In this paper we discuss some branch and bound methods implemented in the UMPIRE mathematical programming system for solving practical integer programming problems and give details of computational ...

Integer programming is a crucial branch of mathematical optimisation that focuses on problems where some or all decision variables are constrained to be integers. This field underpins many practical ...

Methods for NP-hard discrete optimization problems, including general methods like branch-and-bound and cutting planes, as well as special purpose branch-and-cut methods. Students will be able to ...

A new efficient system of representing the decision-maker's preference structure in solving multicriteria integer programming problems is developed. The problem is solved by an interactive ...

Integer programming, a cornerstone of combinatorial optimisation, focuses on the selection of discrete decision variables to solve complex real‐world problems such as scheduling, network design and ...

Integer linear programming can help find the answer to a variety of real-world problems. Now researchers have found a much faster way to do it. The traveling salesperson problem is one of the oldest ...