Title: Comparisons in optimisation: the Eff-Res approach

Authors: Maurice Clerc; Abhi Dattasharma

Addresses: 204, Route de la Nerulaz, 74570 Groisy, France ' A-9/228, PIN: 741235, Kalyani, West Bengal, India

Abstract: 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.

Keywords: optimisation; performance comparison; theoretical approach; Eff-Res structure; quality; cost; efficiency; mean effort; probability density function.

DOI: 10.1504/IJSI.2014.066557

International Journal of Swarm Intelligence, 2014 Vol.1 No.3, pp.266 - 298

Received: 24 Dec 2013
Accepted: 30 Jun 2014
Published online: 14 Jan 2015 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article