A. Bockmayr and T. Kasper. Branch and infer: A unifying framework for integer and nite domain constraint programming. INFORMS Journal on Computing, 10(3):287-300, 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....local consistency methods are used to evaluate them. However, global methods may extract much more information from these constraints. In the special case of a set of linear equations, MP techniques can be used to perform global manipulation and to prove global consistency. Bockmayr and Kasper [BK98] give some possible embeddings of MP techniques in CLP, based on the latter insight. The basic idea is to handle linear equations and inequalities altogether as in MP, and not individually as in CLP. There exist various possibilities for such a combination, which range from using linear ....

A. Bockmayr and T. Kasper. Branch and infer: A unifying framework for integer and finite domain constraint programming. INFORMS Journal on Computing, 10(3):287--300, 1998.

....complete search tree based on refinements Tree search methods decompose a problem into some simpler problems until a solution is reached. The simplification, called a refinement, consists in reducing the number of solutions by adding some constraints. For this, we use only primitive constraints [5] of Eclair , which have a direct impact on the constraint store maintained by Eclair . For instance, the primitive constraint x v reduces the domain of a variable x to the values lower than v. The primitive constraint settle(c 1 or c 2 , left) replaces in the constraint store the logical ....

A. Bockmayr and T. Kasper. Branch-and-infer: A unifying framework for integer and finite domain constraint programming. INFORMS J. Computing, 10(3):287 -- 300, 1998.

....we have previously termed mixed propagation of mixed CLP MIP global constraints [20, 21, 24] This holds regardless of the scheme used, be it (Tight) Cooperation [2, 22] Mixed Logical Linear Programming (MLLP) 15, 16, 20, 21, 24] Branch and Check (see Sec. 3) or some other integration approach [3, 6, 7, 18, 23]. This double modelling could be explicit, but most preferably it should be implicit, i.e. mixed global constraints should post and dynamically update a linear relaxation of themselves, in addition to the classical CLP propagation on their discrete parts and mixed propagation between the discrete ....

....MIP Techniques Branch and Bound: We will assume that the reader is familiar with the classical Branch and Bound approach for solving MIPs. Due to di erent vocabulary in the two elds, however, we would like to note that this is the technique that is sometimes referred to as Branch and Relax [3]. Benders Decomposition: Classical Benders Decomposition exploits the fact that in some problems, xing the values of certain di cult variables simpli es the problem tremendously. By enumerating those di cult variables, solving each resulting subproblem and selecting the best subproblem solution ....

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A. Bockmayr and T. Kasper. Branch-and-infer: A unifying framework for integer and nite domain constraint programming. INFORMS Journal on Computing, 10(3):287 300, 1998.

....relaxations through LP, in order to reduce the size of the search tree. The key decisions to be made for integrating Constraint (Logic) Programming (CLP) and Integer Programming (IP) are the (a) models, b) inference, c) relaxations, and, d) search and branching strategies to use. For example, [4] introduces a framework with a combined constraint store and symbolic constraints that produce cutting planes; 10] combines two di erent models in two synchronized search trees; and, 18] automatically produces and updates a shadow copy of a CLP model on the continuous side, with constraint ....

....modeler it can not be communicated to the solver and the solver has to nd and recognize the structure on its own to be able to apply logical processing to it, resulting in less e cient solution algorithms than what would have been possible. Recently though some work has been done on this topic [4]. In a framework such as MLLP, mixed global constraints serve both as a modeling tool and a way to exploit structure in the solution process. Mixed global constraints are global constraints that have both discrete and continuous elements within them, encapsulating a speci c sub structure in the ....

A. Bockmayr and T. Kasper. Branch-and-infer: A unifying framework for integer and nite domain constraint programming. INFORMS J. Computing, 10(3):287300, 1998.

.... the use of relaxations in addition to constraint propagation techniques like linear relaxations [29, 34, 35, 40, 42] or Lagrangian relaxations [15, 19] to provide tight bounds to constraint programming solvers; embedding cutting planes algorithms in global constraints like polyhedral cuts [8, 19, 32] or local cuts derived from constraint propagation [34] 2 To facilitate this discussion we begin with a short overview on modelling techniques in CP and IP (Sec. 2) and on solution techniques (Sec. 3) We then describe and illustrate the integration of OR and CP techniques on the global ....

....the solver algorithms. To do something more intelligent than basic branch and bound, the solver has to recover the structure of the problem, despite the fact that the structure was already known to the modeller, or assume what the structure of the model was. A recent work by Bockmayr and Kasper [8] addressed this issue by showing how the idea of global constraints can be carried over from CP to IP. The advantages are clearly due to the increased expressive power of the resulting language, more readable and concise models maintaining the problem structure, and the increased e ciency if ....

