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Over-Constrained Problems

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Hybrid Optimization

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

Abstract

Over-constrained problems are ubiquitous in real-world applications. In constraint programming, over-constrained problems can be modeled and solved using soft constraints. Soft constraints, as opposed to hard constraints, are allowed to be violated, and the goal is to find a solution that minimizes the total amount of violation. In this chapter, an overview of recent developments in solution methods for over-constrained problems using constraint programming is presented, with an emphasis on soft global constraints.

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Notes

  1. 1.

    In the literature, domain consistency is also referred to as hyper-arc consistency or generalized arc consistency.

  2. 2.

    In [56], the decomposition-based violation measure is referred to as primal graph based violation cost.

  3. 3.

    Comprehensive to the best of our knowledge.

References

  1. Aarts E, Lenstra JK (eds) (2003) Local search in combinatorial optimization. Princeton University Press, Princeton

    MATH  Google Scholar 

  2. Aggoun A, Beldiceanu N (1993) Extending CHIP in order to solve complex scheduling and placement problems. Math Comput Model 17(7):57–73

    Google Scholar 

  3. Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows Prentice Hall, New Jersey

    Google Scholar 

  4. Apt KR (2003) Principles of constraint programming. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  5. Baptiste P, Le Pape C, Péridy L (1998) Global constraints for partial CSPs: a case-study of resource and due date constraints. In: Maher MJ, Puget J-F (eds) Proceedings of the fourth international conference on principles and practice of constraint programming (CP). Lecture notes in computer science, vol 1520. Springer, Berlin, pp 87–101

    Google Scholar 

  6. Barták R (2003) Dynamic global constraints in backtracking based environments. Ann Oper Res 118(1–4):101–119

    MathSciNet  MATH  Google Scholar 

  7. Beldiceanu N (2000) Global constraints as graph properties on a structured network of elementary constraints of the same type. In: Dechter R (ed) Proceedings of the sixth international conference on principles and practice of constraint programming (CP). Lecture notes in computer science, vol 1894. Springer, Berlin, pp 52–66

    MATH  Google Scholar 

  8. Beldiceanu N, Carlsson M (2001) Revisiting the cardinality operator and introducing the cardinality-path constraint family. In: Codognet P (ed) Proceedings of the 17th international conference on logic programming (ICLP). Lecture notes in computer science, vol 2237. Springer, Berlin, pp 59–73

    Google Scholar 

  9. Beldiceanu N, Contejean E (1994) Introducing global constraints in CHIP. Math Comput Model 20(12):97–123

    MATH  Google Scholar 

  10. Beldiceanu N, Petit T (2004) Cost evaluation of soft global constraints. In: Régin J-C, Rueher M (eds) Proceedings of the first international conference on the integration of AI and OR techniques in constraint programming for combinatorial optimization problems (CPAIOR). Lecture notes in computer science, vol 3011. Springer, Heidelberg, pp 80–95

    MATH  Google Scholar 

  11. Beldiceanu N, Carlsson M, Petit T (2004) Deriving filtering algorithms from constraint checkers. In: Wallace M (ed) Proceedings of the tenth international conference on principles and practice of constraint programming (CP). Lecture notes in computer science, vol 3258. Springer, Berlin, pp 107–122

    MATH  Google Scholar 

  12. Bessiere C, Hebrard E, Hnich B, Kiziltan Z, Quimper C-G, Walsh T (2007) Reformulating global constraints: the slide and regular constraints. In: Miguel I, Ruml W (eds) Proceedings of 7th international symposium on abstraction, reformulation, and approximation (SARA). Lecture notes in computer science, vol 4612. Springer, Berlin, pp 80–92

    Google Scholar 

  13. Bessiere C, Hebrard E, Hnich B, Kiziltan Z, Walsh T (2008) SLIDE: a useful special case of the CARDPATH constraint. In: Ghallab M, Spyropoulos CD, Fakotakis N, Avouris NM, (eds) Proceedings of the 18th European conference on artificial intelligence (ECAI). IOS, Amsterdam, pp 475–479

    Google Scholar 

  14. Bistarelli S, Montanari U, Rossi F (1997) Semiring-based constraint satisfaction and optimization. J ACM 44(2):201–236

    MathSciNet  MATH  Google Scholar 

  15. Bohlin M (2004) Design and implementation of a graph-based constraint constraint model for local search. PhD thesis, Mälardalen University, Licentiate Thesis No. 27

