Integrating Operations Research in Constraint Programming

Milano, Michela; Wallace, Mark

doi:10.1007/s10479-009-0654-9

Cited by 45 publications

(29 citation statements)

References 57 publications

(47 reference statements)

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“…In the recent literature several attempts to combine CP with OR can be found with the intent of integrating the pros of the two approaches. We refer the reader to Milano and Wallace (2006) for a recent survey on hybrid methods that combine CP and OR techniques. CP-CG is one of the most successful examples of such combinations.…”

Section: Graph Coloring Via Constraint Programmingmentioning

confidence: 99%

“…For further details on the CP solving techniques and on more involved CP search strategies, see Milano and Wallace (2006).…”

Section: Constraint Programming-based Column Generationmentioning

confidence: 99%

“…The idea of exploiting good lower bounds obtained via mathematical programming within a CP model gives rise to hybrid methods (e.g., see Milano and Wallace (2006)). A promising hybrid approach is the socalled Constraint Programming-based Column Generation (CP-CG) that formulates and solves the pricing subproblem via CP.…”

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confidence: 99%

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Exact Solution of Graph Coloring Problems via Constraint Programming and Column Generation

Gualandi

Malucelli

2012

INFORMS Journal on Computing

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We consider two approaches for solving the classical minimum vertex coloring problem, that is the problem of coloring the vertices of a graph so that adjacent vertices have different colors, minimizing the number of used colors, namely Constraint Programming and Column Generation. Constraint Programming is able to solve very efficiently many of the benchmarks, but suffers from the lack of effective bounding methods.On the contrary, Column Generation provides tight lower bounds by solving the fractional vertex coloring problem exploited in a Branch-and-Price algorithm, as already proposed in the literature. The Column Generation approach is here enhanced by using Constraint Programming to solve the pricing subproblem and to compute heuristic solutions. Moreover new techniques are introduced to improve the performance of the Column Generation approach in solving both the linear relaxation and the integer problem. We report extensive computational results applied to the benchmark instances: we are able to prove optimality of 11 new instances, and to improve the best known lower bounds on other 17 instances. Moreover we extend the solution approaches to a generalization of the problem known as Minimum Vertex Graph Multicoloring Problem where a given number of colors has to be assigned to each vertex.

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Section: Graph Coloring Via Constraint Programmingmentioning

confidence: 99%

“…For further details on the CP solving techniques and on more involved CP search strategies, see Milano and Wallace (2006).…”

Section: Constraint Programming-based Column Generationmentioning

confidence: 99%

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Exact Solution of Graph Coloring Problems via Constraint Programming and Column Generation

Gualandi

Malucelli

2012

INFORMS Journal on Computing

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“…CP and OR have indeed complementary strengths: on the one hand CP provides an easy way to deal with inference methods, logic processing, high-level problem modelling and local consistency; on the other, OR works well with relaxation methods, duality theory, atomistic problem modelling, and global consistency. Consequently, in order to achieve better performances and solve large combinatorial problems, it has become natural try to integrate these two approaches and the links between the two communities have grown stronger in recent years [138].…”

Section: Operating Research Vs Constraint Programmingmentioning

confidence: 99%

“…Some of the main challenges concern the interaction between the user and the solving process, the resolution of partially unknown or ill-defined problems, the processing of large scale over-constrained problems, and the improvement of the CP solving process, both in the constraints propagation and in the solution search [138].…”

Section: Operating Research Vs Constraint Programmingmentioning

confidence: 99%

Portfolio approaches in constraint programming

Amadini

2015

Constraints

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Recent research has shown that the performance of a single, arbitrarily efficient algorithm can be significantly outperformed by using a portfolio of -possibly onaverage slower-algorithms. Within the Constraint Programming (CP) context, a portfolio solver can be seen as a particular constraint solver that exploits the synergy between the constituent solvers of its portfolio for predicting which is (or which are) the best solver(s) to run for solving a new, unseen instance.In this thesis we examine the benefits of portfolio solvers in CP. Despite portfolio approaches have been extensively studied for Boolean Satisfiability (SAT) problems, in the more general CP field these techniques have been only marginally studied and used. We conducted this work through the investigation, the analysis and the construction of several portfolio approaches for solving both satisfaction and optimization problems. We focused in particular on sequential approaches, i.e., single-threaded portfolio solvers always running on the same core.We started from a first empirical evaluation on portfolio approaches for solving Constraint Satisfaction Problems (CSPs), and then we improved on it by introducing new data, solvers, features, algorithms, and tools. Afterwards, we addressed the more general Constraint Optimization Problems (COPs) by implementing and testing a number of models for dealing with COP portfolio solvers. Finally, we have come full circle by developing sunny-cp: a sequential CP portfolio solver that turned out to be competitive also in the MiniZinc Challenge, the reference competition for CP solvers.iii iv

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Solving a resource allocation problem in wireless mesh networks: A comparison between a CP‐based and a classical column generation

et al. 2009

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This article presents a column generation approach to a resource allocation problem arising in managing Wireless Mesh Networks. The problem consists in routing the given demands over the network and to allocate time resource to pairs of nodes. Half-duplex constraints are taken into account together with the aggregate interference due to simultaneous transmissions, which affects the signal quality. Different problems are considered, according to the assumptions on the transmission power and rate. The resource allocation problem can be formulated as a Mixed Integer Linear Programming (MILP) problem and dealt with a column generation-based approach. The pricing problem, due to signal quality constraints, turns out to be computationally demanding. To tackle these difficulties, besides a classical mathematical programming approach, we have applied a hybrid column generation approach where the pricing subproblem is solved using Constraint Programming. Numerical results show that the two methods are comparable. The results of the column generation are then used to solve heuristically the problem. The obtained results provide very small gaps (between lower bounds and Heuristic solutions) for two of the three considered problems and reasonable gaps for the third problem.

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Integrating Operations Research in Constraint Programming

Cited by 45 publications

References 57 publications

Exact Solution of Graph Coloring Problems via Constraint Programming and Column Generation

Exact Solution of Graph Coloring Problems via Constraint Programming and Column Generation

Portfolio approaches in constraint programming

Solving a resource allocation problem in wireless mesh networks: A comparison between a CP‐based and a classical column generation

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