on the behaviour of weighted multi-recombination evolution strategies optimising noisy cigar functions
Cigar functions are convex quadratic functions that are characterised by the presence of only two distinct eigenvalues of their Hessian, the smaller one of which occurs with multiplicity one. Their ridge-like topology makes them a useful test case for optimisation strategies. This paper extends previous work on modelling the behaviour of evolution strategies with isotropically distributed mutations optimising cigar functions by considering weighted recombination as well as the effects of noise on optimisation performance. It is found that the same weights that have previously been seen to be optimal for the sphere and parabolic ridge functions are optimal for cigar functions as well. The influence of the presence of noise on optimisation performance depends qualitatively on the trajectory of the search point, which in turn is determined by the strategy's mutation strength as well as its population size and recombination weights. Analytical results are obtained for the case of cumulative step length adaptation.
evolution strategy noise cigar function weighted recombination cumulative step length adaptation