Integrating Operations Research in Constraint Programming

This paper presents Constraint Programming as a natural formalism for modelling problems, and as a flexible platform for solving them. CP has a range of techniques for handling constraints including several forms of propagation and tailored algorithms for global constraints. It also allows linear programming to be combined with propagation and novel and varied search techniques which can be easily expressed in CP. The paper describes how CP can be used to exploit linear programming within different kinds of hybrid algorithm. In particular it can enhance techniques such as Lagrangian relaxation, Benders decomposition and column generation.

[1]  Barry Richards,et al.  Hybrid Lagrangian relaxation for bandwidth-constrained routing: knapsack decomposition , 2005, SAC '05.

[2]  J. Hooker,et al.  Logic-based Benders decomposition , 2003 .

[3]  J. Carlier,et al.  An algorithm for solving the job-shop problem , 1989 .

[4]  Toby Walsh,et al.  Stochastic Constraint Programming: A Scenario-Based Approach , 2009, Constraints.

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

[6]  François Laburthe,et al.  LS and CP illustrated on a transportation problem , 2004 .

[7]  Christian Bessiere,et al.  Arc Consistency for General Constraint Networks: Preliminary Results , 1997, IJCAI.

[8]  J. F. Benders.  Partitioning procedures for solving mixed-variables programming problems , 1962 .

[9]  Christian Prins,et al.  Applications of optimisation with Xpress-MP , 2002 .

[10]  Michel Gendreau,et al.  A Constraint Programming Framework for Local Search Methods , 1999, J. Heuristics.

[11]  Ernest Davis,et al.  Constraint Propagation with Interval Labels , 1987, Artif. Intell..

[12]  Nicolas Beldiceanu,et al.  Global Constraint Catalog , 2005 .

[13]  Thom W. Frühwirth,et al.  Theory and Practice of Constraint Handling Rules , 1998, J. Log. Program..

[14]  Farhad Arbab,et al.  Coordination of heterogeneous distributed cooperative constraint solving , 1998, SIAP.

[15]  Hani El Sakkout,et al.  Local Probing Applied to Scheduling , 2002, CP.

[16]  Michael Jünger,et al.  The ABACUS system for branch‐and‐cut‐and‐price algorithms in integer programming and combinatorial optimization , 2000, Softw. Pract. Exp..

[17]  Mark Wallace,et al.  Integrating operations research in constraint programming , 2006, 4OR.

[18]  Vipul Jain,et al.  Algorithms for Hybrid MILP/CP Models for a Class of Optimization Problems , 2001, INFORMS J. Comput..

[19]  Narendra Jussien,et al.  Local search with constraint propagation and conflict-based heuristics , 2000, Artif. Intell..

[20]  P. Langley.  Systematic and nonsystematic search strategies , 1992 .

[21]  Jimmy Ho-Man Lee,et al.  Speeding Up Constraint Propagation By Redundant Modeling , 1996, CP.

[22]  Laurent Perron,et al.  Propagation Guided Large Neighborhood Search , 2004, CP.

[23]  Claude Le Pape,et al.  Integration of Rules and Optimization in Plant PowerOps , 2005, CPAIOR.

[24]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

[25]  Gilles Pesant,et al.  Constraint Programming Based Column Generation for Employee Timetabling , 2005, CPAIOR.

[26]  Pascal Van Hentenryck.  In Memoriam: Paris C. Kanellakis , 1996, J. Log. Program..

[27]  Peter J. Stuckey,et al.  Finite Domain Bounds Consistency Revisited , 2004, Australian Conference on Artificial Intelligence.

[28]  Claude Lemaréchal,et al.  The omnipresence of Lagrange , 2007, Ann. Oper. Res..

[29]  Yishai A. Feldman,et al.  Portability by automatic translation: a large-scale case study , 1999 .

[30]  Peter J. Stuckey,et al.  When do bounds and domain propagation lead to the same search space? , 2005, ACM Trans. Program. Lang. Syst..

[31]  Tobias Achterberg,et al.  SCIP: solving constraint integer programs , 2009, Math. Program. Comput..

[32]  Pascal Van Hentenryck.  The OPL optimization programming language , 1999 .

[33]  Matthew L. Ginsberg,et al.  Limited Discrepancy Search , 1995, IJCAI.

[34]  John N. Hooker,et al.  A Hybrid Method for Planning and Scheduling , 2004, CP.

