Skip to main content
SpringerLink
Log in

A Survey on CP-AI-OR Hybrids for Decision Making Under Uncertainty

  • Chapter
  • First Online:
Hybrid Optimization

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 45))

Abstract

In this survey, we focus on problems of decision making under uncertainty. First, we clarify the meaning of the word “uncertainty” and we describe the general structure of problems that fall into this class. Second, we provide a list of problems from the Constraint Programming, Artificial Intelligence, and Operations Research literatures in which uncertainty plays a role. Third, we survey existing modeling frameworks that provide facilities for handling uncertainty. A number of general purpose and specialized hybrid solution methods are surveyed, which deal with the problems in the list provided. These approaches are categorized into three main classes: stochastic reasoning-based, reformulation-based, and sample-based. Finally, we provide a classification for other related approaches and frameworks in the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Alternatively, in the literature, these variables are also denoted as “stochastic”.

  2. 2.

    http://www.csplib.org

  3. 3.

    The original formulation, proposed in [78], does not directly encode the stage structure in the tuple and actually defines a SCSP as a 6-tuple; consequently the stage structure is given separately. We believe that a more adequate formulation is the one proposed in [30], that explicitly encodes the stage structure as a part of the tuple, giving a 7-tuple.

  4. 4.

    We recall that in SP this corresponds to using a wait-and-see policy and performing a posterior analysis.

References

  1. Apt K (2003) Principles of constraint programming. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  2. Balafoutis T, Stergiou K (2006) Algorithms for stochastic csps. In: Benhamou F (ed) Principles and practice of constraint programming, CP 2006, Proceedings. Lecture notes in computer science, vol 4204. Springer, Heidelberg, pp 44–58

    Google Scholar 

  3. Beck JC, Wilson N (2007) Proactive algorithms for job shop scheduling with probabilistic durations. J Artif Intell Res 28:183–232

    MathSciNet  MATH  Google Scholar 

  4. Bellman RE (1957) Dynamic Programming. Princeton University Press, Princeton

    MATH  Google Scholar 

  5. Benoist T, Bourreau E, Caseau Y, Rottembourg B (2001) Towards stochastic constraint programming: a study of online multi-choice knapsack with deadlines. In: Walsh T (ed) Principles and practice of constraint programming, CP 2001, Proceedings. Lecture notes in computer science, vol 2239. Springer, Heidelberg, pp 61–76

    MATH  Google Scholar 

  6. Bent R, Van Hentenryck P (2004) Regrets only! online stochastic optimization under time constraints. In: Proceedings of the nineteenth national conference on artificial intelligence, sixteenth conference on innovative applications of artificial intelligence, San Jose, California, 25–29 July 2004, pp 501–506

    Google Scholar 

  7. Bent R, Katriel I, Van Hentenryck P (2005) Sub-optimality approximations. In: van Beek P (ed) Principles and practice of constraint programming- CP 2005. 11th International Conference, Sitges, Spain, 1–5 October 2005. Lecture notes in computer science, vol 3709. Springer, Heidelberg, pp 122–136

    Google Scholar 

  8. Berman O, Wang J, Sapna KP (2005) Optimal management of cross-trained workers in services with negligible switching costs. Eur J Oper Res 167(2):349–369

    MathSciNet  MATH  Google Scholar 

  9. Bertsekas DP (1995) Dynamic programming and optimal control. Athena Scientific, Belmont

    MATH  Google Scholar 

  10. Bianchi L, Dorigo M, Gambardella L, Gutjahr W (2009) A survey on metaheuristics for stochastic combinatorial optimization. Nat Comput 8(2):239–287

    MathSciNet  MATH  Google Scholar 

  11. Birge JR, Louveaux F (1997) Introduction to stochastic programming. Springer Verlag, New York

    MATH  Google Scholar 

  12. Bistarelli S, Montanari U, Rossi F (1995) Constraint solving over semirings. In: Proceedings of the fourteenth international joint conference on artificial intelligence, IJCAI ’95, pp 624–630

    Google Scholar 

  13. Bordeaux L, Samulowitz H (2007) On the stochastic constraint satisfaction framework. In: SAC ’07: Proceedings of the 2007 ACM symposium on applied computing, New York, pp 316–320

    Google Scholar 

  14. Brown KN, Miguel I (2006) Uncertainty and change. In: Rossi F, van Beek P, Walsh T (eds) Handbook of constraint programming, chapter 21. Elsevier, Amsterdam

