A branch and cut algorithm is developed for solving 0-1 MINLP problems. The algorithm integrates Branch and Bound, Outer Approximation and Gomory Cutting Planes. Only the initial Mixed Integer Linear Programming (MILP) master problem is considered. At integer solutions Nonlinear Programming (NLP) problems are solved, using a primal-dual interior point algorithm. The objective and constraints ar...

The bounded diameter minimum spanning tree (BDMST) problem is NP-hard and appears e.g. in communication network design when considering certain quality of service requirements. Prior exact approaches for the BDMST problem mostly rely on network flow-based mixed integer linear programming and Miller-Tucker-Zemlin-based formulations. This article presents a new, compact 0–1 integer linear program...

In the rst part of the paper we present a framework for describing basic tech niques to improve the representation of a mixed integer programming problem We elaborate on identi cation of infeasibility and redundancy improvement of bounds and coe cients and xing of binary variables In the second part of the paper we discuss recent extensions to these basic techniques and elaborate on the investi...

Given a double round-robin tournament, the Traveling Umpire Problem (TUP) seeks to assign umpires to the games of the tournament while minimizing the total distance traveled by the umpires. The assignment must satisfy constraints that prevent umpires from seeing teams and venues too often, while making sure all games have umpires in every round, and all umpires visit all venues. We propose a ne...

Many combinatorial optimization problems have relaxations that are semidefinite programming problems. In principle, the combinatorial optimization problem can then be solved by using a branch-and-cut procedure, where the problems to be solved at the nodes of the tree are semidefinite programs. It is desirable that the solution to one node of the tree should be exploited at the child node in ord...

In this paper, we identify some of the computational advances that have been contributing to the efficient solution of mixed-integer linear programming (MILP) problems. Recent features added to MILP solvers at the algorithmic level and at the hardware level have been contributing to the increasingly efficient solution of more difficult and larger problems. Therefore, we will focus on the main a...

is the objective function to be optimized over P . Whenever all variables in (1.1) are restricted to be integral, the problem is known as a linear integer programming (IP) problem. Conversely, a pure linear programming (LP) problem results when all variables in (1.1) are restricted to be real valued. As is frequently the case for MIP, instead of attempting to optimize (1.3) directly over P , it...

Combinatorial optimization problems can often be formulated as mixed integer linear programming problems, as discussed in Section 1.4.1.1 in this encyclopedia. They can then be solved using branch-and-cut, which is an exact algorithm combining branch-and-bound (see Section 1.4.1.2 of this encyclopedia) and cutting planes (see Section 1.4.3 of this encyclopedia). The basic idea is to take a line...

A new method of sensitivity analysis for mixed integer linear programming MILP is derived from the idea of inference duality The inference dual of an optimization problem asks how the optimal value can be deduced from the constraints In MILP a deduction based on the resolution method of theorem proving can be obtained from the branch and cut tree that solves the primal problem One can then inve...