Lifting is a procedure for deriving valid inequalities formixed-integer sets from valid inequalities for suitable restrictions of those sets. Lifting has been shown to be very effective in developing strong valid inequalities for linear integer programming and it has been successfully used to solve such problems with branch-and-cut algorithms. Here we generalize the theory of lifting to conic i...

We investigate the algorithmic and implementation issues related to the e ective and e cient use of lifted cover inequalities and lifted GUB cover inequalities in a branch and cut algorithm for integer programming We have tried various strategies on several test problems and we identify the best ones for use in practice

Dual fractional cutting plane algorithms, in which cutting planes are used to iteratively tighten a linear relaxation of an integer program, are well-known and form the basis of the highly successful branch-and-cut method. It is rather less well-known that various primal cutting plane algorithms were developed in the 1960s, for example by Young. In a primal algorithm, the main role of the cutti...

In this paper we consider a problem that arises in the process of reconstruction of DNA fragments. We present a graph theoretical formulation of the problem and mention some extensions. We show this problem to be NP-hard. A 0-1 integer linear programming formulation of the problem is given and some preliminary results of a branch-and-cut algorithm based on this formulation are discussed. 1 We t...

Branch-and-cut methods are among the most important techniques for solving integer programming problems. They can also be used to prove that all solutions of an integer program satisfy a given linear inequality. We examine the complexity of branch-and-cut proofs in the context of 0-1 integer programs. We prove an exponential lower bound on the length of branch-and-cut proofs which use 0-1 branc...

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...

Controlled tabular adjustment (CTA) is an emerging protection technique for tabular data protection. CTA formulates a mixed integer linear programming problem, which is tough for tables of moderate size. Finding a feasible initial solution may even be a challenging task for large instances. On the other hand, end users of tabular data protection techniques give priority to fast executions and a...

an interactive heuristic approach can offer a practical solution to the problem of linear integer programming (lip) by combining an optimization technique with the decision maker’s (dm) judgment and technical supervision. this is made possible using the concept of bicriterion linear programming (blp) problem in an integer environment. this model proposes two bicriterion linear programs for iden...

This tutorial describes a logic based approach to formulating and solving pure and mixed integer programming problems It develops logical counterparts for ideas associated with traditional branch and cut methods such as cutting planes facet de ning cuts re laxations etc The motivations for doing this are a to exploit the structure of a wide range of problems that are too complex for polyhedral ...