Abstract
Genetic algorithms have been applied to many different optimization problems and they are one of the most promising metaheuristics. However, there are few published studies concerning the design of efficient genetic algorithms for resource allocation in project scheduling. In this work we present a robust genetic algorithm for the single-mode resource constrained project scheduling problem. We propose a new representation for the solutions, based on the standard activity list representation and develop new crossover techniques with good performance in a wide sample of projects. Through an extensive computational experiment, using standard sets of project instances, we evaluate our genetic algorithm and demonstrate that our approach outperforms the best algorithms appearing in the literature.
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J. Alcaraz and C. Maroto, A genetic algorithm for the resource-constrained project scheduling problem, in: Proceedings of the Sixth International Workshop on Project Management and Scheduling, eds. G. Barbaroso?lu, S. Karabat?, L. Özdamar and G. Ulusoy (Bo?aziçi University Printing Office, 1998) pp. 7-10.
R. Álvarez-Valdés and J.M. Tamarit, Heuristic algorithms for resource-constrained project scheduling: A review and an empirical analysis, in: Advances in Project Scheduling, eds. R. Slowinski and J. W?glarz (Elsevier, 1989) pp. 114-134.
R. Álvarez-Valdés and J.M. Tamarit, Algoritmos heurísticos deterministas y aleatorios en secuenciación de proyectos con recursos limitados, Qüestiiò 13 (1989) 173–191.
T. Baar, P. Brucker and S. Knust, Tabu-search algorithms and lower bounds for the resourceconstrained project scheduling problem, in: Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, eds. S. Voss, S. Martello, I. Osman and C. Roucairol (Kluwer Academic, 1998) pp. 1-18.
E. Balas, Project scheduling with resource constraints, in: Applications of Mathematical Programming Techniques, ed. E.M.L. Beale (English University Press, 1971) pp. 187-200.
C.E. Bell and J. Han. A new heuristic solution method in resource-constrained project scheduling, Naval Research Logistics 38 (1991) 315–331.
C.E. Bell and K. Park, Solving resource-constrained project scheduling problems by A*-search, Naval Research Logistics 37 (1990) 61–84.
F.F. Boctor, Some efficient multi-heuristic procedures for resource-constrained project scheduling, European Journal of Operational Research 49 (1990) 3–13.
F.F. Boctor, Resource-constrained project scheduling by simulated annealing, International Journal in Production Research 34 (1996) 2335–2351.
K. Bouleimen and H. Lecocq, A new efficient simulated annealing algorithm for the resourceconstrained project scheduling problem, in: Proceedings of the Sixth International Workshop on Project Management and Scheduling, eds. G. Barbaroso?lu, S. Karabat?, L. Özdamar and G. Ulusoy (Bo?aziçi University Printing Office, Istanbul, 1998) pp. 19–22.
P. Brucker, A. Drexl, R. Möhring, K. Neumann and E. Pesch, Resource-constrained project scheduling: Notation, classification, models, and methods, European Journal of Operational Research 112 (1998) 3–41.
P. Brucker, S. Knust, A. Schoo and O. Thiele, A branch and bound algorithm for the resourceconstrained project scheduling problem, European Journal of Operational Research 107 (1998) 272–288.
J.A. Carruthers and A. Battersby, Advances in critical path methods, Operational Research Quarterly 17 (1966) 359–380.
L.D. Chambers, Practical Handbook of Genetic Algorithms: Applications, Vol. I (CRC Press, 1995).
J.-H. Cho and Y.-D. Kim, A simulated annealing algorithm for resource constrained project scheduling problems, Journal of the Operational Research Society 48 (1997) 735–744.
N. Christofides, R. Álvarez-Valdés and J.M. Tamarit, Project scheduling with resource constraints: A branch and bound approach, European Journal of Operational Research 29 (1987) 262–273.
D.F. Cooper, Heuristics for scheduling resource-constrained projects: An experimental investigation, Management Science 22 (1976) 1186–1194.