    Google Scholar 

  15. Charnes A, Cooper WW (1963) Deterministic equivalents for optimizing and satisficing under chance constraints. Oper Res 11(1):18–39

    MathSciNet  MATH  Google Scholar 

  16. Davis M, Logemann G, Loveland D (1962) A machine program for theorem-proving. Comm ACM 5(7):394–397

    MathSciNet  MATH  Google Scholar 

  17. Davis M, Putnam H (1960) A computing procedure for quantification theory. J ACM 7(3):201–215

    MathSciNet  MATH  Google Scholar 

  18. Dechter R, Dechter A (1988) Belief maintenance in dynamic constraint networks. In: Proceedings of the 7th national conference on artificial intelligence, AAAI ’88, pp 37–42

    Google Scholar 

  19. Fargier H, Lang J, Martin-Clouaire R, Schiex T (1995) A constraint satisfaction framework for decision under uncertainty. In: UAI ’95: Proceedings of the eleventh annual conference on uncertainty in artificial intelligence, 18–20 August 1995, Montreal, Quebec, Canada, pp 167–174

    Google Scholar 

  20. Freuder EC (1989) Partial constraint satisfaction. In: Proceedings of the eleventh international joint conference on artificial intelligence, IJCAI ’89. Morgan Kaufmann, San Francisco, pp 278–283

    Google Scholar 

  21. Freuder EC, Hubbe PD (1995) Extracting constraint satisfaction subproblems. In: Proceedings of the fourteenth international joint conference on artificial intelligence, IJCAI ’95, Montral, Qubec, Canada, 20–25 August 1995. Morgan Kaufmann, San Francisco, pp 548–557

    Google Scholar 

  22. Freuder EC, Wallace RJ (1992) Partial constraint satisfaction. Artif Intell 58(1–3):21–70

    MathSciNet  Google Scholar 

  23. Garey MR, Johnson DS (1979) Computer and intractability. a guide to the theory of NP-completeness. Bell Laboratories, Murray Hill, New Jersey

    Google Scholar 

  24. Gomez FJ, Schmidhuber J, Miikkulainen R (2006) Efficient non-linear control through neuroevolution. In: Fürnkranz J, Scheffer T, Spiliopoulou M (eds) Machine learning: ECML 2006. 17th European conference on machine learning, Berlin, Germany, 18–22 September 2006 Proceedings. Lecture notes in computer science, vol 4212. Springer, Heidelberg, pp 654–662

    Google Scholar 

  25. Gosavi A (2003) Simulation-based optimization: parametric optimization techniques and reinforcement learning. Kluwer, Norwell

    MATH  Google Scholar 

  26. Hebrard E, Hnich B, Walsh T (2004) Super solutions in constraint programming. In: Régin J-C, Rueher M (eds) Integration of AI and OR techniques in constraint programming for combinatorial optimization problems. First international conference, CPAIOR 2004, Nice, France, 20–22 April 2004, Proceedings. Lecture notes in computer science, vol 3011. Springer, Heidelberg, pp 157–172

    MATH  Google Scholar 

  27. Van Hentenryck P, Bent R, Vergados Y (2006) Online stochastic reservation systems. In: Beck JC, Smith BM (eds) Integration of AI and OR techniques in constraint programming for combinatorial optimization problems. Third international conference, CPAIOR 2006, Cork, Ireland, 31 May–2 June 2006, Proceedings. Lecture notes in computer science, vol 3990. Springer, Heidelberg, pp 212–227

    Google Scholar 

  28. Van Hentenryck P, Michel L, Perron L, Régin J-C Constraint programming in opl. In: Nadathur G (ed) PPDP’99: Proceedings of the international conference on principles and practice of declarative programming. Lecture notes in computer science, vol 1702. 29 September–1 October 1999, pp 98–116

    Google Scholar 

  29. Hewahi NM (2005) Engineering industry controllers using neuroevolution. AI EDAM 19(1):49–57

    Google Scholar 

  30. Hnich B, Rossi R, Tarim SA, Prestwich SD (2009) Synthesizing filtering algorithms for global chance-constraints. In: Principles and practice of constraint programming, proceedings, CP 2009, Proceedings. Lecture notes in computer science, vol 5732. Springer, Heidelberg, pp 439–453