    Google Scholar 

  16. Bohlin M (2005) A local search system for solving constraint problems. In: Seipel D, Hanus M, Geske U, Bartenstein O (eds) Applications of declarative programming and knowledge management. Lecture notes in artificial intelligence, vol 3392. Springer, Berlin, pp 166–184

    Google Scholar 

  17. Borning A, Duisberg R, Freeman-Benson B, Kramer A, Woolf M (1987) Constraint hierarchies. In: Proceedings of the ACM conference on object-oriented programming systems, languages, and applications (OOPSLA), pp 48–60

    Google Scholar 

  18. Cambazard H, Hebrard E, O’Sullivan B, Papadopoulos A (2008) Local search and constraint programming for the post enrolment-based course timetabling problem. In: Proceedings of the 7th international conference on the practice and theory of automated timetabling (PATAT)

    Google Scholar 

  19. Cormen TH, Leiserson CE, Rivest RL, Stein C (2001) Introduction to algorithms – second edition. MIT, Cambridge

    MATH  Google Scholar 

  20. Dechter R (1990) On the expressiveness of networks with hidden variables. In: Proceedings of the 8th national conference on artificial intelligence (AAAI). AAAI/MIT, Cambridge, pp 555–562

    Google Scholar 

  21. Dechter R (2003) Constraint processing Morgan Kaufmann, San Mateo

    Google Scholar 

  22. Dubois D, Fargier H, Prade H (1993) The calculus of fuzzy restrictions as a basis for flexible constraint satisfaction. In: Proceedings of the second IEEE international conference on fuzzy systems, vol 2, pp 1131–1136

    Google Scholar 

  23. Faltings B, Macho-Gonzalez S (2002) Open constraint satisfaction. In: Van Hentenryck P (ed) Proceedings of the 8th international conference on principles and practice of constraint programming (CP 2002). Lecture notes in computer science, vol 2470. Springer, Heidelberg, pp 356–370

    Google Scholar 

  24. Fargier H, Lang J, Schiex T (1993) Selecting preferred solutions in fuzzy constraint satisfaction problems. In: Proceedings of the first European congress on fuzzy and intelligent technologies

    Google Scholar 

  25. Focacci F, Lodi A, Milano M (2002) Optimization-oriented global constraints. Constraints 7(3):351–365

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  Google Scholar 

  27. Galinier P, Hao JK (2000) A general approach for constraint solving by local search. In: Proceedings of the second international workshop on integration of AI and OR techniques in constraint programming for combinatorial optimization problems (CPAIOR)

    MATH  Google Scholar 

  28. Galinier P, Hao JK (2004) A general approach for constraint solving by local search. J Math Model Algorithm 3(1):73–88

    MathSciNet  MATH  Google Scholar 

  29. Hebrard E, O’Sullivan B, Walsh T (2007) Distance constraints in constraint satisfaction. In: Veloso MM (ed) Proceedings of the twentieth international joint conference on artificial intelligence (IJCAI), pp 106–111. Available online at http://ijcai.org/.

  30. Hebrard E, O’Sullivan B, Razgon I (2008) A soft constraint of equality: complexity and approximability. In: Stuckey PJ (ed) Proceedings of the 14th international conference on principles and practice of constraint programming (CP). Lecture notes in computer science, vol 5202. Springer, Berlin, pp 358–371

    Google Scholar 

  31. Hebrard E, Marx D, O’Sullivan B, Razgon I (2009) Constraints of difference and equality: a complete taxonomic characterization. In: Gent IP (ed) Proceedings of the 15th international conference on principles and practice of constraint programming (CP). Lecture notes in computer science, vol 5732. Springer, Berlin, pp 424–438

    Google Scholar 

  32. Hopcroft JE, Karp RM (1973) An n 5 ∕ 2 algorithm for maximum matchings in bipartite graphs. SIAM J Comput 2(4):225–231

    MathSciNet  MATH  Google Scholar 

  33. Hopcroft JE, Ullman JD (1979) Introduction to automata theory, languages, and computation. Addison-Wesley, Reading

    MATH  Google Scholar 

  34. Joseph R-R, Chan P, Hiroux M, Weil G (2007) Decision-support with preference constraints. Eur J Oper Res 177(3):1469–1494

