11 Parameter Control in Evolutionary Optimisation
379
indicators that are also used as input to parameter control are the crowding distance
and the contributing hypervolume [82, 83]. Other metrics can also be applied such
as ε-dominance, generational distance, delta indicator, two-set coverage and so on
[84]. Compared to adaptive control, self-adaptive control is easier to design and
implement because less modifications are needed to upgrade an existing multiobjective optimisation algorithm [85, 86].
In general, the multi-objective optimisation approach is able to find highquality solutions by adapting to specific dynamic conditions through selection of
appropriate solutions from Pareto front [55]. To further improve its performance,
the control parameter values should also be adapted to lead the search through the
changing system.
11.5.5 Multilevel Optimisation
In many real-world processes, there is a hierarchy of decision-makers and therefore
decisions are taken at different levels [87]. The constraint domain associated with
a multilevel problem is implicitly determined by a series of optimisation problems
that must be solved in a predetermined sequence. The simplest form of a multilevel
problem is the one with two levels, called bilevel optimisation problem. The
optimisation of such problem aims to achieve the optimum solution of the upper (in
hierarchy) level, whilst the optimum of the lower optimisation level is also taken into
account. This forms a challenging complex problem, as for every upper-level vector,
a whole optimisation task of the lower level problem is required. This usually leads
to a problem that is non-linear and non-convex and in general does not follow any
simplified assumptions. Since the lower-level landscape changes for every upperlevel vector, parameter control when using EAs to tackle with this problem can be
useful. More details about multi-/bilevel optimisation and how it is solved can be
found in Chap. 9.
Another very interesting application of bilevel optimisation that was developed
recently and is connected to parameter tuning was formulating the parameter
tuning of EAs as bilevel optimisation problem. In [88] the authors proposed the
parameter tuning problem as an inherently bilevel programming problem involving
algorithmic performance as the objective(s), introducing an evolutionary bilevel
algorithm for parameter tuning. They tested it to few commonly used optimisation
algorithms (differential evolution and Nelder-Mead) and it was found to obtain a fast
convergence to the most efficient control parameter values. In the same vein, [89]
created a bilevel framework for parallel tuning of optimisation control parameters
and compared it to irace proving that it can be competitive. Bilevel control parameter
tuning can be used to design a parameter control mechanism [90].
379
indicators that are also used as input to parameter control are the crowding distance
and the contributing hypervolume [82, 83]. Other metrics can also be applied such
as ε-dominance, generational distance, delta indicator, two-set coverage and so on
[84]. Compared to adaptive control, self-adaptive control is easier to design and
implement because less modifications are needed to upgrade an existing multiobjective optimisation algorithm [85, 86].
In general, the multi-objective optimisation approach is able to find highquality solutions by adapting to specific dynamic conditions through selection of
appropriate solutions from Pareto front [55]. To further improve its performance,
the control parameter values should also be adapted to lead the search through the
changing system.
11.5.5 Multilevel Optimisation
In many real-world processes, there is a hierarchy of decision-makers and therefore
decisions are taken at different levels [87]. The constraint domain associated with
a multilevel problem is implicitly determined by a series of optimisation problems
that must be solved in a predetermined sequence. The simplest form of a multilevel
problem is the one with two levels, called bilevel optimisation problem. The
optimisation of such problem aims to achieve the optimum solution of the upper (in
hierarchy) level, whilst the optimum of the lower optimisation level is also taken into
account. This forms a challenging complex problem, as for every upper-level vector,
a whole optimisation task of the lower level problem is required. This usually leads
to a problem that is non-linear and non-convex and in general does not follow any
simplified assumptions. Since the lower-level landscape changes for every upperlevel vector, parameter control when using EAs to tackle with this problem can be
useful. More details about multi-/bilevel optimisation and how it is solved can be
found in Chap. 9.
Another very interesting application of bilevel optimisation that was developed
recently and is connected to parameter tuning was formulating the parameter
tuning of EAs as bilevel optimisation problem. In [88] the authors proposed the
parameter tuning problem as an inherently bilevel programming problem involving
algorithmic performance as the objective(s), introducing an evolutionary bilevel
algorithm for parameter tuning. They tested it to few commonly used optimisation
algorithms (differential evolution and Nelder-Mead) and it was found to obtain a fast
convergence to the most efficient control parameter values. In the same vein, [89]
created a bilevel framework for parallel tuning of optimisation control parameters
and compared it to irace proving that it can be competitive. Bilevel control parameter
tuning can be used to design a parameter control mechanism [90].