E-mail this page
Request WebMeeting
Mixed Integer Nonlinear Programming
Mixed Integer Nonlinear Programming (MINLP) problems contain nonlinear expressions and integer variables. Mixed Integer Nonlinear Programming problems are in general more difficult to solve than mixed integer programming problems and nonlinear programming problems.
Benefits of Using AIMMS as Mixed Integer Nonlinear Programming Software
Besides the general benefits of using AIMMS, there is some specific functionality that makes AIMMS an excellent tool for modeling mixed integer nonlinear programming problems. For example, AIMMS is equipped with an open implementation of the outer approximation algorithm to solve mixed integer nonlinear programming problems. This AIMMS Outer Approximation (AOA) is written with the AIMMS GMP functions and can be customized by the user to fine tune the algorithm for their specific problem. Customization is however not needed which makes AIMMS Outer Approximation usable as an out of the box solver for large scale MINLP models. AIMMS Outer Approximation uses a combination of a MIP and NLP solver to solve the MINLP problems. Any combination of the MIP and NLP solvers available can be used.
Mixed Integer Nonlinear Programming Solvers
Standard Solvers
Next to AIMMS outer approximation algorithm AIMMS supports BARON as a solver to solve Mixed Integer Nonlinear Programming problems. BARON is a global optimizer while AIMMS Outer Approximation can only guarantee local optima.
Open Solver Interface
The AIMMS Open Solver Interface allows solver developers to link their own mixed integer nonlinear programming solvers to AIMMS themselves.
Mixed Integer Nonlinear Programming Examples
Investment Portfolio Selection
In a company top management wants to understand how it can spread their overall budget over several investment categories. Once their budget allocation becomes available, tactical investment decisions at the next decision level must be made concerning individual securities within each investment category. Such a two-phase approach supports hierarchical decision making which is typical in large financial institutions. The model can be extended with a cost budget. In this case, there are nonlinear costs associated with the investments, making it a mixed integer nonlinear programming model. For a full description of the model see 
Chapter 18 in the Optimization Modeling Guide.
Download the Investment Portfolio Selection Example
Free Trial License
Download a free trial license of AIMMS to experience the benefits of using AIMMS as your mixed integer nonlinear programming software.
