the best predicted performance to run for one generation; and (5)
repeat step (3) and (4) until a given computational budget is
reached.
Note that as the algorithm which has the best predicted
performance may be different at different stages of the search, our
approach will switch from one algorithm to another and back
automatically and seamlessly.
In a nutshell, we propose to choose, at any point of the search, the
algorithm which has the best predicted performance to run (for
one generation). A typical scenario of running our algorithm is
that after some trials in which each algorithm runs in parallel and
interacts indirectly, an algorithm which has the best predicted
performance by a considerable margin stands out, and only it is
run for quite some time. If it is a very good algorithm that excels
in small, medium and large budgets, then only it will run from
then on. However, if it is an algorithm that converges fast to a
local optimum, as discussed above, then it will run for awhile and
gradually the predicted performance will not be as good compared
with other algorithms. At which time, a second algorithm, which
has a better predicted performance, will take over. Like changes
would occur as the search progresses.
A novel online performance prediction metric is proposed to
advise which algorithm should be chosen to generate the next new
generation of solutions. The metric is parameter-less - it does not
introduce any new control parameter to the system - thus avoiding
the difficult parameter tuning and control problem [2]. We name
our algorithm Multiple Evolutionary Algorithm (MultiEA).
Currently in the EC community, CMA-ES [3] is one of the
strongest algorithms. It is the clear winner in the BBOB2010
competition [4]. On the other hand, several improved variants of
DE have won several competitions held in recent years [5].
Amongst these variants, Composite DE (CoDE) [6] and Self
adaptive DE (SaDE) [7] are the state of the art. For the influential
swarm intelligence methods, the current “standard” PSO
algorithm is PSO2011 [8], and ABC [9] is one of the most
recently proposed methods with the advantage of competitive
performance and few control parameters. In this paper, ABC,
CMA-ES, CoDE, PSO2011 and SaDE shall be chosen by us for
further investigations since they are our choice algorithms if we
were to recommend to outsiders. Other EC researchers may of
course have other choices. In the companion paper [10], we report
a novel way to automatically and parameter-lessly compose a
portfolio, i.e., find its member algorithms.
The rest of this paper is organized as follows: Section 2 discusses
the relationships of our approach with existing works. Section 3
reports MultiEA. Section 4 reports the numerical experiments.
Section 5 investigates the properties of the prediction measures.
Section 6 concludes