A. Bockmayr and T. Kasper. Branch-and-infer: A unifying framework for integer and nite domain constraint programming. INFORMS J. Computing, 10(3):287300, 1998.

....for an overview. The integration of OR and CP techniques applied to airline CAP is investigated in the ESPRIT project Parrot (Parallel Crew Rostering) 27] where this work has been carried out. In principle there are two main ways of integrating CP and OR: Embed OR algorithms in a CP framework. [4, 6, 30] did this for a linear solver. The purpose of the OR algorithm is usually to provide bounds and possibly other information to guide the search. In certain cases, OR algorithms can also be exploited for domain reduction. A famous example are global resource constraints in scheduling that use the ....

A. Bockmayr and T. Kasper. Branch and infer: A unifying framework for integer and nite domain constraint programming. INFORMS Journal on Computing, 10(3):287-300, 1998.

....of column generation, we formulate the subproblem as a CSP and thus extend the modeling facilities of column generation. Compared to co operative solvers (cf. 4 In Parrot, these software components are currently further developed and significant performance improvements can be expected. e.g. [2, 4, 15]) the CP and LP solver do not communicate only by reducing domains, but mainly by exchanging solutions and dual values. The use of the duals in the negative reduced cost constraint reduces the domains for the next solution. Optimization methods that are usually used for solving the subproblem can ....

A. Bockmayr and T. Kasper. Branch-and-Infer: A unifying framework for integer and finite domain constraint programming. INFORMS Journal of Computing, 10(3):287--300, 1998.

....A double modeling scheme can be implemented with ILOG s OPL Studio [144] a modeling language that can invoke both constraint programming (ILOG) and linear programming (CPLEX) solvers and pass some information from one to the other. 21 4.1. 2 Branch and Infer In 1998 Bockmayr and Kasper [22] proposed an interesting perspective on the integration of constraint programming with integer programming, based on the parallel between cutting planes and inference. It characterizes both constraint programming and integer programming as using a branch and infer principle. As the branching ....

Bockmayr, A., and T. Kasper, Branch and infer: A unifying framework for integer and finite domain constraint programming, INFORMS Journal on Computing 10 (1998): 287-300.

....and establish bounds. A systematic procedure is used to create a shadow MIP model, from a CLP model with logical and symbolic constraints. The modeler may annotate constraints to indicate which solver should handle them CP, LP or both. Bockmayr and Kasper propose an interesting framework in [1] for combining CLP and IP, in which several approaches of integration or synergy are possible. They investigate how symbolic constraints can be incorporated into IP much as cutting planes are. They also show how a linear system of inequalities can be used in CLP by incorporating them as symbolic ....

....capacity. S j is the net supply available at node j. A nice property of this model is that it can be given a relaxation that not only is as strong as the traditional LP relaxation but is smaller and, because of its network ow structure, can be solved much more rapidly [3] Using the framework of [1], MLLP has two constraint stores. Agent 1 ## ## ## ## # # # # # # # # # # # # # : Agent n ## ## ## ### # # # # # # # # # # # # FD Store LP Store A classical nite domain (FD) constraint store contains domains, and the LP constraint store contains linear inequalities. The ....

A. Bockmayr and T. Kasper. Branch-and-infer: A unifying framework for integer and nite domain constraint programming. INFORMS J. Computing, 10(3):287  300, 1998.

....the solver algorithms. To do something more intelligent than basic branch and bound the solver has to recover the structure of the problem, despite the fact that the structure was already known to the modeler, or assume what the structure of the model was. Some recent work by Bockmayr and Kasper (Bockmayr Kasper 1998) has addressed this issue by showing how the idea of global constraints can be carried over from CP to IP. As an example they introduce global tsp and assign constraints that exploit various results from polyhedral theory to generate cutting planes for these structures. Furthermore, the black box ....

Bockmayr, A., and Kasper, T. 1998. Branch-and-infer: A unifying framework for integer and finite domain constraint programming. INFORMS J. Computing 10(3):287 -- 300.

.... network design [20, 27, 37] truss structure design [10] machine scheduling [21, 31] scheduling with resource constraints [34] highly combinatorial scheduling [27, 44] dynamic scheduling [15] production planning and transportation with piecewise linear functions [33, 38] warehouse location [9, 48], traveling salesman problem with time windows [16] hoist scheduling [43] and problems with specially ordered sets [14] A recent commercially available modeling system, OPL, invokes both linear programming (ILOG Planner CPLEX) and constraint programming (ILOG Solver) solvers [48] Despite these ....

