Mixed-Integer Linear Programming Reformulations for Some Nonlinear Discrete Design Optimization Problems

Abstract

This paper deals with a special class of nonlinear discrete design optimization problems which involve nonlinear separable objective functions and bilinear constraints. These constraints involve products of design and state variables in which the former are restricted to take discrete values Two special cases are identified for which advantage can be taken of the discrete nature of the design variables to reformulate these problems as MILP models which can be solved to global optimality. The computational expense can be reduced with SOS 1 sets and a simple solution strategy that is proposed. The application of the MILP reformulations is applied to multiproduct batch plant problems in chemical engineering and 1 Engineering Design Research Center, Carnegie Mellon University, Pittsburgh, PA 15213. The authors gratefully acknowledge financial support from the Engineering Design Research Center. University Ubraritt Carnegie Msiion y | Pittsburgh PA l to structural design problems in civil engineering. Numerical results and comparisons with other methods are also presented.