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 ...

Mixed-integer nonlinear programming (MINLP) optimisation constitutes a critical methodology in tackling complex decision-making problems where both discrete choices and continuous variables are ...

This paper studies a class of integer programming problems in which squares of variables may occur in the constraints, and shows that no computing device can be programmed to compute the optimum ...