A Simplex-Like Method for Pareto Optimisation of Bi-objective Problems
Dr Tom Peachey, Nimrod expert and Melbourne-based consultant
Classical numerical optimisation may be summed up as go downhill (or uphill). Recently methods based on biological systems present an alternative; they use populations of trial solutions and the rule breed and winnow. The first approach works well if the response surface is smooth, the second becomes competitive for a rough surface. The Nimrod team has experience with optimising a wide range of computational models. In such problems the computed objective is typically smooth with an overlay of computational noise. We usually found that the go downhill Nelder and Mead simplex method is sufficient for such problems, robust enough to cope with moderate noise.
When optimising two competing objectives one searches for Pareto optima, points for which one objective can only be improved at the expense of the other. Here current research is almost entirely devoted to population-based methods, typically using genetic algorithms.
This talk will present an alternative, go downhill, approach based on minimisation of a novel objective. Instead of a simplex, it uses a complex (a set of connected simplices) that walks around the search space and then shrinks over a Pareto point. Moreover, once a Pareto point has been found, the method indicates the direction of adjacent Pareto points, so the efficient curve of such points may be tracked with minimal computation. How all this works will be explained in the talk.
The new method has been implemented in the Nimrod suite of tools and hence interfaced with a powerful system for concurrent execution of computational models.
This is joint work with Mike Riley of the Lincoln School of Engineering, UK. The speaker is seeking people with practical optimisation problems with a view to joint publications.
Tom is a mathematician with an interest in computational modelling. He spent 11 years working on the Nimrod suite of tools. He now alternates between Australia and Thailand trying to write up those unfinished ideas.