    MathSciNet  MATH  Google Scholar 

  35. Katsirelos G, Narodytska N, Walsh T (2008) The weighted Cfg constraint. In: Perron L, Trick MA (eds) Proceedings of the 5th international conference on the integration of AI and OR techniques in constraint programming for combinatorial optimization problems (CPAIOR). Lecture notes in computer science, vol 5015. Springer, Heidelberg, pp 323–327

    Google Scholar 

  36. Larrosa J (2002) Node and arc consistency in weighted CSP. In: Dechter R, Kearns M, Sutton R (eds) Proceedings of the eighteenth national conference on artificial intelligence. AAAI, Canada, pp 48–53

    Google Scholar 

  37. Larrosa J, Schiex T (2003) In the quest of the best form of local consistency for weighted CSP. In: Gottlob G, Walsh T (eds) Proceedings of the eighteenth international joint conference on artificial intelligence. Morgan Kaufmann, San Francisco, pp 239–244

    Google Scholar 

  38. Lauriere J-L (1978) A language and a program for stating and solving combinatorial problems. Artif intell 10(1):29–127

    MathSciNet  MATH  Google Scholar 

  39. Lee JHM, KL Leung (2009). Towards efficient consistency enforcement for global constraints in weighted constraint satisfaction. In: Boutilier C (ed) Proceedings of the twenty-first international joint conference on artificial intelligence (IJCAI), pp 559–565. Available online at http://ijcai.org/.

  40. Lesaint D, Mehta D, O’Sullivan B, Quesada L, Wilson N (2009) A soft global precedence constraint. In: Boutilier C (ed) Proceedings of the twenty-first international joint conference on artificial intelligence (IJCAI), pp 566–571. Available online at http://ijcai.org/.

  41. Maher MJ (2009) SOGgy constraints: soft open global constraints. In: Gent IP (ed) Proceedings of the 15th international conference on principles and practice of constraint programming (CP). Lecture notes in computer science, vol 5732. Springer, Heidelberg, pp 584–591

    Google Scholar 

  42. Maher MJ (2009) Open contractible global constraints. In: Boutilier C (ed) Proceedings of the twenty-first international joint conference on artificial intelligence (IJCAI), pp 578–583. Available online at http://ijcai.org/

  43. Maher MJ, Narodytska N, Quimper C-G, Walsh T (2008) Flow-based propagators for the SEQUENCE and related global constraints. In: Stuckey PJ (ed) Proceedings of the 14th international conference on principles and practice of constraint programming (CP). Lecture notes in computer science, vol 5202. Springer, Heidelberg, pp 159–174

    Google Scholar 

  44. Métivier J-P, Boizumault P, Loudni S (2007) Σ-alldifferent: softening alldifferent in weighted CSPs. In: Proceedings of the 19th IEEE international conference on tools with artificial Intelligence (ICTAI), IEEE, pp 223–230

    Google Scholar 

  45. Métivier J-P, Boizumault P, Loudni S (2009) Softening Gcc and regular with preferences. In: Proceedings of the 2009 ACM symposium on applied computing (SAC) ACM, pp 1392–1396

    Google Scholar 

  46. Métivier J-P, Boizumault P, Loudni S (2009) Solving nurse rostering problems using soft global constraints. In: Gent IP (ed) Proceedings of the 15th international conference on principles and practice of constraint programming (CP). Lecture notes in computer science, vol 5732. Springer, Berlin, pp 73–87

    Google Scholar 

  47. Michel L, Van Hentenryck P (2002) A constraint-based architecture for local search. In: Proceedings of the ACM conference on object-oriented programming systems, languages, and applications (OOPSLA), pp 101–110

    Google Scholar 

  48. Michel L, Van Hentenryck P (2000) Localizer. Constraints 5:43–84

    MATH  Google Scholar 

  49. Michel L, Van Hentenryck P (1997) Localizer: a modeling language for local search. In: Smolka G (ed) Proceedings of the third international conference on principles and practice of constraint programming (CP). Lecture notes in computer science, vol 1330. Springer, Berlin, pp 237–251

    Google Scholar 

  50. Nareyek A (2001) Using global constraints for local search. In: Constraint programming and large scale discrete optimization: DIMACS workshop constraint programming and large scale discrete optimization, September 14–17, 1998, DIMACS Center. DIMACS series in discrete mathematics and theoretical computer science, vol 54. American Mathematical Society, pp 9–28