[35]  Georg Ch. Pflug,et al.  A branch and bound method for stochastic global optimization , 1998, Math. Program..

[36]  Peter J. Stuckey,et al.  Propagation via lazy clause generation , 2009, Constraints.

[37]  Gilbert Laporte,et al.  The integer L-shaped method for stochastic integer programs with complete recourse , 1993, Oper. Res. Lett..

[38]  Gilles Pesant,et al.  Improving the Cooperation Between the Master Problem and the Subproblem in Constraint Programming Based Column Generation , 2005, CPAIOR.

[39]  Peter J. Stuckey,et al.  The Design of the Zinc Modelling Language , 2008, Constraints.

[40]  Bjørn N. Freeman-Benson,et al.  Multi‐way versus one‐way constraints in user interfaces: Experience with the deltablue algorithm , 1993, Softw. Pract. Exp..

[41]  E. Nowicki,et al.  A Fast Taboo Search Algorithm for the Job Shop Problem , 1996 .

[42]  Philippe Baptiste,et al.  Constraint-based scheduling , 2001 .

[43]  John N. Hooker,et al.  Planning and Scheduling to Minimize Tardiness , 2005, CP.

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

[45]  Frédéric Goualard,et al.  Interval Constraints: Results and Perspectives , 1999, New Trends in Constraints.

[46]  Stefan E. Karisch,et al.  Constraint Programming Based Column Generation for Crew Assignment , 2002, J. Heuristics.

[47]  Michel Gendreau,et al.  A Simplex-Based Tabu Search Method for Capacitated Network Design , 2000, INFORMS J. Comput..

[48]  Thorsten Koch,et al.  Constraint Integer Programming: A New Approach to Integrate CP and MIP , 2008, CPAIOR.

[49]  Paul Shaw,et al.  Using Constraint Programming and Local Search Methods to Solve Vehicle Routing Problems , 1998, CP.

[50]  Henri Beringer,et al.  Combinatorial Problem Solving in Constraint Logic Programming with Cooperating Solvers , 1995, Logic Programming: Formal Methods and Practical Applications.

[51]  Josef Stoer,et al.  Infeasible-interior-point paths for sufficient linear complementarity problems and their analyticity , 1998, Math. Program..

[52]  Philippe Codognet,et al.  Compiling Constraints in clp(FD) , 1996, J. Log. Program..

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

[54]  Mark Wallace,et al.  Generalized Constraint Propagation over the CLP Scheme , 1993, J. Log. Program..

[55]  Cid C. de Souza,et al.  Hybrid Column Generation Approaches for Urban Transit Crew Management Problems , 2005, Transp. Sci..

[56]  Peter J. Stuckey,et al.  From High-Level Model to Branch-and-Price Solution in G12 , 2008, CPAIOR.

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

[58]  Mats Carlsson,et al.  A New Multi-resource cumulatives Constraint with Negative Heights , 2002, CP.

[59]  A. Shapiro,et al.  The Sample Average Approximation Method for Stochastic Programs with Integer Recourse , 2002 .

[60]  Toby Walsh,et al.  Stochastic Constraint Programming , 2002, ECAI.

[61]  François Laburthe,et al.  SALSA: A Language for Search Algorithms , 1998, Constraints.

[62]  Jan Maluszynski,et al.  Analysis and Visualization Tools for Constraint Programming , 2000, Lecture Notes in Computer Science.

[63]  Neng-Fa Zhou.  Programming finite-domain constraint propagators in Action Rules , 2006, Theory Pract. Log. Program..

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

[65]  Jean-Louis Laurière,et al.  A Language and a Program for Stating and Solving Combinatorial Problems , 1978, Artif. Intell..

[66]  Jean-Charles Régin,et al.  Global Constraints and Filtering Algorithms , 2004 .

[67]  Mark Wallace,et al.  Probe Backtrack Search for Minimal Perturbation in Dynamic Scheduling , 2000, Constraints.

[68]  Joao Marques-Silva,et al.  GRASP: A Search Algorithm for Propositional Satisfiability , 1999, IEEE Trans. Computers.

[69]  Laurence A. Wolsey,et al.  bc–opt: a branch-and-cut code for mixed integer programs , 1999, Math. Program..

[70]  Krzysztof R. Apt,et al.  Constraint logic programming using Eclipse , 2007 .