Fuzzy-based adaptive sample-sort simulated annealing for resource-constrained project scheduling

  • Sanjay Kumar Shukla
  • Young Jun SonEmail author
  • M. K. Tiwari


This paper deals with the resource-constrained project scheduling problems (RCPSP), where the activities of a project have to be scheduled with the objective of minimizing the makespan subject to both temporal and resource constraints. Being one of the most intractable problems in the operations research area, RCPSP has often been a target and test bed for establishing new optimization tools and techniques. In order to efficiently solve this computationally complex problem in real time, we propose a parallel intelligent search technique named the fuzzy-based adaptive sample-sort simulated annealing (FASSA) heuristic. The basic ingredients of the proposed heuristic are the serial schedule generation scheme (SGS), sample-sort simulated annealing (SSA), and the fuzzy logic controller (FLC). The serial SGS generates the initial schedules following both the precedence and resource constraints. SSA is basically a serial simulated annealing algorithm, artificially extended across an array of samplers operating at statistically monotonically increasing temperatures. The FLC makes the SSA adaptive in nature by regulating the swapping rate of an activity’s priority during an improved schedule generation process. The implementation results of the FASSA heuristic over extremely hard test bed, adopted from the Project Scheduling Problem Library (PSPLIB), reveal its superiority over most of the currently existing approaches.


