Mixed-integer nonlinear programming: Some modeling and solution issues

We examine various aspects of modeling and solution via mixed-integer nonlinear programming (MINLP). MINLP has much to offer as a powerful modeling paradigm. Recently, significant advances have been made in MINLP solution software. To fully realize the power of MINLP to solve complex business optimization problems, we need to develop knowledge and expertise concerning MINLP modeling and solution methods. Some of this can be drawn from conventional wisdom of mixed-integer linear programming (MILP) and nonlinear programming (NLP), but theoretical and practical issues exist that are specific to MINLP. This paper discusses some of these, concentrating on an aspect of a classical facility location problem that is well-known in the MILP literature, although here we consider a nonlinear objective function. © 2007 IBM.