    Google Scholar 

  31. Jeffreys H (1961) Theory of probability. Clarendon Press, Oxford, UK

    MATH  Google Scholar 

  32. Kall P, Wallace SW (1994) Stochastic programming. Wiley, Chichester

    MATH  Google Scholar 

  33. Katriel I, Kenyon-Mathieu C, Upfal E (2007) Commitment under uncertainty: two-stage stochastic matching problems. In: Arge L, Cachin C, Jurdzinski T, Tarlecki A (eds) Automata, languages and programming. 34th international colloquium, ICALP 2007, Wroclaw, Poland, 9–13 July 2007, Proceedings. Lecture notes in computer science, vol 4596. Springer, Heidelberg, pp 171–182

    Google Scholar 

  34. Kleywegt AJ, Shapiro A, T Homem-De-Mello (2001) The sample average approximation method for stochastic discrete optimization. SIAM J Optim 12(2):479–502

    MathSciNet  MATH  Google Scholar 

  35. Littman ML, Goldsmith J, Mundhenk M (1998) The computational complexity of probabilistic planning. J Artif Intell Res 9:1–36

    MathSciNet  MATH  Google Scholar 

  36. Littman ML, Majercik SM, Pitassi T (2001) Stochastic boolean satisfiability. J Automat Reas 27(3):251–296

    MathSciNet  MATH  Google Scholar 

  37. Liu B (1997) Dependent-chance programming: a class of stochastic optimization. Comput Math Appl 34:89–104

    MathSciNet  MATH  Google Scholar 

  38. Liu B, Iwamura K (1997) Modelling stochastic decision systems using dependent-chance programming. Eur J Oper Res 101:193–203

    MATH  Google Scholar 

  39. Lombardi M, Milano M (2006) Stochastic allocation and scheduling for conditional task graphs in mpsocs. In: Benhamou F (ed) CP 2006: principles and practice of constraint programming. 12th international conference, CP 2006, Nantes, France, 25–29 September 2006, Proceedings. Lecture notes in computer science, vol 4204. Springer, Heidelberg, pp 299–313

    Google Scholar 

  40. Lombardi M, Milano M (2007) Scheduling conditional task graphs. In: Bessiere C (ed) CP 2007: principles and practice of constraint programming. 13th international conference, CP 2007, Providence, RI, USA, 23–27 September 2007, Proceedings. Lecture notes in computer science, vol 4741. Springer, Heidelberg, pp 468–482

    Google Scholar 

  41. Majercik SM (2000) Planning under uncertainty via stochastic satisfiability. PhD thesis, Durham, NC, USA. Supervisor-Littman, Michael L

    Google Scholar 

  42. Majercik SM (2007) Appssat: approximate probabilistic planning using stochastic satisfiability. Int J Approx Reason 45(2):402–419

    MATH  Google Scholar 

  43. Majercik SM (2009) Stochastic boolean satisfiability. In: Frontiers in artificial intelligence and applications, vol 185, chapter 27. IOS Press, Amsterdam, pp 887–925

    Google Scholar 

  44. Majercik SM, Boots B (2005) Dc-ssat: a divide-and-conquer approach to solving stochastic satisfiability problems efficiently. In: Veloso MM, Kambhampati S (eds) Proceedings of the twentieth national conference on artificial intelligence and the seventeenth innovative applications of artificial intelligence conference, 9–13 July 2005, Pittsburgh, Pennsylvania, USA. AAAI Press/The MIT Press, Cambridge, MA, pp 416–422

    Google Scholar 

  45. Majercik SM, Littman ML (1998) Maxplan: a new approach to probabilistic planning. In: Proceedings of the fourth international conference on artificial intelligence planning systems, Pittsburgh, Pennsylvania, USA. AAAI Press, pp 86–93

    Google Scholar 

  46. Majercik SM, Littman ML (2003) Contingent planning under uncertainty via stochastic satisfiability. Artif Intell 147(1–2):119–162

    MathSciNet  MATH  Google Scholar 

  47. Michel L, Van Hentenryck P (2004) Iterative relaxations for iterative flattening in cumulative scheduling. In: Zilberstein S, Koehler J, Koenig S (eds) ICAPS 2004: proceedings of the fourteenth international conference on automated planning and scheduling, 3–7 June 2004, Whistler, British Columbia, Canada. AAAI Press, CA, USA, pp 200–208

    Google Scholar 

  48. Minton S, Johnston MD, Philips AB, Laird P (1992) Minimizing conflicts: a heuristic repair method for constraint satisfaction and scheduling problems. Artif Intell 58(1–3):161–205

    MathSciNet  MATH  Google Scholar 

  49. Powell WB (2007) Approximate dynamic programming: solving the curses of dimensionality (Wiley Series in Probability and Statistics). Wiley-Interscience, New York

