CBC User Guide

Abstract

The Computational Infrastructure for Operations Research (COIN-OR) branchand-cut solver (CBC) is an open-source mixed-integer program (MIP) solver. The performance of branch-and-cut algorithms can vary greatly with problem-specific customization, such as dictating that the order nodes in the search tree are traversed. CBC provides operations research professionals with a well-tested, robust, reusable code base for experimenting with advanced customizations of branch-and-cut algorithms. The CBC design makes the most commonly desired customizations readily possible: (a) dynamically selecting the next node in the search tree for processing, (b) using specialized criteria for determining which variable(s) to branch on, (c) calling tailormade heuristics to generate MIP-feasible solutions quickly, (d) including standard (or user-provided) cut generation in solving the linear program (LP) relaxations of the MIP, and (e) invoking customized subproblem solvers. CBC is written in C++ and is intended to be used primarily as a callable library. CBC requires a linear program (LP) solver. CBC uses the COIN-OR open solver interface (OSI) to communicate with the user's choice of LP solver. CBC can use any LP solver with an OSI. The LP solver expected to be used most commonly is the freely available COIN-OR LP solver (CLP). CBC can be used as a branch-and-bound solver or as a branch-and-cut solver. For cut generators, CBC relies on the COIN-OR Cut Generation Library (CGL). CBC can use any cut generator written to CGL standards. CBC is an active open-source project led by John Forrest. The full CBC source code is available under the Common Public License for industrial and academic use at www.coin-or.org. This chapter introduces CBC and illustrates how to implement a variety of common branch-and-cut customizations in CBC. The chapter assumes familiarity with C++, fundamentals of mixed-integer programming, and basic knowledge of OSI. Keywords software; branch and bound; cutting planes; mixed-integer programming; open-source software * C International Business Machines Corporation 2005. Reproduced by permission of International Business Machines, Armonk, NY. 1 The complete acronym is "COIN-OR" which stands for the Compuational Infrastructure for Operations Research. For simplicity (and in keeping with the directory and function names) we will simply use "COIN.

Mixed Integer NonLinear Programs featuring “On/Off” constraints: convex analysis and applications

“…Table 1 summarizes the main characteristics of these networks. To solve the convex MINLP models, we used the open source solver Bonmin [7] (release 1.1.3, see http://www.coin-or.org/Bonmin) with CBC [11] as underlying mixed-integer linear programming (MILP) solver and Ipopt [23] for the nonlinear programming solver. The four models were coded in C++ to be solved by Bonmin and all tests were performed on an Intel Xeon 1.6 Ghz CPU.…”

Feature Selection for Nonlinear Kernel Support Vector Machines

“…value generated by the first and the next-to-the-last sets of constraints of (4). Note that f (E) still depends on E even for the case when σ = 0.…”

“…When using Condor, we used the freely available CLP linear programming solver [4] to solve the linear programs and the MATLAB compiler version 4.5 to produce a standalone executable which ran Algorithm 2.1 for given values of ν and µ. On the same machine described above, the average time to run this executable for the parameters chosen by the tuning procedure was 115 seconds.…”

Gomory Cuts from a Position-Indexed Formulation of 1D Stock Cutting

“…For solving the LP relaxation we embedded the COIN-LP Solver 1.5.0 [15]. In each iteration we added one cut.…”

“…It rises the bound to 5.05 which is enough to prove the optimality of a solution with value 6 if we had one. Adding two further cuts, on x 10,20 and on x 15,30 , gives an integer solution with value 6. In each iteration, the maximally violated cut could be properly found, i.e., (2) was exactly solvable and we could construct a Gomory fractional cut.…”