "Experimental investigation of heuristics
for recourse-constrained project scheduling: An update". European
Journal of Operational Research, vol.174, pp.23-37, 2006.
[11] M. Mika, G. Waligora and J. weglarz, "Simulated annealing and tabu
search for multi-mode resource-constrained project scheduling with
positive discounted cash flows and different payment models",
European Journal of Operational Research, vol. 164, pp. 639-668,
2005.
[12] G. Ulusoy, F. Sivrikaya and ┼×. ┼×ahin, "Four payment models for the
multi-mode resource constrained project scheduling problem
withdiscounted cash flows". Annals of Operations research, vol. 102,
pp. 237-261, 2001.
[13] G.Waligora, "Discrete-continuous project scheduling with discounted
Cash Flows-a tabu search approach". Computers &Operations Research,
vol.35, pp. 2141- 2153,2008.
[14] N. Nudtasomboon, S.U. Randhawa, "Resource-constrained project
scheduling with renewable and non-renewable resources and timeresource
tradeoffs", Computers and Industrial Engineering, vol.32,
pp.227-242,1997.
[15] S. Vob, A. Witt., "Hybrid flow shop scheduling as multi-mode multiproject
scheduling problem with batching requirements: A real-world
application", International Journal of Production Economics,
vol.105,pp. 445-458, 2007.
[16] R.Slowinski, B.Soniewicki, J.Weglarz,"DSS for multi-objective project
scheduling", European journal of operational research, vol.79, pp. 220-
229,1994.
[17] J. Nabrzyunski, J. Weglarz, Knowledge-based multi-objective project
scheduling problems, In: J. Welgarz, editor. Project scheduling: recent
models, algorithms and applications. Kluwer academic Publishers, pp.
383-411,1999.
[18] C.A. CoelloCoello, G.B. Lamont and D.A. Van Veldhuizen.and G.B.
Lamont, Evolutionary algorithms for solving multi-objective problems.
Norwell, MA: Kluwer, 2002.
[19] A. Schirmer, "New insight on the complexity of resource-constrained
Project scheduling-two cases of multi-mode scheduling", University of
Kiel, Germany, 1996.
[20] J. Kennedy and R .Eberhart, "Particle swarm optimization". In
IEEEInternational Conference on Neural Networks, Pert, Australia,
1995, pp. 1942-1498.
[21] C.A.CoelloCoello and M.S. Lechuga, "A proposal for Multi-objective
particle swarm optimization". In Congress on Evolutionary
Computation, Piscataway,New Jersey, 2002, pp.1051-1056
[22] M. Reyes and C.A.CoelloCoello, "Multi-objective particle Swarm
optimizers: A survey of the state-of-the-arT". International Journal of
Computational Intelligence Research, vol.2, pp. 287-308, 2006.
[23] C.A. CoelloCoello, G.T.Pulido and M.S.Lechuga, "Handling multiobjectives
with particle swarm optimization". IEEE Transactions on
Evolutionary Computation, vol. 8, pp.256-279,2004.
[24] J. R. Scott, "Fault tolerant design using single and multi-criteria genetic
algorithm optimization". Master's thesis, Department of Aeronautics and
Astronautics, Massachusetts Institute of Technology, USA, 1995.
[25] E. Zitzler and L. Thiele, "Multi objective optimization using
evolutionary algorithms, a comparative case study". InFifth
International Conference on Parallel Problem Solving, Berlin,
Germany, 1998, pp. 292-301.
[26] R. Kolisch and A. Sprecher, "PSPLIB- a project scheduling problem
library", European Journal of Operational Research, vol.96, pp.205-
216, 1996.
[27] J. Welgarz, editor.Project scheduling: recent models, algorithms and
applications. Kluwer academic Publishers, 1999.
[1] J. Blazewicz, J.K. Lenstra and A.H.G RinnooyKan, "SchedulingSubject
to resource constraints:classification and complexity",Discrete Applied
Mathematics, vol. 5, pp. 11-24, 1983.
[2] P. Bricker, A. Drexl, R. Mohring, K. Neumann and E. Pesch, "Resourceconstrained
project scheduling: Notation, classification, models and
methods", European Journal of Operational Research, vol. 112, pp.3-
41,1999.
[3] S. Hartmann and D. Briskorn, "A Survey of variants and extensions of
the resource-constrained project scheduling problem", European Journal
of Operational Research, to be published.
[4] J. Jozefowska, M. Mika, R. Rozycki, G. Waligora, and J.
welgarez,"Simulated annealing for multi-mode recourse-constrained
project scheduling",Annals of Operational Research,vol. 102, pp.137-
155, 2001.
[5] K. Bouleimen and H. Lecocq, "A new efficient simulated annealing for
the recourse constrained project scheduling problem and its multiple
mode version",European Journal of Operational Research, vol.149,
pp.268-281, 2003.
[6] J. ALcaraz, C. Maroto and R. Ruiz, "Solving the multi-mode recourseconstrained
project scheduling problem with genetic algorithms".
Journal of the Operational Research Society, vol. 54, pp.614-626, 2003.
[7] S. Hartmann and A. Drexl, "Project scheduling with multi modes: A
comparison of exact algorithms",Network, vol. 32, pp. 283-297, 1998.
