Structural Redundancy in Large-Scale Optimization Models

Abstract

This paper discusses automatic detection and exploitation of structural redundancy in large-scale mathematical programming models. From our perspective, such redundancy represents embedded special structure which can give significant insight to the model proponent as well as greatly reduce solution effort. We report experiments with real-life linear programming (LP) and mixed-integer (MIP) models in which various methods are developed and tested as integral modules in an optimization system of advanced design. We seek to understand the modeling implications of these embedded redundancies as well as to exploit them during actual optimization. The latter goal places heavy emphasis on efficient, as well as effective, identification techniques for economic application to large models. Several (polynomially bounded) heuristic detection algorithms are presented from our work. In addition, bounds are reported for a maximum row dimension of the more complex structures. These bounds are useful for objectively estimating the quality of heuristically derived assessments of structural redundancy. Finally, some additional suggestions are made for analyzing nonlinear programming (NLP) models.