    Google Scholar 

  50. Prestwich SD, Tarim A, Rossi R, Hnich B (2008) A cultural algorithm for pomdps from stochastic inventory control. In: Blesa MJ, Blum C, Cotta C, Fernández AJ, Gallardo JE, Roli A, Sampels M (eds) Hybrid metaheuristics. 5th International Workshop, HM 2008, Málaga, Spain, 8–9 October 2008. Proceedings. Lecture notes in computer science, vol 5296. Springer, pp 16–28

    Google Scholar 

  51. Prestwich SD, Tarim A, Rossi R, Hnich B (2008) A steady-state genetic algorithm with resampling for noisy inventory control. In: Rudolph G, Jansen T, Lucas SM, Poloni C, Beume N (eds) PPSN X: parallel problem solving from nature. 10th international conference, Dortmund, Germany, September 13–17, 2008, Proceedings. Lecture notes in computer science, vol 5199. Springer, pp 559–568

    Google Scholar 

  52. Prestwich SD, Tarim SA, Hnich B (2006) Template design under demand uncertainty by integer linear local search. Int J Prod Res 44(22):4915–4928

    MATH  Google Scholar 

  53. Prestwich SD, Tarim SA, Rossi R, Hnich B (2009) Evolving parameterised policies for stochastic constraint programming. In: Principles and practice of constraint programming, CP 2009, Proceedings. Lecture notes in computer science, vol 5732. Springer, pp 684–691

    Google Scholar 

  54. Prestwich SD, Tarim SA, Rossi R, Hnich B (2009) Neuroevolutionary inventory control in multi-echelon systems. In: 1st international conference on algorithmic decision theory, Lecture notes in computer science, vol 5783. Springer, pp 402–413

    Google Scholar 

  55. Proll L, Smith B (1998) Integer linear programming and constraint programming approaches to a template design problem. INFORMS J Comput 10(3):265–275

    MathSciNet  MATH  Google Scholar 

  56. Rossi R, Tarim SA, Hnich B, Prestwich SD (2007) Replenishment planning for stochastic inventory systems with shortage cost. In: Van Hentenryck P, Wolsey LA (eds) Integration of AI and OR techniques in constraint programming for combinatorial optimization problems. 4th International Conference, CPAIOR 2007, Brussels, Belgium, 23–26 May 2007, Proceedings. Lecture notes in computer science, vol 4510. Springer Verlag, pp 229–243

    Google Scholar 

  57. Rossi R, Tarim SA, Hnich B, Prestwich SD (2008) Cost-based domain filtering for stochastic constraint programming. In: Stuckey PJ (ed) Principles and practice of constraint programming. 14th international conference, CP 2008, Sydney, Australia, 14–18 September 2008. Proceedings Lecture notes in computer science, vol 5202. Springer, pp 235–250

    Google Scholar 

  58. Rossi R, Tarim SA, Hnich B, Prestwich SD (2008) A global chance-constraint for stochastic inventory systems under service level constraints. Constraints 13(4):490–517

    MathSciNet  MATH  Google Scholar 

  59. Rossi R, Tarim SA, Hnich B, Prestwich SD, Guran C (2009) A note on liu-iwamura’s dependent-chance programming. Eur J Oper Res 198(3):983–986

    MathSciNet  MATH  Google Scholar 

  60. Rossi R, Tarim SA, Hnich B, Prestwich SD, Karacaer S (2008) Scheduling internal audit activities: a stochastic combinatorial optimization problem. J Comb Optim

    Google Scholar 

  61. Rummery GA, Niranjan M (1994) On-line q-learning using connectionist systems. Technical report, CUED/F-INFENG/TR 166, Cambridge University

    Google Scholar 

  62. Sahinidis NV (2004) Optimization under uncertainty: State-of-the-art and opportunities. Comput Chem Eng 28:971–983

    Google Scholar 

  63. Schiex T, Fargier H, Verfaillie G (1995) Valued constraint satisfaction problems: hard and easy problems. In: Proceedings of the fourteenth international joint conference on artificial intelligence, IJCAI ’95. Morgan Kaufmann, San Francisco, pp 631–639

    Google Scholar 

  64. Stanley KO, Miikkulainen R (2002) Evolving neural network through augmenting topologies. Evol Comput 10(2):99–127

    Google Scholar 

  65. Stein ML (1987) Large sample properties of simulation using latin hypercube sampling. Technometrics 29:143–151

    MathSciNet  MATH  Google Scholar 

  66. Sutton RS, Barto AG (1998) Reinforcement learning: an introduction. The MIT Press, Cambridge

    MATH  Google Scholar 

  67. Tarim SA, Hnich B, Prestwich SD, Rossi R (2008) Finding reliable solution: event-driven probabilistic constraint programming. Ann Oper Res 171(1):77–99

