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Dantzig-Wolfe Decomposition and Branch-and-Price Solving in G12
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"... The date of receipt and acceptance will be inserted by the editor Abstract The G12 project is developing a software environment for stating and solving combinatorial problems by mapping a high-level model of the problem to an efficient combination of solving methods. Model annotations are used to co ..."
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Cited by 7 (0 self)
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The date of receipt and acceptance will be inserted by the editor Abstract The G12 project is developing a software environment for stating and solving combinatorial problems by mapping a high-level model of the problem to an efficient combination of solving methods. Model annotations are used to control this process. In this paper we explain the mapping to branch-and-price solving. Dantzig-Wolfe decomposition is automatically performed using the additional information given by the model annotations. The obtained models can then be solved using column generation and branch-and-price. G12 supports the selection of specialised subproblem solvers, the aggregation of identical subproblems to reduce symmetries, automatic disaggregation when required by branch-and-bound, the use of specialised subproblem constraint-branching rules, and different master problem solvers including a hybrid solver based on the volume algorithm. We demonstrate the benefits of the G12 framework on three examples: a trucking problem, cutting stock, and two-dimensional bin packing.
Extending a CIP framework to solve MIQCPs
, 2010
"... This paper discusses how to build a solver for mixed integer quadratically constrained programs (MIQCPs) by extending a framework for constraint integer programming (CIP). The advantage of this approach is that we can utilize the full power of advanced MILP and CP technologies, in particular for th ..."
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Cited by 6 (2 self)
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This paper discusses how to build a solver for mixed integer quadratically constrained programs (MIQCPs) by extending a framework for constraint integer programming (CIP). The advantage of this approach is that we can utilize the full power of advanced MILP and CP technologies, in particular for the linear relaxation and the discrete components of the problem. We use an outer approximation generated by linearization of convex constraints and linear underestimation of nonconvex constraints to relax the problem. Further, we give an overview of the reformulation, separation, and propagation techniques that are used to handle the quadratic constraints efficiently. We implemented these methods in the branch-cut-and-price framework SCIP. Computational experiments indicating the potential of the approach and evaluating the impact of the algorithmic components are provided.
Mixed Integer Programming vs. Logic-based Benders Decomposition for Planning and Scheduling ⋆
"... Abstract. A recent paper by Heinz and Beck (CPAIOR 2012) found that mixed integer software has become competitive with or superior to logic-based Benders decomposition for the solution of facility assignment and scheduling problems. Their implementation of Benders differs, however, from that describ ..."
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Abstract. A recent paper by Heinz and Beck (CPAIOR 2012) found that mixed integer software has become competitive with or superior to logic-based Benders decomposition for the solution of facility assignment and scheduling problems. Their implementation of Benders differs, however, from that described in the literature they cite and therefore results in much slower performance than previously reported. We find that when correctly implemented, the Benders method remains 2 to 3 orders of magnitude faster than the latest commercial mixed integer software on larger instances, thus reversing the conclusion of the earlier paper. 1
Connections and Integration with SAT Solvers: A Survey and a Case Study in Computational Biology
"... Boolean constraints play a fundamental rôle in optimization and constraint satisfaction. The resolution of these constraints has been the subject of intense and successful work during the past decade, and SAT solvers have reached a spectacular maturity. This chapter gives a brief overview of the rel ..."
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Boolean constraints play a fundamental rôle in optimization and constraint satisfaction. The resolution of these constraints has been the subject of intense and successful work during the past decade, and SAT solvers have reached a spectacular maturity. This chapter gives a brief overview of the relevant literature on modern SAT solvers and on the recent efforts to better integrate Boolean reasoning with other constraint satisfaction techniques. As a case study that illustrates the use of SAT and CP we consider an application in computational biology: the task to build gene regulatory networks (GRNs). We report on experiments made on this problem with a combined SAT/CP approach.
J.C.: Recent improvements using constraint integer programming for resource allocation and scheduling
- Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. Volume 7874 of LNCS
, 2013
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Developing constraint programming applications with aimms. Presented at CP2013, COSpel workshop
, 2013
"... Abstract. We describe the constraint programming interface of the optimization modeling systems Aimms. First, we present the modeling language for basic constraint programming and advanced scheduling constructs, and specify how search can be controlled. Then we provide three example applications tha ..."
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Abstract. We describe the constraint programming interface of the optimization modeling systems Aimms. First, we present the modeling language for basic constraint programming and advanced scheduling constructs, and specify how search can be controlled. Then we provide three example applications that illustrate how Aimms can be used for developing constraint programming applications. 1
Software Tools Supporting Integration
"... Abstract This chapter provides a brief survey of existing software tools that enable, facilitate and/or support the integration of different optimization techniques. We focus on tools that have achieved a reasonable level of maturity and whose published results have demonstrated their effectiveness ..."
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Abstract This chapter provides a brief survey of existing software tools that enable, facilitate and/or support the integration of different optimization techniques. We focus on tools that have achieved a reasonable level of maturity and whose published results have demonstrated their effectiveness. The description of each tool is not intended to be comprehensive. We include references and links to detailed accounts of each tool for the interested reader, and we recommend that the reader consult their developers and/or vendors for the latest information about upgrades and improvements. Our purpose is to summarize the main features of each tool, highlighting what it can (or cannot) do, given the current version at the time of writing. We conclude the chapter with suggestions for future research directions.
The Aimms Interface to Constraint Programming
"... Abstract. We present an extension of the modeling system Aimms to handle constraint programming problems. Our goal is to provide a more accessible interface to CP technology than current systems offer. We first present basic CP modeling constructs that can be realized with minimum changes to the exi ..."
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Abstract. We present an extension of the modeling system Aimms to handle constraint programming problems. Our goal is to provide a more accessible interface to CP technology than current systems offer. We first present basic CP modeling constructs that can be realized with minimum changes to the existing syntax. We then discuss the handling of global constraints. Lastly, we present our extensions to modeling scheduling problems, based on the now-classical representation as activities and resources. An important benefit of the Aimms interface to CP is the ease with which hybrid CP/OR solution methods can be developed. 1
Constraints manuscript No. (will be inserted by the editor) A Constraint-Based Local Search
"... the date of receipt and acceptance should be inserted later Abstract MiniZinc is a modelling language for combinatorial problems, which can then be solved by a solver provided in a backend. There are many backends, based on technologies such as constraint programming, integer programming, or Boolean ..."
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the date of receipt and acceptance should be inserted later Abstract MiniZinc is a modelling language for combinatorial problems, which can then be solved by a solver provided in a backend. There are many backends, based on technologies such as constraint programming, integer programming, or Boolean satisfiability solving. However, to the best of our knowledge, there is currently no constraint-based local search (CBLS) backend. We discuss the challenges to develop such a backend and give an overview of the design of a CBLS backend for MiniZinc. Experimental results show that for some MiniZinc models, our CBLS backend, based on the OscaR/CBLS solver, is able to give good-quality results in short time.
