Branch-Price-and-Cut Algorithms
نویسندگان
چکیده
In many mixed integer programs there is some embedded problem structure which can be exploited, often by a decomposition. When the relaxation in each node of a branch-andbound tree is solved by column generation, one speaks of branch-and-price. Optionally, cutting planes can be added in order to strengthen the relaxation, and this is called branchprice-and-cut. We introduce the common concepts of convexification and discretization to arrive at a Dantzig-Wolfe type reformulation of a mixed integer program. The relation between the original and the extended formulations helps us understand how cutting planes should be formulated and how branching decisions can be taken while keeping the column generation subproblems manageable.
منابع مشابه
The Design of the Branch - and - Cut SystemABACUSMichael
The software system ABACUS is an object-oriented framework for the implementation of branch-and-cut and branch-and-price algorithms. This paper describes the design of ABACUS including the design principles and the most important classes.
متن کاملThe Design of the Branch-and-cut System Abacus
The software system ABACUS is an object-oriented framework for the implementation of branch-and-cut and branch-and-price algorithms. This paper describes the design of ABACUS including the design principles and the most important classes.
متن کاملThe ABACUS system for branch-and-cut-and-price algorithms in integer programming and combinatorial optimization
The development of new mathematical theory and its application in software systems for the solution of hard optimization problems have a long tradition in mathematical programming. In this tradition we implemented ABACUS, an object-oriented software framework for branch-and-cut-and-price algorithms for the solution of mixed integer and combinatorial optimization problems. This paper discusses s...
متن کاملComputational Experience with Branch, Cut and Price Algorithms in Grid Environments
This paper presents our computational experience with parallel Branch, Cut and Price algorithms in a geographically-distributed grid environment. After a brief description of our framework for solving large-scale optimization problems, we describe the experimental grid environment and the tests performed, presenting the obtained performance
متن کاملParallel branch, cut, and price for large-scale discrete optimization
In discrete optimization, most exact solution approaches are based on branch and bound, which is conceptually easy to parallelize in its simplest forms. More sophisticated variants, such as the so-called branch, cut, and price algorithms, are more difficult to parallelize because of the need to share large amounts of knowledge discovered during the search process. In the first part of the paper...
متن کاملComputational Experience with Hypergraph-Based Methods for Automatic Decomposition in Discrete Optimization
Branch-and-price algorithms based on Dantzig-Wolfe decomposition have shown great success in solving mixed integer linear optimization problems (MILPs) with specific identifiable structure, such as vehicle routing and crew scheduling problems. For unstructured MILPs, the most frequently used methodology is branch-and-cut, which depends on generation of “generic” classes of valid inequalities to...
متن کامل