Citation Context

...lar parallel machines. Our approach is strongly connected to Benders decomposition and the related concepts. It is inspired from methods used to integrate constraint programming into a Benders scheme =-=[21, 3]-=-. The allocation and ressource problem will be considered on one side and schedulability on the other side. The subproblem checks the schedulability of an allocation, finds out why it is unschedulable...

Citation Context

...R literature in this area extending the original approach, it has only recently been used by the constraint programming community in developing hybrid models. The reader is directed to Benoist et al. =-=[3]-=-, Xia et al. [17], Eremin and Wallace [4], Hooker and Ottosson [7], Thorsteinsson [16], Jain and Grossmann [9] for applications of BD in constraint programming. Benders decomposition [2, 5] was presen...

Citation Context

...els and techniques using the complementary strengths of constraint programming and optimization techniques. Hybridization schemes have appeared recently and provided interesting computational results =-=[4, 5, 7, 8]-=-. They have been extended [2, 3, 6] to take into account other kinds of sub-problems and not only the classical linear programming ones. However, decomposition has never been proposed to our knowledge...

Citation Context

...napsack problems and constrained flow problems can be respectively modelled with (in addition to problem specific constraints) TSP constraints [2] [21], Knapsack constraints [3,4] or flow constraints =-=[5,6]-=-. For such problems where a principal global constraint can be identified, we propose a support-guided branching scheme and an associated cooperation betweensImproving Global Constraints Support by Lo...

Citation Context

...no advanced knowledge of flow algorithms literature (c.f. 4.4). To the best of our knowledge CHOCO’s Flow constraint was the first to give access to its internal reference flow, used as an oracle in [=-=Benoist et al. 2002-=-]. While keeping internal sophisticated OR algorithms in the constraint black box, we claim that constraint programmers can offer safe 6 APIs for reading or modifying the support of a constraint, allo...

Citation Context

...m ours, their results have shown the ability of such an innovative approach to solve an allocation problem for embedded systems and have encouraged us to go further. Like numerous hybridation schemes =-=[9, 4]-=-, the way we are investigating uses the complementary strengths of constraint programming and optimization methods from operational research. In this paper, we present its principle and study its perf...

Citation Context

...n this paper we try to propose new parameters to measure the number of required constraints. 2 Breaking Variable Symmetry A variable symmetry is a permutation σ on the set of variables {xi}i∈1..n that maps solutions onto solutions. More formally, any assignment (xi = vi)i∈1..n is a solution if and only if (xσ(i) = vi)i∈1..n is also a solution. The general method for breaking variable symmetry is to add lexicographical constraints [?]. Given an order xi1 , . . . xin on variables, we post, for any symmetry σ, the lexicographical ordering constraint: xi1 , . . . , xin ≤lex xσ(i1), . . . , xσ(in) (1) Unfortunately, the number of variable symmetries can be exponential. It is equal to the size of the corresponding permutation group G. This group is generally given as a set S of generators. For instance, Nauty [10] or Saucy are well known programs to compute the permutation group of a graph (automorphisms). Even if their theoretical worst-case time complexity is exponential, they are very efficient in practice. In the special case of “piecewise symmetry” – where the set of variables (resp. values) is partitioned into subsets of interchangeable variables (resp. values) – both variable and val...

Citation Context

... t 5 1 0,1 Variables Values Fig. 1. The network used for GCC propagation in [4], allowing to solve problems involving flow and additional constraints, for instance large workforce scheduling problems =-=[1]-=- . In this flow constraint, the flow allowed to an edge (i, j) is expressed as a CSP variable xflow(i,j). To compute the minimal number of values which can be assigned to exactly one variable while re...