....two dualities: the duality of search vs. inference and the duality of strengthening vs. relaxation. Some of these ideas are anticipated in [22] Branching algorithms provide one example of these dualities at work. The search inference duality is evident in Bockmayr and Kasper s observation [9] that both optimization and constraint satisfaction rely on branch and infer. Branching is a search mechanism. During the branching process, one can generate inferences in the form of cutting planes (as in optimization) or constraint propagation to achieve domain reduction (as in constraint ....

[Article contains additional citation context not shown here]

A. Bockmayr and T. Kasper. Branch-and-infer: A unifying framework for integer and nite domain constraint programming. INFORMS J. Computing, 10(3):287  300, 1998.

....are not faulty. As discussed in [8] this choice has strong in uences on fault detection. 3 Practical Modeling: From Qualitative Equations to CSPs In order to implement a qualitative equation system in a language which supports ecient inference methods, there are several choices, see e.g. [1] for a comparison of Integer Linear Programming and Constraint Programming over Finite Domains (cp(F D) In this work, non binary CSPs and cp(FD) have been chosen for several reasons: CSPs provide a well known declarative semantics and expressive power; cp(FD) gains expressive power from ....

A. Bockmayr and T. Kasper. Branch-and-infer: A unifying framework for integer and nite domain constraint programming. INFORMS J. Computing, 10(3):287 { 300, 1998.

....and establish bounds. A systematic procedure is used to create a shadow MIP model, from a CLP model with logical and symbolic constraints. The modeler may annotate constraints to indicate which solver should handle them CP, LP or both. Bockmayr and Kasper propose an interesting framework in [1] for combining CLP and IP, in which several approaches of integration or synergy are possible. They investigate how symbolic constraints can be incorporated into IP much as cutting planes are. They also show how a linear system of inequalities can be used in CLP by incorporating them as symbolic ....

....capacity. S j is the net supply available at node j. A nice property of this model is that it can be given a relaxation that not only is as strong as the traditional LP relaxation but is smaller and, because of its network flow structure, can be solved much more rapidly [3] Using the framework of [1], MLLP has two constraint stores. Agent 1 Fnan Fnan OO Fnan Fnan fflffl Fnan Fnan ii Fnan Fnan ) R R R R R R R R R R R R R R : Agent n Fnan Fnan OO Fnan Fnan fflffl Fnan Fnan 55 Fnan Fnan uul l l l l l l l l l l l l l FD Store LP Store A classical finite domain (FD) ....

A. Bockmayr and T. Kasper. Branch-and-infer: A unifying framework for integer and finite domain constraint programming. INFORMS J. Computing, 10(3):287 -- 300, 1998.

....The constraint programming community normally views in domain constraints as comprising a constraint store that propagates the implications of one constraint to other constraints. But they can also be viewed as comprising a relaxation that is easily solved: merely choose one value from each domain [6]. This relaxation is weaker than the original constraint set, except in the unlikely event that full consistency has been achieved. Even if hyperarc consistency has been maintained, it implies only that every value in every domain belongs to some feasible solution, not that any combination of ....

A. Bockmayr and T. Kasper. Branch-and-infer: A unifying framework for integer and finite domain constraint programming. INFORMS J. Computing, 10(3):287 -- 300, 1998.

....relaxations through LP, in order to reduce the size of the search tree. The key decisions to be made for integrating Constraint (Logic) Programming (CLP) and Integer Programming (IP) are the (a) models, b) inference, c) relaxations, and, d) search and branching strategies to use. For example, [3] introduces a framework with a combined constraint store and symbolic constraints that produce cutting planes; 7] combines two dioeerent models in two synchronized search trees; and, 17] automatically produces and updates a shadow copy of a CLP model on the continuous side, with constraint ....

....modeler it can not be communicated to the solver and the solver has to nd and recognize the structure on its own to be able to apply logical processing to it, resulting in less eOEcient solution algorithms than what would have been possible. Recently though some work has been done on this topic [3]. In a framework such as MLLP, mixed global constraints serve both as a modeling tool and a way to exploit structure in the solution process. Mixed global constraints can be written in the form (1) as conditionals, analogous to global constraints in CLP, but improve the solution process by ....

A. Bockmayr and T. Kasper. Branch-and-infer: A unifying framework for integer and ønite domain constraint programming. INFORMS J. Computing, 10(3):287 300, 1998.