D.F. Cooper, A note on serial and parallel heuristics for resource-constrained project scheduling, Foundations of Control Engineering 2 (1977) 131–133.
E.M. Davies, An experimental investigation of resource allocation in multiactivity projects, Operational Research Quarterly 24 (1973) 587–591.
E.W. Davis and G.E. Heidorn, An algorithm for optimal project scheduling under multiple resource constraints, Management Science 17 (1971) 803–816.
E.W. Davis and J.H. Patterson, A comparison of heuristic and optimum solutions in resource-constrained project scheduling, Management Science 21 (1975) 944–955.
B. De Reyck and W. Herroelen, A branch-and-bound procedure for the resource-constrained project scheduling problem with generalized precedence relations, European Journal of Operational Research 111 (1998) 152–174
E. Demeulemeester and W. Herroelen, A branch-and-bound procedure for the multiple resource-constrained project scheduling problem, Management Science 38 (1992) 1803–1818.
E. Demeulemeester and W. Herroelen, New benchmark results for the resource-constrained project scheduling problem, Management Science 43 (1997) 1485–1492.
E. Demeulemeester and W. Herroelen, A branch-and-bound procedure for the generalized resourceconstrained project scheduling problem, Operations Research 45 (1997) 201–212.
A. Drexl, Scheduling of project networks by job assignment, Management Science 37 (1991) 1590–1602.
S.E. Elmaghraby, Activity Networks: Project Planning and Control by Network Models (Wiley, 1977).
E.A. Elsayed, Algorithms for project scheduling with resource constraints, International Journal of Production Research 20 (1982) 95–103.
E. Falkenauer, Genetic Algorithms and Grouping Problems (Wiley, 1998).
F. Glover, Tabu search-Part I, ORSA Journal on Computing 1 (1989) 190–206.
F. Glover, Tabu search-Part II, ORSA Journal on Computing 2 (1989) 4–32.
D.E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, 1989).
S. Hartmann, A competitive genetic algorithm for resource-constrained project scheduling, Naval Research Logistics 45 (1998) 733–750.
N.A.J. Hastings, On resource allocation in project networks, Operational Research Quarterly 23 (1972) 217–221.
W. Herroelen, E. Demeulemeester, B. De Reyck, A classification scheme for project scheduling, in: Project Scheduling: Recent Models, Algorithms and Applications, ed. J. W?glarz (Kluwer Academic, 1998) pp. 1-26.
H.J. Holland, Adaptation in Natural and Artificial Systems (University of Michigan Press, 1975).
T. Jones, Crossover, macromutation, and population-based search, in: Proceedings of the Sixth International Conference on Genetic Algorithms, ed. L.J. Eshelman (Morgan Kaufmann, 1995).
J.E. Kelley, The critical-path method: Resources planning and scheduling, in: Industrial Scheduling, eds. J.F. Muth and G.L. Thompson (Prentice-Hall, 1963) pp. 347-365.
S. Kirkpatrick, C.D. Gelatt Jr. and M.P. Vecchi, Optimization by simulated annealing, Science 220 (1983) 671–680.
U. Kohlmorgen, H. Schmeck and K. Haase, Experiences with fine-grained parallel genetic algorithms, Working paper, Institut für Angewandte Informatik und Formale Beschreibungsverfahren, Universität Karlsruhe, Karlsruhe, Germany (1996).
R. Kolisch, Efficient priority rules for the resource-constrained project scheduling problem, Journal of Operations Management 14 (1996) 179–192.
R. Kolisch, Serial and parallel resource-constrained project scheduling methods revisited: Theory and computation, European Journal of Operational Research 90 (1996) 320–333.
R. Kolisch and A. Drexl, Adaptive search for solving hard project scheduling problems, Naval Research Logistics 43 (1996) 23–40.
R. Kolisch and S. Hartmann, Heuristic algorithms for the resource-constrained project scheduling problem: classification and computational analysis, in: Project Scheduling: Recent Models, Algorithms and Applications, ed. J. W?glarz (Kluwer Academic, 1998) pp. 147-178.
