Multi-objective analysis of computational models

Computational models are of increasing complexity and their behavior may in particular emerge from the interaction of different parts. Studying such models becomes then more and more difficult and there is a need for methods and tools supporting this process. Multi-objective evolutionary algorithms generate a set of trade-off solutions instead of a single optimal solution. The availability of a set of solutions that have the specificity to be optimal relative to carefully chosen objectives allows to perform data mining in order to better understand model features and regularities. We review the corresponding work, propose a unifying framework, and highlight its potential use. Typical questions that such a methodology allows to address are the following: what are the most critical parameters of the model? What are the relations between the parameters and the objectives? What are the typical behaviors of the model? Two examples are provided to illustrate the capabilities of the methodology. The features of a flapping-wing robot are thus evaluated to find out its speed-energy relation, together with the criticality of its parameters. A neurocomputational model of the Basal Ganglia brain nuclei is then considered and its most salient features according to this methodology are presented and discussed. Nomenclature X parameter to be optimized (X ∈ R) f(X) function to be optimized ≺ dominance relation dominance or equality relation χ set of Pareto set approximations Γ set of independent runs of the optimizer αχ(z) attainment function Ψ1 attainment surface corresponding to a value of 1 of the attainment function Ψ0 attainment surface corresponding to a value of 0 of the attainment function I H(χ0) hypervolume of the set of points χ0 relative to the reference point p η(χ0) nadir point ι(χ0) ideal point η̄ conservative nadir point Flapping wing aircraft example DI wing dihedral TWi internal twist TWe external twist aDI amplitude of the wing dihedral pDI period of the wing dihedral aTWi amplitude of the internal twist pTWi phase of the internal twist ar X iv :1 50 7. 06 87 7v 1 [ cs .N E ] 2 4 Ju l 2 01 5