Selective Optimization

This project focuses on developing algorithms for optimization problems that have intrinsic limitations preventing the utilization of all available decision alternatives problem variables andor the satisfaction of all constraints. Part of the optimization decision in these problems is the selection of which variables to use andor which subset of constraints to satisfy. We refer to these problems as selective optimization SO problems. The combinatorial aspects of selection make these problems extremely difficult. In this project we develop a set of generic tools applicable to a wide class of selective optimization problems. Our approach is based on standard mixed-integer programming MIP formulations of selective optimization problems.While such formulations can be attacked by commercial optimization solvers, they typically exhibit extremely poor performance. We develop a variety of effective model and algorithm enhancement techniques for the standardMIP formulations. These techniques are easily integrable into commercial MIP solvers, thereby making them readily usable in applications of selective optimization.