....has also been crucial for solving various real world industrial applications. In this paper, we study how CP can be used inside a branch and cut framework in order to detect infeasibility and to generate cutting planes for MIP. For other uses of cutting planes in hybrid solvers, see for example [3, 9, 5, 8]. The ability of existing CP software to generate cuts using infeasibility is limited. If a filtering procedure for some constraint detects a reason of infeasibility independently of the other constraints, it may possibly infer a cut. However, this happens very seldom. In general, infeasibility ....

A. Bockmayr and T. Kasper. Branch-and-infer: A unifying framework for integer and finite domain constraint programming. INFORMS J. Computing, 10(3):287 -- 300, 1998.

....later used in further CP systems like ILOG OPL Studio [ILO] and OZ [Smo96] On the one hand, symbolic constraints allow for high level and intuitive problem formulations. On the other hand, they improve eciency by integrating problem speci c algorithms into a general solver. Bockmayr and Kasper [BK98, Kas98] suggested to extend ILP by symbolic constraints. SCIL realizes this suggestion. An optimization problem is speci ed by a set of variables (ranging over the rational numbers) a linear objective function and a set of constraints. A constraint may be a linear constraint (a linear inequality ....

A. Bockmayr and T. Kasper. Branch and infer: a unifying framework for integer and nite domain constraint programming. INFORMS Journal on Computing, 10:287-300, 1998.

....first introduced in the CP system CHIP [BC94, ADH 87] and later used in further CP systems like ILOG OPL Studio [ILO, vHPP00] and OZ [Smo96] These systems have highly developed modeling systems, which support high level and intuitive problem formulations. Alexander Bockmayr and Thomas Kasper [BK98, Kas98] suggested to extend ILP by symbolic constraints. SCIL realizes their suggestion. An optimization problem is specified by a set of variables (ranging over the rational numbers) a linear objective function and a set of constraints. A constraint may be a linear constraint (a linear ....

A. Bockmayr and T. Kasper. Branch and infer: a unifying framework for integer and finite domain constraint programming. INFORMS Journal on Computing, 10:287--300, 1998. 11

....studied in the literature. Recent work on global constraints includes, e.g. 12, 16, 17] A classification scheme for global constraints is presented in [4] The role of global constraints for the integration of constraint programming and mathematical programming is discussed, among others, in [7, 9, 15, 13, 14]. There are two main benefits of global constraints. On the one hand, they provide high level abstractions for modeling complex combinatorial problems in # This work was partially supported by the European Commission, Growth Programme, Research Project LISCOS Large Scale Integrated Supply ....

....(0,3) 2,5) 1,4) 2,5) 1,3) 1,3) 0,8) 0,9) 1,5) 7 3 5 4 1 2 1 3 5 5 3 1 1 3 8 4 Fig. 3. Maximum flow: network n = 8; m = 16; s = 0; t = 7; NodeType = supply,supply,supply,supply,supply,supply,demand] Edge = 0,1] 0,2] 0,3] 1,2] 1,3] 1,4] 2,3] 2,5] 2,6] 3,4] 3,5] 4,5] [4,7], 5,7] 6,5] 6,7] LoCap = 2,1,0,1,2,1,0,0,2,1,1,2,1,0,1,0] UpCap = 8,5,3,6,4,5,5,3,5,5,4,5,3,8,3,9] Demand[v] 0, v #= s, t; Demand[s] # [0,16] Demand[t] # [0,16] Flow[e] # [LoCap[e] UpCap[e] e = 0, m 1; flow(NodeType,Edge, Demand,Flow,0) Demand[s] # ....

[Article contains additional citation context not shown here]

A. Bockmayr and T. Kasper. Branch-and-infer: A unifying framework for integer and finite domain constraint programming. INFORMS J. Computing, 10(3):287 -- 300, 1998.

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A. Bockmayr and T. Kasper. Branch and infer: A unifying framework for integer and nite domain constraint programming. INFORMS Journal on Computing, 10(3):287-300, 1998.

No context found.

A. Bockmayr and T. Kasper. Branch and infer: A unifying framework for integer and nite domain constraint programming. INFORMS Journal on Computing, 10(3):287-300, 1998.

No context found.

A. Bockmayr and T. Kasper. Branch and infer: A unifying framework for integer and finite domain constraint programming. INFORMS Journal on Computing, 10(3):287--300, 1998.

No context found.

Math. 4:238252. Bockmayr, A., and Kasper, T. 1998. Branch-andinfer: A unifying framework for integer and ønite domain constraint programming. INFORMS J. Computing 10(3):287 300.

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