  Wind energy is one of the cleanest renewable electricity sources and can help
in addressing the challenge of climate change. One of the drawbacks of
wind-generated energy is the large space necessary to install a wind farm; this
arises from the fact that placing wind turbines in a limited area would hinder
their productivity and therefore not be economically convenient. This naturally
leads to an optimisation problem, which has three specific challenges: (1)
multiple conflicting objectives (2) computationally expensive simulation models
and (3) optimisation over design sets instead of design vectors. The first and
second challenges can be addressed by using surrogate-assisted e.g.\ Bayesian
multi-objective optimisation. However, the traditional Bayesian optimisation
cannot be applied as the optimisation function in the problem relies on design
sets instead of design vectors. This paper extends the applicability of
Bayesian multi-objective optimisation to set based optimisation for solving the
wind farm layout problem. We use a set-based kernel in Gaussian process to
quantify the correlation between wind farms (with a different number of
turbines). The results on the given data set of wind energy and direction
clearly show the potential of using set-based Bayesian multi-objective
optimisation.