    Google Scholar 

  51. Pesant G (2004) A regular language membership constraint for finite sequences of variables. In: Wallace M (ed) Proceedings of the tenth international conference on principles and practice of constraint programming (CP). Lecture notes in computer science, vol 3258. Springer, Berlin, pp 482–495

    MATH  Google Scholar 

  52. Pesant G, Régin J-C (2005) Spread: a balancing constraint based on statistics. In: van Beek P (ed) Proceedings of the 11th international conference on principles and practice of constraint programming (CP). Lecture notes in computer science, vol 3709. Springer, Berlin, pp 460–474

    MATH  Google Scholar 

  53. Petit T (2002) Modélisation et Algorithmes de Résolution de Problèmes Sur-Contraints. PhD thesis, Université Montpellier II. In French

    Google Scholar 

  54. Petit T, Poder E (2008) Global propagation of practicability constraints. In: Perron L, Trick MA (eds) Proceedings of the 5th international conference on the integration of AI and OR techniques in constraint programming for combinatorial optimization problems (CPAIOR). Lecture notes in computer science, vol 5015. Springer, Berlin, pp 361–366

    Google Scholar 

  55. Petit T, Régin J-C, Bessière C (2000) Meta constraints on violations for over constrained problems. In: Proceedings of the 12th IEEE international conference on tools with artificial intelligence (ICTAI). IEEE, pp 358–365

    Google Scholar 

  56. Petit T, Régin J-C, Bessière C (2001) Specific filtering algorithms for over-constrained problems. In: Walsh T (ed) Proceedings of the seventh international conference on principles and practice of constraint programming (CP). Lecture notes in computer science, vol 2239. Springer, Berlin, pp 451–463

    Google Scholar 

  57. Quimper C-G, Walsh T (2006) Decomposing global grammar constraints. In: Benhamou F (ed) Proceedings of the twelfth international conference on principles and practice of constraint programming (CP). Lecture notes in computer science, vol 4204. Springer, Heidelberg, pp 751–755

    Google Scholar 

  58. Quimper C-G, López-Ortiz A, van Beek P, Golynski P (2004) Improved algorithms for the global cardinality constraint. In: Wallace M (ed) Proceedings of the tenth international conference on principles and practice of constraint programming (CP). Lecture notes in computer science, vol 3258. Springer, New York, pp 542–556

    MATH  Google Scholar 

  59. Régin J-C (1994) A filtering algorithm for constraints of difference in CSPs. In: Proceedings of the twelfth national conference on artificial intelligence (AAAI), vol 1. AAAI, pp 362–367

    Google Scholar 

  60. Régin J-C (1996) Generalized arc consistency for global cardinality constraint. In: Proceedings of the thirteenth national conference on artificial intelligence and eighth innovative applications of artificial intelligence conference (AAAI/IAAI), vol 1. AAAI/MIT, pp 209–215

    Google Scholar 

  61. Régin J-C (2003) Global constraints and filtering algorithms. In: Milano M (ed) Constraint and integer programming – toward a unified methodology. Operations research/computer science interfaces, chapter 4, vol 27. Kluwer Academic, Dordrecht

    Google Scholar 

  62. Régin J-C, Petit T, Bessière C, Puget J-F (2000) An original constraint based approach for solving over constrained problems. In: Dechter R (ed) Proceedings of the sixth international conference on principles and practice of constraint programming (CP). Lecture notes in computer science, vol 1894. Springer, Berlin, pp 543–548

    MATH  Google Scholar 

  63. Régin J-C, Petit T, Bessière C, Puget J-F (2001) New lower bounds of constraint violations for over-constrained problems. In: Walsh T (ed) Proceedings of the seventh international conference on principles and practice of constraint programming (CP). Lecture notes in computer science, vol 2239. Springer, Berlin, pp 332–345

    MATH  Google Scholar 

  64. Rossi F, Petrie C, Dhar V (1990) On the equivalence of constraint satisfaction problems. In: Proceedings of the 9th European conference on artificial intelligence (ECAI), pp 550–556

    Google Scholar 

  65. Rossi F, Van Beek P, Walsh T (eds) (2006) Handbook of constraint programming. Elsevier, Amsterdam

    MATH  Google Scholar 

  66. Ruttkay Z (1994) Fuzzy constraint satisfaction. In: Proceedings of the first IEEE conference on evolutionary computing, pp 542–547

