Integrative Population Analysis for Better Solutions to Large-Scale Mathematical Programs

Abstract

Integrative Population Analysis unties the learning process called target analysis and a generalized form of sensitivity analysis to yield improved approaches for optimization, particularly where problems from a particular domain must be solved repeatedly. The resulting framework introduces an adaptive design for mapping problems to groups, as a basis for identifying processes that permit problems within a given group to be solved more effectively. We focus in this paper on processes embodied in parameter-based definitions of regionality,accompanied by decision rules that extract representative solutions from given regions in order to yield effective advanced starting points for our solution methods. Applied to several industrial areas, our approach generates regions and representations that give an order of magnitude improvement in the time required to solve new problems that enter the population and therefore makes the application of large scale optimization models practical in reality.