In this paper, we consider a class of 0–1 programs which, although innocent looking, is a challenge for existing solution methods. Solving even small instances from this class is extremely difficult for conventional branch-and-bound or branch-and-cut algorithms. We also experimented with basis reduction algorithms and with dynamic programming without much success. The paper then examines the pe...

An interior-point algorithm within a branch-and-bound framework for solving nonlinear mixed integer programs is described. In contrast to solving the relaxation to optimality at each tree node, the relaxation is only solved to near-optimality. Analogous to using advanced bases for warmstart solutions in the case of linear MIP, a \dynamic" collection of warmstart vectors is kept. Computational r...

Search-based methods like Branch and Bound and Branch and Cut are essential tools in solving diicult problems to optimality in the eld of combinatorial optimization, and much experience has been gathered regarding the design and implementation of parallel methods in this eld. Search-based methods appear, however, also in connection with certain continuous optimization problems and problems in A...

This paper analyzes the computational performance of the deterministic optimization approach for the Security Constrained Unit Commitment problem (SCUC) addressing thermal generating units, that was developed in its companion paper. The technique proposed in the first part is based on suitable integer cutting planes, specific for the SCUC problem, and a Branch and Bound search which incorporate...

In recent years the branch-and-cut method, a synthesis of the classical branch-and-bound and cutting plane methods, has proven to be a highly successful approach to solving large-scale integer programs to optimality. This is especially true for mixed 0-1 and pure 0-1 problems. However, other approaches to integer programming are possible. One alternative is provided by so-called augmentation al...

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 int...

Given a graph with nonnegative edge weights and node pairs Q, we study the problem of constructing a minimum weight set of edges so that the induced subgraph contains at least K edge-disjoint paths containing at most L edges between each pair in Q. Using the layered representation introduced by Gouveia (1998), we present a formulation for the problem valid for any K, L ! 1. We use a Benders dec...

We propose to solve the break minimization problem in sports scheduling by transforming it into a maximum cut problem in an undirected graph and applying a branch-and-cut algorithm. Our approach outperforms previous approaches with constraint programming and integer programming techniques.

In a previous work, we proposed a new integer programming formulation for the graph coloring problem which, to a certain extent, avoids symmetry. We studied the facet structure of the 0/1-polytope associated with it. Based on these theoretical results, we present now a Branch-and-Cut algorithm for the graph coloring problem. Our computational experiences compare favorably with the well-known ex...