The Algorithm Selection Problem

This chapter starts with a discussion on abstract models: the basic model and associated problems, the model with selection based on features, and themodel with variable performance criteria, to explore the applicability of the approximation theory to the algorithm selection problem.

Abstract

The problem of selecting an effective algorithm arises in a wide variety of situations. This chapter starts with a discussion on abstract models: the basic model and associated problems, the model with selection based on features, and the model with variable performance criteria. One objective of this chapter is to explore the applicability of the approximation theory to the algorithm selection problem. There is an intimate relationship here and that the approximation theory forms an appropriate base upon which to develop a theory of algorithm selection methods. The approximation theory currently lacks much of the necessary machinery for the algorithm selection problem. There is a need to develop new results and apply known techniques to these new circumstances. The final pages of this chapter form a sort of appendix, which lists 15 specific open problems and questions in this area. There is a close relationship between the algorithm selection problem and the general optimization theory. This is not surprising since the approximation problem is a special form of the optimization problem. Most realistic algorithm selection problems are of moderate to high dimensionality and thus one should expect them to be quite complex. One consequence of this is that most straightforward approaches (even well-conceived ones) are likely to lead to enormous computations for the best selection. The single most important part of the solution of a selection problem is the appropriate choice of the form for selection mapping. It is here that theories give the least guidance and that the art of problem solving is most crucial.