Comparisons in optimisation: the Eff-Res approach
Maurice Clerc, Abhi Dattasharma · International Journal of Swarm Intelligence · 2014
To compare performances of optimisation methods, we formally define an abstract structure called Eff-Res, which is a probability density function involving the effort given by an algorithm and the obtained results. We show how to develop this structure, both theoretically as well as computationally, for several problems. By using Eff-Res, we develop measures like mean cost of result, mean efficiency of an effort, or mean effort needed to guarantee a result. We also introduce the notion of quality of a result, and combine the idea of cost and efficiency with quality. The approach is demonstrated on some classical problems with two different algorithms: Adaptive Population-based Simplex and Standard PSO 2007. We briefly discuss some open questions, and in the appendices we discuss some implementation issues