Pursuing the Pareto Paradigm: Tournaments, Algorithm Variations and Ordinal Optimization

Abstract

The ParetoGP algorithm which adopts a multi-objective optimization approach to balancing expression complexity and accuracy has proven to have significant impact on symbolic regression of industrial data due to its improvement in speed and quality of model development as well as user model selection, (Smits and Kotanchek, 2004), (Smits et al., 2005), (Castillo et al., 2006). In this chapter, we explore a range of topics related to exploiting the Pareto paradigm. First we describe and explore the strengths and weaknesses of the ClassicGP and Pareto-Front GP variants for symbolic regression as well as touch on related algorithms, Next, we show a derivation for the selection intensity of tournament selection with multiple winners (albeit, in a single-objective case). We then extend classical tournament and elite selection strategies into a multi-objective framework which allows classical GP schemes to be readily Pareto-aware. Finally, we introduce the latest extension of the Pareto paradigm which is the melding with ordinal optimization. It appears that ordinal optimization will provide a theoretical foundation to guide algorithm design. Application of these insights has already produced at least a four-fold improvement in the ParetoGP performance for a suite of test problems.