No abstract

Multi-objective evolutionary algorithms are widely established and well developed for problems with two or three objectives. However, it is known that for many-objective optimisation, where there are typically more than three objectives, the algorithms applying Pareto optimality as a ranking metric may loose their effectiveness [1]. This paper compares three different approaches to generating Pareto surfaces on both multi and many objective problems. The first approach is using an established Pareto ranking method (NSGA II), the second combines multiple single objective optimisations in a single run (MSOPS), and the third uses multiple runs of a single objective optimiser.The results demonstrate that much can be gained by generating the entire Pareto set in a single run, when compared to repeated single objective optimisations. It is also clear that NSGA II loses its effectiveness as the problem dimensionality increases -it is more effective to use many single objective optimisations than a Paretoranking based optimiser on many-objective problems. Ultimately though, "many once or once many" is dependent on algorithm choice, not problem scale.

This paper details a new non-Pareto evolutionary multi-objective algorithm, Multiple Single Objective Pareto Sampling (MSOPS), that performs a parallel search of multiple conventional target vector based optimisations, e.g. weighted min-max.The method can be used to generate the Pareto set and analyse problems with large numbers of objectives. The method allows bounds and discontinuities of the Pareto set to be identified and the shape of the surface to be analysed, despite not being able to visualise the surface easily.A new combination metric is also introduced that allows the shape of the objective surface that gives rise to discontinuities in the Pareto surface to be analysed easily.

DNA Microarrays are used to simultaneously measure the levels of thousands of mRNAs in a sample. We illustrate here that a collection of such measurements in different cell types and states is a sound source of functional predictions, provided the microarray experiments are analogous and the cell samples are appropriately diverse. We have used this approach to study stem cells, whose identity and mechanisms of control are not well understood, generating Affymetrix microarray data from more than 200 samples, including stem cells and their derivatives, from human and mouse. The data can be accessed online (StemBase;

Existing evolutionary methods capable of true Many-Objective optimisation have been limited in their application: for example either initial search directions need to be specified a-priori, or the use of hypervolume limits the search in practice to less than 10 objective dimensions.This paper describes two extensions to the Multiple Single Objective Pareto Sampling (MSOPS) algorithm. The first provides automatic target vector generation, removing the requirement for initial a-priori designer intervention; and secondly redefines the fitness assignment method to simplify analysis and allow more comprehensive constraint handling.The significant enhancements allow the new MSOPS-II ranking process to be used as part of a general-purpose multi/many objective optimisation algorithm, requiring minimal initial configuration.