    Google Scholar 

  67. Schaus P (2009) Solving balancing and Bin-packing problems with constraint programming. PhD thesis, Université catholique de Louvain

    Google Scholar 

  68. Schaus P, Deville Y, Dupont P (2007) Bound-consistent deviation constraint. In: Bessiere C (ed) Proceedings of the 13th international conference on principles and practice of constraint programming (CP). Lecture notes in computer science, vol 4741. Springer, Berlin, pp 620–634

    Google Scholar 

  69. Schaus P, Deville Y, Dupont P, Régin J-C (2007) The deviation constraint. In: Van Hentenryck P, Wolsey LA (eds) Proceedings of the 4th international conference on the integration of AI and OR techniques in constraint programming for combinatorial optimization problems (CPAIOR). Lecture notes in computer science, vol 4510. Springer, Berlin, pp 260–274

    MATH  Google Scholar 

  70. Schiex T (1992) Possibilistic constraint satisfaction problems or “How to handle soft constraints?”. In: Dubois D, Wellman MP (eds) Proceedings of the eighth annual conference on uncertainty in artificial intelligence. Morgan Kaufmann, San Francisco, pp 268–275

    Google Scholar 

  71. 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. Morgan Kaufmann, San Francisco, pp 631–639

    Google Scholar 

  72. Schrijver A (2003) Combinatorial optimization – polyhedra and efficiency. Springer, Berlin

    MATH  Google Scholar 

  73. Sellmann M (2006) The theory of grammar constraints. In: Benhamou F (ed) Proceedings of the twelfth international conference on principles and practice of constraint programming (CP). Lecture notes in computer science, vol 4204. Springer, Heidelberg, pp 530–544

    MATH  Google Scholar 

  74. Tarjan R (1972) Depth-first search and linear graph algorithms. SIAM J Comput 1:146–160

    MathSciNet  MATH  Google Scholar 

  75. Van Hentenryck P, Michel L (2005) Constraint-based local search. MIT, Cambridge

    MATH  Google Scholar 

  76. van Hoeve W-J (2004) A hyper-arc consistency algorithm for the soft alldifferent constraint. In: Wallace M (ed) Proceedings of the tenth international conference on principles and practice of constraint programming (CP). Lecture notes in computer science, vol 3258. Springer, Berlin, pp 679–689

    Google Scholar 

  77. van Hoeve W-J, Katriel I (2006) Global constraints. In: Rossi F, Van Beek P, Walsh T (eds) Handbook of constraint programming, chapter 6. Elsevier, New York

    Google Scholar 

  78. van Hoeve W-J, Régin J-C (2006) Open constraints in a closed world. In: Beck JC, Smith BM (eds) Proceedings of the third international conference on the integration of AI and OR techniques in constraint programming for combinatorial optimization problems (CPAIOR). Lecture notes in computer science, vol 3990. Springer, Heidelberg, pp 244–257

    Google Scholar 

  79. van Hoeve W-J, Pesant G, Rousseau L-M (2006) On global warming:flow-based soft global constraints. J Heuristics 12(4):347–373

    MATH  Google Scholar 

  80. van Hoeve W-J, Pesant G, Rousseau L-M, Sabharwal A (2006) Revisiting the sequence constraint. In: Benhamou F (ed) Proceedings of the twelfth international conference on principles and practice of constraint programming (CP). Lecture Notes in Computer Science, vol 4204. Springer, Berlin, pp 620–634

    Google Scholar 

  81. van Hoeve W-J, Pesant G, Rousseau L-M, Sabharwal A (2009) New filtering algorithms for combinations of among constraints. Constraints 14:273–292

    MathSciNet  MATH  Google Scholar 

  82. Zanarini A, Milano M, Pesant G (2006) Improved Algorithm for the Soft Global Cardinality Constraint. In: Beck JC, Smith BM (eds) Proceedings of the third international conference on the integration of AI and OR techniques in constraint programming for combinatorial optimization problems (CPAIOR). Lecture notes in computer science, vol 3990. Springer, New York, pp 288–299

    MATH  Google Scholar 

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Acknowledgements

As parts of this chapter are based on the paper [79], I wish to thank Gilles Pesant and Louis-Martin Rousseau.

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  1. Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA, USA

    Willem-Jan van Hoeve

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    Pascal van Hentenryck

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

    Michela Milano

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van Hoeve, WJ. (2011). Over-Constrained Problems. 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_6

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