R. Kolisch and A. Sprecher, PSPLIB-a project scheduling problem library, European Journal of Operational Research 96 (1996) 205–216.
R. Kolisch, A. Sprecher and A. Drexl, Characterization and generation of a general class of resourceconstrained project scheduling problems, Management Science 41 (1995) 1693–1703.
S.R. Lawrence, Resource constrained project scheduling-A computational comparison of heuristic scheduling techniques, Working paper, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, USA (1985).
J.-K. Lee, and Y.-D. Kim, Search heuristics for resource constrained project scheduling, Journal of the Operational Research Society 47 (1996) 678–689.
V.J. Leon and R. Balakrishnan, Strength and adaptability of problem-space based neighborhoods for resource-constrained scheduling, OR Spektrum 17 (1995) 173–182.
R.K.-Y. Li and J. Willis, An iterative scheduling technique for resource-constrained project scheduling, European Journal of Operational Research 56 (1992) 370–379.
A. Lova, Programación de multiproyectos con recursos limitados: Un enfoque multicriterio, Unpublished Ph.D., Department of Statistics and Operations Research, Universidad Politécnica de Valencia, Valencia, Spain (1997).
A. Mingozzi, V. Maniezzo, S. Ricciardelli and L. Bianco, An exact algorithm for the resource-constrained project scheduling based on a new mathematical formulation, Management Science 44 (1998) 714–729.
M. Mori and C.C. Tseng, A genetic algorithm for multi-mode resource constrained project scheduling problem, European Journal of Operational Research 100 (1997) 134–141.
K.S. Naphade, S.D. Wu and R.H. Storer, Problem space search algorithms for resource-constrained project scheduling, Annals of Operations Research 70 (1997) 307–326.
T. Nazareth, S. Verma, S. Bhattacharya and A. Bagchi, The multiple resource-constrained project scheduling problem: A breadth-first approach, Working Paper, Indian Institute of Management, Calcutta, India (1996).
K. Nonobe and T. Ibaraki, Formulation and tabu search algorithm for the resource constrained project scheduling problem (RCPSP), Working paper, Department of Applied Mathematics and Physics, Kyoto University, Kyoto, Japan (1999).
M.J. Norusis, SPSS Advanced Statistics 6.1 (SPSS, 1994).
L. Özdamar, A genetic algorithm approach to a general category project scheduling problem, IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews 29 (1999) 44–59.
L. Özdamar and G. Ulusoy, An iterative local constraint based analysis for solving the resource constrained project scheduling problem, Journal of Operations Management 14 (1996) 193–208.
L. Özdamar and G. Ulusoy, A note on an iterative forward/backward scheduling technique with reference to a procedure by Li and Willis, European Journal of Operational Research 89 (1996) 400–407.
J.H. Patterson, Alternate methods of project scheduling with limited resources, Naval Research Logistics Quarterly 20 (1973) 767–784.
J.H. Patterson, Project scheduling: The effect of problem structure on heuristic performance, Naval Research Logistics Quarterly 23 (1976) 95–124.
J.H. Patterson, A comparison of exact approaches for solving the multiple constrained resource project scheduling problem, Management Science 30 (1984) 854–867.
J.H. Patterson and W.D. Huber, A horizon-varying, zero-one approach to project scheduling, Management Science 20 (1974) 990–998.
J.H. Patterson and G.W. Roth, Scheduling a project under multiple resource constraints: a zero-one programming approach, AIIE Transactions 8 (1976) 449–455.
J.H. Patterson, R. Slowinski, F.B. Talbot and J. W?glarz, An algorithm for a general class of precedence and resource constrained scheduling problems, in: Advances in Project Scheduling, eds. R. Slowinski and J. W?glarz (Elsevier, 1989) pp. 3-28.
E. Pinson, C. Prins, and F. Rullier, Using tabu search for solving the resource-constrained project scheduling problem, in: Proceedings of the Fourth International Workshop on Project Management and Scheduling (Katholieke Universiteit Leuven, 1994) pp. 102-106.
