The Benefits of Global Constraints for the Integration of Constraint Programming and Integer Programming

Efforts aimed at combining Operations Research and Constraint Programming have become increasingly prominent and successful in the last few years. It is now widely recognized that integrating inference in the form of constraint propagation and relaxation in the form of linear programming can yield substantial results. In this paper we argue the benefits of global constraints as a basis for such an integration. We demonstrate the advantages of modeling with global constraints, explain their operational benefits and illustrate this with a series of case studies.

[1]  Philippe Baptiste,et al.  Incorporating Efficient Operations Research Algorithms in Constraint-Based Scheduling , 1995 .

[2]  John N. Hooker,et al.  On Integrating Constraint Propagation and Linear Programming for Combinatorial Optimization , 1999, AAAI/IAAI.

[3]  G. Nemhauser,et al.  Integer Programming , 2020 .

[4]  Philippe Refalo,et al.  Linear Formulation of Constraint Programming Models and Hybrid Solvers , 2000, CP.

[5]  Erlendur S. Thorsteinsson,et al.  Mixed Global Constraints and Inference in Hybrid CLP-IP Solvers , 2000, Electron. Notes Discret. Math..

[6]  Ehl Emile Aarts,et al.  A computational study of constraint satisfaction for multiple capacitated job shop scheduling , 1996 .

[7]  Matteo Fischetti,et al.  A polyhedral study of the asymmetric traveling salesman problem with time windows , 2000, Networks.

[8]  François Laburthe,et al.  Solving Various Weighted Matching Problems with Constraints , 1997, Constraints.

[9]  François Laburthe,et al.  Solving Small TSPs with Constraints , 1997, ICLP.

[10]  Philippe Refalo.  Tight Cooperation and Its Application in Piecewise Linear Optimization , 1999, CP.

[11]  Jean-Charles Régin,et al.  A Filtering Algorithm for Constraints of Difference in CSPs , 1994, AAAI.

[12]  María Auxilio Osorio Lama,et al.  Mixed Logical-linear Programming , 1999, Discret. Appl. Math..

[13]  Jean-Charles Régin,et al.  Arc Consistency for Global Cardinality Constraints with Costs , 1999, CP.

[14]  Eric Pinson,et al.  A Practical Use of Jackson''s Preemptive Schedule for Solving the Job-Shop Problem. Annals of Opera , 1991 .

[15]  Andrea Lodi,et al.  Cutting Planes in Constraint Programming: A Hybrid Approach , 2000, CP.

[16]  J. Carlier,et al.  Adjustment of heads and tails for the job-shop problem , 1994 .

[17]  Pascal Van Hentenryck.  Improved CLP Scheduling with Task Intervals , 1994 .

[18]  Jean-Charles Régin,et al.  Generalized Arc Consistency for Global Cardinality Constraint , 1996, AAAI/IAAI, Vol. 1.

[19]  Danny De Schreye.  Solving TSP with Time Windows with Constraints , 1999 .

[20]  Mark Wallace,et al.  A new approach to integrating mixed integer programming and constraint logicprogramming , 1999, Ann. Oper. Res..

[21]  Erlendur S. Thorsteinsson,et al.  Linear Relaxations and Reduced-Cost Based Propagation of Continuous Variable Subscripts , 2002, Ann. Oper. Res..

[22]  Giovanni Rinaldi,et al.  An efficient algorithm for the minimum capacity cut problem , 1990, Math. Program..

[23]  C. Berge.  Graphes et hypergraphes , 1970 .

[24]  John N. Hooker,et al.  Optimization and , 2000 .

[25]  Alexander Bockmayr,et al.  Branch and Infer: A Unifying Framework for Integer and Finite Domain Constraint Programming , 1998, INFORMS J. Comput..

[26]  Andrea Lodi,et al.  Cost-Based Domain Filtering , 1999, CP.