[8] M. Mori and CC. Tseng, "A genetic algorithm for multi-mode recourseconstrained
project scheduling problem". European Journal of
Operational Research, vol. 100, pp.134-141, 1997.
[9] B. Jarboui, N. Damak, P. siarry and A. Rebai, "A combinatorial particle
swarm optimization for solving multi-mode resource-constrained project
scheduling problem",Applied Mathematics and Computation,vol. 115,
pp.195-299, 2008.
[10] R. Kolisch and S. Hartmann, "Experimental investigation of heuristics
for recourse-constrained project scheduling: An update". European
Journal of Operational Research, vol.174, pp.23-37, 2006.
[11] M. Mika, G. Waligora and J. weglarz, "Simulated annealing and tabu
search for multi-mode resource-constrained project scheduling with
positive discounted cash flows and different payment models",
European Journal of Operational Research, vol. 164, pp. 639-668,
2005.
[12] G. Ulusoy, F. Sivrikaya and ┼×. ┼×ahin, "Four payment models for the
multi-mode resource constrained project scheduling problem
withdiscounted cash flows". Annals of Operations research, vol. 102,
pp. 237-261, 2001.
[13] G.Waligora, "Discrete-continuous project scheduling with discounted
Cash Flows-a tabu search approach". Computers &Operations Research,
vol.35, pp. 2141- 2153,2008.
[14] N. Nudtasomboon, S.U. Randhawa, "Resource-constrained project
scheduling with renewable and non-renewable resources and timeresource
tradeoffs", Computers and Industrial Engineering, vol.32,
pp.227-242,1997.
[15] S. Vob, A. Witt., "Hybrid flow shop scheduling as multi-mode multiproject
scheduling problem with batching requirements: A real-world
application", International Journal of Production Economics,
vol.105,pp. 445-458, 2007.
[16] R.Slowinski, B.Soniewicki, J.Weglarz,"DSS for multi-objective project
scheduling", European journal of operational research, vol.79, pp. 220-
229,1994.
[17] J. Nabrzyunski, J. Weglarz, Knowledge-based multi-objective project
scheduling problems, In: J. Welgarz, editor. Project scheduling: recent
models, algorithms and applications. Kluwer academic Publishers, pp.
383-411,1999.
[18] C.A. CoelloCoello, G.B. Lamont and D.A. Van Veldhuizen.and G.B.
Lamont, Evolutionary algorithms for solving multi-objective problems.
Norwell, MA: Kluwer, 2002.
[19] A. Schirmer, "New insight on the complexity of resource-constrained
Project scheduling-two cases of multi-mode scheduling", University of
Kiel, Germany, 1996.
[20] J. Kennedy and R .Eberhart, "Particle swarm optimization". In
IEEEInternational Conference on Neural Networks, Pert, Australia,
1995, pp. 1942-1498.
[21] C.A.CoelloCoello and M.S. Lechuga, "A proposal for Multi-objective
particle swarm optimization". In Congress on Evolutionary
Computation, Piscataway,New Jersey, 2002, pp.1051-1056
[22] M. Reyes and C.A.CoelloCoello, "Multi-objective particle Swarm
optimizers: A survey of the state-of-the-arT". International Journal of
Computational Intelligence Research, vol.2, pp. 287-308, 2006.
[23] C.A. CoelloCoello, G.T.Pulido and M.S.Lechuga, "Handling multiobjectives
with particle swarm optimization". IEEE Transactions on
Evolutionary Computation, vol. 8, pp.256-279,2004.
[24] J. R. Scott, "Fault tolerant design using single and multi-criteria genetic
algorithm optimization". Master's thesis, Department of Aeronautics and
Astronautics, Massachusetts Institute of Technology, USA, 1995.
[25] E. Zitzler and L. Thiele, "Multi objective optimization using
evolutionary algorithms, a comparative case study". InFifth
International Conference on Parallel Problem Solving, Berlin,
Germany, 1998, pp. 292-301.
[26] R. Kolisch and A. Sprecher, "PSPLIB- a project scheduling problem
library", European Journal of Operational Research, vol.96, pp.205-
216, 1996.
[27] J. Welgarz, editor.Project scheduling: recent models, algorithms and
applications. Kluwer academic Publishers, 1999.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:61300", author = "Fatemeh Azimi and Razeeh Sadat Aboutalebi and Amir Abbas Najafi", title = "Using Multi-Objective Particle Swarm Optimization for Bi-objective Multi-Mode Resource-Constrained Project Scheduling Problem", abstract = "In this paper the multi-mode resource-constrained project scheduling problem with discounted cash flows is considered. Minimizing the makespan and maximization the net present value (NPV) are the two common objectives that have been investigated in the literature. We apply one evolutionary algorithm named multiobjective particle swarm optimization (MOPSO) to find Pareto front solutions. We used standard sets of instances from the project scheduling problem library (PSPLIB). The results are computationally compared respect to different metrics taken from the literature on evolutionary multi-objective optimization.
", keywords = "Evolutionary multi-objective optimization makespan, multi-mode, resource constraint, net present value.", volume = "5", number = "6", pages = "1119-5", }
