Theory of linear and integer programming
Theory of linear and integer programming
Communications of the ACM
Integer and combinatorial optimization
Integer and combinatorial optimization
Parallel depth first search. Part I. implementation
International Journal of Parallel Programming
Parallel depth first search. Part II. analysis
International Journal of Parallel Programming
The design and analysis of algorithms
The design and analysis of algorithms
Computing edge-connectivity in multigraphs and capacitated graphs
SIAM Journal on Discrete Mathematics
Solving airline crew scheduling problems by branch-and-cut
Management Science
Polyhedral study of the capacitated vehicle routing problem
Mathematical Programming: Series A and B
Analyzing scalability of parallel algorithms and architectures
Journal of Parallel and Distributed Computing - Special issue on scalability of parallel algorithms and architectures
PVM: Parallel virtual machine: a users' guide and tutorial for networked parallel computing
PVM: Parallel virtual machine: a users' guide and tutorial for networked parallel computing
Parallel branch and cut for vehicle routing
Parallel branch and cut for vehicle routing
Parallel branch and cut and its application to the traveling salesman problem
Parallel branch and cut and its application to the traveling salesman problem
Mixed 0-1 programming by lift-and-project in a branch-and-cut framework
Management Science
The Design of the XMP Linear Programming Library
ACM Transactions on Mathematical Software (TOMS)
Software—Practice & Experience - Special issue on discrete algorithm engineering
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Control Schemes in a Generalized Utility for Parallel Branch-and-Bound Algorithms
IPPS '97 Proceedings of the 11th International Symposium on Parallel Processing
Building a parallel branch and bound library
Solving Combinatorial Optimization Problems in Parallel - Methods and Techniques
Branch-And-Price: Column Generation for Solving Huge Integer Programs
Operations Research
A generalized utility for parallel branch and bound algorithms
SPDP '95 Proceedings of the 7th IEEE Symposium on Parallel and Distributeed Processing
Finding Cuts in the TSP (A preliminary report)
Finding Cuts in the TSP (A preliminary report)
Topics in parallel integer optimization
Topics in parallel integer optimization
Validity of the single processor approach to achieving large scale computing capabilities
AFIPS '67 (Spring) Proceedings of the April 18-20, 1967, spring joint computer conference
Implementing Scalable Parallel Search Algorithms for Data-Intensive Applications
ICCS '02 Proceedings of the International Conference on Computational Science-Part I
Solving hub arc location problems on a cluster of workstations
Parallel Computing - Special issue: Parallel computing in logistics
Parallel branch and cut for capacitated vehicle routing
Parallel Computing - Special issue: Parallel computing in logistics
A Library Hierarchy for Implementing Scalable Parallel Search Algorithms
The Journal of Supercomputing
A parallel macro partitioning framework for solving mixed integer programs
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
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Branch, cut, and price (BCP) is an LP-based branch and bound technique for solving large-scale discrete optimization problems (DOPs). In BCP, both cuts and variables can be generated dynamically throughout the search tree. The ability to handle constantly changing sets of cuts and variables allows these algorithms to undertake the solution of very large-scale DOPs; however, it also leads to interesting implementational challenges. These lecture notes, based on our experience over the last six years with implementing a generic framework for BCP called SYMPHONY (Single- or Multi-Process Optimization over Networks), address these challenges. They are an attempt to summarize some of what we and others have learned about implementing BCP, both sequential and parallel, and to provide a useful reference for those who wish to use BCP techniques in their own research.SYMPHONY, the software from which we have drawn most of our experience, is a powerful, state-of-the-art library that implements the generic framework of a BCP algorithm. The library's modular design makes it easy to use in a variety of problem settings and on a variety of hardware platforms. All library subroutines are generic--their implementation does not depend on the problem-setting. To develop a full-scale BCP algorithm, the user has only to specify a few problem-specific methods such as cut generation. The vast majority of the computation takes place within a "black box," of which the user need have no knowledge. Within the black box, SYMPHONY performs all the normal functions of branch and cut--tree management, LP solution, cut pool management, as well as inter-process communication (if parallelism is used). Source code and documentation for SYMPHONY are available at http://branchandcut.org/SYMPHONY.