Project scheduling Precedence constraints Resource constraints Sample-sort simulated annealing (SSA) Schedule generation scheme (SGS) Fuzzy logic controller (FLC) 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Jozefowska J, Mika M, Rozycki R, Waligora G, Weglarz J (2000) Solving the discrete-continuous project scheduling problem via its discretization. Math Methods Oper Res 52(3):489–499zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Yun YS, Gen M (2002) Advanced scheduling problem using constraint programming techniques in SCM environment. Comput Ind Eng 43(1–2):213–229CrossRefGoogle Scholar
  3. 3.
    Schäffter M (1997) Scheduling with respect to forbidden sets. Discrete Appl Math 72:141–154CrossRefMathSciNetGoogle Scholar
  4. 4.
    Blazewicz J, Lenstra JK, Rinnooy Kan AHG (1983) Scheduling subject to resource constraints: classification and complexity. Discrete Appl Math 5:11–24zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Herroelen W, Demeulemeester E, De Reyck B (1998) Resource-constrained project scheduling: a survey of recent developments. Comput Oper Res 25(4):279–302zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Kolisch R, Padman R (2001) An integrated survey of deterministic project scheduling. OMEGA Int J Manage Sci 29(3):249–272CrossRefGoogle Scholar
  7. 7.
    Klein R (2000) Bidirectional planning: improving priority rule-based heuristics for scheduling resource-constrained projects. Eur J Oper Res 127(3):619–638zbMATHCrossRefGoogle Scholar
  8. 8.
    Kolisch R (1996) Serial and parallel resource-constrained project scheduling methods revisited: theory and computation. Eur J Oper Res 90(2):320–333zbMATHCrossRefGoogle Scholar
  9. 9.
    Sprecher A (2000) Scheduling resource-constrained projects competitively at modest memory requirements. Manage Sci 46(5):710–723CrossRefGoogle Scholar
  10. 10.
    Hartmann S (2002) A self-adapting genetic algorithm for project scheduling under resource constraints. Naval Res Logist 49(5):433–448zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Hindi KS, Yang H, Fleszar K (2002) An evolutionary algorithm for resource-constrained project scheduling. IEEE Trans Evol Comput 6(5):512–518CrossRefGoogle Scholar
  12. 12.
    Valls V, Ballestin F, Quintanilla MS (2003) A hybrid genetic algorithm for the RCPSP. Technical report, Department of Statistics and Operations Research, University of Valencia, SpainGoogle Scholar
  13. 13.
    Valls V, Ballestin F, Quintanilla MS (2004) Justification and RCPSP: a technique that pays. Eur J Oper Res 162(2):375–386Google Scholar
  14. 14.
    Valls V, Quintanilla MS, Ballestin F (2004) Resource-constrained project scheduling: a critical activity reordering heuristic. Eur J Oper Res 149(2):282–301CrossRefGoogle Scholar
  15. 15.
    Bouleimen K, Lecocq H (2003) A new efficient simulated annealing algorithm for the resource-constrained project scheduling problem and its multiple mode version. Eur J Oper Res 149(2):268–281zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Merkle D, Middendorf M, Schmeck H (2002) Ant colony optimization for resource-constrained project scheduling. IEEE Trans Evol Comput 6(4):333–346CrossRefGoogle Scholar
  17. 17.
    Fleszar K, Hindi KS (2004) Solving the resource-constrained project scheduling problem by a variable neighbourhood search. Eur J Oper Res 155(2):402–413zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Debels D, De Reyck B, Leus R, Vanhoucke M (2004) A hybrid scatter search/electromagnetism meta-heuristic for project scheduling. Eur J Oper Res 169(2):638–653CrossRefGoogle Scholar
  19. 19.
    Thompson DR, Bilbro GL (2005) Sample-sort simulated annealing. IEEE Trans Syst Man Cybern Part B Cybern 35(3):625–632CrossRefGoogle Scholar
  20. 20.
    Azencott R (1992) Simulated annealing: parallelization techniques. Wiley, New YorkzbMATHGoogle Scholar
  21. 21.
    Lee SY, Lee KG (1996) Synchronous and asynchronous parallel simulated annealing with multiple Markov chains. IEEE Trans Parallel Distrib Syst 7(10):993–1008CrossRefGoogle Scholar
  22. 22.
    Casotto A, Romeo F, Sangiovanni-Vincentelli A (1987) A parallel simulated annealing algorithm for the placement of macro-cells. IEEE Trans Computer-Aided Design Integr Circuits Syst 6(5):838–847CrossRefGoogle Scholar
  23. 23.
    Witte EE, Chamberlain RD, Franklin MA (1991) Parallel simulated annealing using speculative computation. IEEE Trans Parallel Distrib Syst 2(4):483–494CrossRefGoogle Scholar
  24. 24.
    Nabhan TM, Zomaya AY (1995) A parallel simulated annealing algorithm with low communication overhead. IEEE Trans Parallel Distrib Syst 6(12):1226–1233CrossRefGoogle Scholar
  25. 25.
    Onbaşoglu E, Özdamar L (2001) Parallel simulated annealing algorithms in global optimization. J Global Optim 19(1):27–50CrossRefMathSciNetzbMATHGoogle Scholar
  26. 26.
    Bevilacqua A (2002) A methodological approach to parallel simulated annealing on an SMP system. J Parallel Distrib Comput 62(10):1548–1570zbMATHGoogle Scholar
  27. 27.
    Pao DCW, Lam SP, Fong AS (1999) Parallel implementation of simulated annealing using transaction processing. IEE Proc Comput Digit Tech 46(2):107–113CrossRefGoogle Scholar
  28. 28.
    Mahfoud SW, Goldberg DE (1995) Parallel recombinative simulated annealing: a genetic algorithm. Parallel Comput 21(1):1–28zbMATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Gen M, Cheng R (2000) Genetic algorithms and engineering optimization. Wiley, New YorkGoogle Scholar
  30. 30.
    Lee MA, Takagi H (1993) Dynamic control of genetic algorithm using fuzzy logic techniques. In: Proceedings of the 5th International Conference on Genetic Algorithms (ICGA’93), Urbana-Champaign, Illinois, July 1993, pp 76–83Google Scholar
  31. 31.
    Xu H, Vukovich G (1994) Fuzzy evolutionary algorithm and automatic robot trajectory generation. In: Proceedings of the 1st IEEE International Conference on Evolutionary Computation (EC-IEEE’94), Orlando, Florida, June 1994, pp 595–600Google Scholar
  32. 32.
    Kirkpatrick S, Gelatt CD Jr, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680CrossRefMathSciNetGoogle Scholar
  33. 33.
    Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equations of state calculations by fast computing machines. J Chem Phys 21(6):1087–1092CrossRefGoogle Scholar
  34. 34.
    Hajek B (1998) Cooling schedules for optimal annealing. Math Oper Res 13(2):311–329MathSciNetCrossRefGoogle Scholar
  35. 35.
    Wang PT, Wang GS, Hu ZG (1997) Speeding up the search process of genetic algorithm by fuzzy logic. In: Proceedings of the 5th European Congress on Intelligent Techniques and Soft Computing (EUFIT’97), Aachen, Germany, September 1997, pp 665–671Google Scholar
  36. 36.
    Ross TJ (1995) Fuzzy logic with engineering applications. McGraw-Hill, New YorkzbMATHGoogle Scholar
  37. 37.
    PSPLIB (2000) Project Scheduling Problem Library. Home page at
  38. 38.
  39. 39.
    Kolisch R, Sprecher A (1996) PSPLIB—a project scheduling problem library. Eur J Oper Res 96(1):205–216CrossRefGoogle Scholar
  40. 40.
    Kolisch R, Hartmann A (2005) Experimental investigation of heuristics for resource-constrained project scheduling: an update. Eur J Oper Res (in press)Google Scholar
  41. 41.
    Stinson JP, Davis EW, Khumawala BM (1978) Multiple resource-constrained scheduling using branch and bound. AIIE Trans 10(3):252–259Google Scholar

Copyright information

© Springer-Verlag London Limited 2007

Authors and Affiliations

  • Sanjay Kumar Shukla
    • 1
  • Young Jun Son
    • 2
    Email author
  • M. K. Tiwari
    • 3
  1. 1.Department of Manufacturing EngineeringNational Institute of Foundry and Forge TechnologyRanchiIndia
  2. 2.Department of Systems and Industrial EngineeringUniversity of ArizonaTucsonUSA
  3. 3.Department of Forge TechnologyNational Institute of Foundry and Forge TechnologyRanchiIndia

Personalised recommendations