    MathSciNet  MATH  Google Scholar 

  68. Tarim SA, Hnich B, Rossi R, Prestwich SD (2009) Cost-based filtering techniques for stochastic inventory control under service level constraints. Constraints 14(2):137–176

    MathSciNet  MATH  Google Scholar 

  69. Tarim SA, Kingsman BG (2004) The stochastic dynamic production/inventory lot-sizing problem with service-level constraints. Int J Prod Econ 88:105–119

    Google Scholar 

  70. Tarim SA, Kingsman BG (2006) Modelling and computing (R n,S n) policies for inventory systems with non-stationary stochastic demand. Eur J Oper Res 174:581–599

    MATH  Google Scholar 

  71. Tarim SA, Manandhar S, Walsh T (2006) Stochastic constraint programming: a scenario-based approach. Constraints 11(1):53–80

    MathSciNet  MATH  Google Scholar 

  72. Tarim SA, Miguel I (2005) A hybrid benders’ decomposition method for solving stochastic constraint programs with linear recourse. In: Hnich B, Carlsson M, Fages F, Rossi F (eds) Recent advances in constraints. Joint ERCIM/CoLogNET international workshop on constraint solving and constraint logic programming, CSCLP 2005, Uppsala, Sweden, June 20–22, 2005, revised selected and invited papers, Lecture notes in computer science, vol 3978. Springer, pp 133–148

    Google Scholar 

  73. Tarim SA, Smith B (2008) Constraint programming for computing non-stationary (R,S) inventory policies. Eur J Oper Res 189:1004–1021

    MathSciNet  MATH  Google Scholar 

  74. Terekhov D, Beck JC (2008) A constraint programming approach for solving a queueing control problem. J Artif Intell Res 32:123–167

    MathSciNet  MATH  Google Scholar 

  75. Terekhov D, Beck JC (2007) Solving a stochastic queueing control problem with constraint programming. In: Van Hentenryck P, Wolsey LA (eds) Integration of AI and OR techniques in constraint programming for combinatorial optimization problems. 4th international conference, CPAIOR 2007, Brussels, Belgium, May 23–26, 2007, Proceedings. Lecture notes in computer science, vol 4510. Springer, Heidelberg, pp 303–317

    Google Scholar 

  76. Verfaillie G, Jussien N (2005) Constraint solving in uncertain and dynamic environments: a survey. Constraints 10(3):253–281

    MathSciNet  MATH  Google Scholar 

  77. Walsh T (2000) Sat v csp. In: Dechter R (ed) Principles and practice of constraint programming, CP 2000, Proceedings. Lecture notes in computer science, vol 1894. Springer, Heidelberg, pp 441–456

    Google Scholar 

  78. Walsh T (2002) Stochastic constraint programming. In: van Harmelen F (ed) European conference on artificial intelligence, ECAI’2002, Proceedings. IOS Press, Amsterdam, pp 111–115

    Google Scholar 

  79. Zhuang Y, Majercik SM Walkssat: an approach to solving large stochastic satisfiability problems with limited time. Technical report

    Google Scholar 

Download references

Acknowledgements

S. Armagan Tarim and Brahim Hnich are supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under Grant No. SOBAG-108K027. S. Armagan Tarim is supported also by Hacettepe University BAB.

Author information

Authors and Affiliations

  1. Faculty of computer science, Izmir University of Economics, Izmir, Turkey

    Brahim Hnich

Authors
  1. Brahim Hnich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roberto Rossi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Armagan Tarim
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Steven Prestwich
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Brahim Hnich .

Editor information

Editors and Affiliations

  1. , Department of Computer Science, Brown University, Providence, 02912, Rhode Island, USA

    Pascal van Hentenryck

  2. , Department of Electronics, Computer Scie, Università di Bologna, Viale Risorgimento 2, Bologna, 40136, Italy

    Michela Milano

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media LLC

About this chapter

Cite this chapter

Hnich, B., Rossi, R., Tarim, S.A., Prestwich, S. (2011). A Survey on CP-AI-OR Hybrids for Decision Making Under Uncertainty. In: van Hentenryck, P., Milano, M. (eds) Hybrid Optimization. Springer Optimization and Its Applications, vol 45. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1644-0_7

Download citation

Publish with us

Policies and ethics

Search

Navigation