B. Pollack-Johnson, Hybrid structures and improving forecasting and scheduling in project management, Journal of Operations Management 12 (1995) 101–117.
A.A.B. Pritsker, L.J.Watters and P.M. Wolfe, Multiproject scheduling with limited resources: a zero-one programming approach, Management Science 16 (1969) 93–107.
F.J. Radermacher, Scheduling of project networks, Annals of Operations Research 4 (1985/86) 227–252.
S.E. Sampson and E.N. Weiss, Local search techniques for the generalized resource constrained project scheduling problem, Naval Research Logistics 40 (1993) 665–675.
A. Schirmer and S. Riesenberg, Parameterized heuristics for project scheduling-Biased random sampling methods, Working paper, Instituten für Betriebswirtschaftslehre, Universität Kiel, Kiel, Germany (1997).
A. Schirmer and S. Riesenberg, Class-based control schemes for parameterized project scheduling heuristics, Working paper, Instituten für Betriebswirtschaftslehre, Universität Kiel, Kiel, Germany (1998).
L.R. Shaffer, J.B. Ritter and W.L. Meyer, The Critical-Path Method (McGraw-Hill, 1965).
W.P. Simpson and J.H. Patterson, A multiple-tree search procedure for the resource-constrained project scheduling problem, European Journal of Operational Research 89 (1996) 525–542.
A. Sprecher, Resource Constrained Project Scheduling-Exact Methods for the Multi-Mode Case (Springer, 1994).
A. Sprecher, Solving the RCPSP efficiently at modest memory requirements, Instituten für Betriebswirtschaftslehre, Universität Kiel, Kiel, Germany (1996).
A. Sprecher and A. Drexl, Solving multi-mode resource-constrained project scheduling problems by a simple, general and powerful sequencing algorithm, European Journal of Operational Research 107 (1998) 431–450.
A. Sprecher, R. Kolisch and A. Drexl, Semi-active, active, and non-delay schedules for the resource-constrained project scheduling problem, European Journal of Operational Research 80 (1995) 94–102.
J.P. Stinson, E.W. Davis and B.M. Khumawala, Multiple resource-constrained scheduling using branch and bound, AIIE Transactions 10 (1978) 252–259.
F.B. Talbot and J.H. Patterson, An efficient integer programming algorithm with network cuts for solving resource-constrained scheduling problems, Management Science 24 (1978) 1163–1174.
A. Thesen, Heuristic scheduling of activities under resource and precedence restrictions, Management Science 23 (1976) 412–422.
P.R. Thomas and S. Salhi, An investigation into the relationship of heuristic performance with network-resource characteristics, Journal of the Operational Research Society 48 (1997) 34–43.
P. Tormos, Programación de proyectos con recursos limitados: Técnicas heurísticas basadas en reglas de prioridad, Unpublished Ph.D., Department of Statistics and Operations Research, Universidad Politécnica de Valencia, Valencia, Spain (1996).
G. Ulusoy and L. Özdamar, Heuristic performance and network/resource characteristics in resourceconstrained project scheduling, Journal of the Operational Research Society 40 (1989) 1145–1152.
G. Ulusoy and L. Özdamar, A constraint-based perspective in resource constrained project scheduling, International Journal of Production Research 32 (1994) 693–705.
V. Valls, M.A. Pérez and M.S. Quintanilla, Heuristic performance in large resource-constrained projects, Working paper, Departament of Statistics and Operations Research, Universitat de València, Valencia, Spain (1992).
G.E. Whitehouse and J.R. Brown, GENRES: An extension of Brooks algorithm for project scheduling with resource constraints, Computers and Industrial Engineering 3 (1979) 261–268.
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Alcaraz, J., Maroto, C. A Robust Genetic Algorithm for Resource Allocation in Project Scheduling. Annals of Operations Research 102, 83–109 (2001). https://doi.org/10.1023/A:1010949931021
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DOI: https://doi.org/10.1023/A:1010949931021