6. EA/VND/VNS HYBRIDS
Over the last years, hybrid metaheuristics have become
increasingly popular as they are often able to exploit the advantages
of dierent simpler optimization techniques yielding
an improved overall performance [8, 18]. In fact, in our
case it is an obvious idea to combine the EA with the described
VND or VNS. In our rst approach, we do this as
in the MA of the previous section: The VND is always only
applied to new best solutions as a strong local improvement.
This EA/VND hybrid will be denoted by HybB.
Another combination possibility is to run the EA and the
VNS in a pure sequential way: The EA's nally best solution
is used as the starting point for the VNS. We term this
algorithmic setting as HybS.
A renement of this approach is the intertwined execution
of the EA and the VNS, as it is shown in Algorithm 3: A
prespecied total execution time T is divided into 2 slots
and both algorithms are alternately applied. The EA starts
and retains its population during its pauses. When the VNS
takes over, it always begins with the EA's so far best solution
and with its rst neighborhood. Of course, each nal
solution of the VNS at the end of its slots is also inserted
into the EA's population, replacing the worst solution and
rejecting solutions having the same TreeRank scores as already
existing ones. We denote such an intertwined setting
with EA/VNS phases by HybI .
One might think it is even better to use the MA instead of
the EA in the hybrid variants, but this is not true in general.
Preliminary tests have clearly shown a worse performance of
a sequential MA/VNS combination. This is probably due to
the MA already focusing too strongly on local optima and
thus seeding the VNS with a solution less suitable for further
improvement. In the following, we therefore only consider
in more detail an intertwined MA/VNS hybrid which we
denote by Hyb
I .
6. EA/VND/VNS HYBRIDSOver the last years, hybrid metaheuristics have becomeincreasingly popular as they are often able to exploit the advantagesof di erent simpler optimization techniques yieldingan improved overall performance [8, 18]. In fact, in ourcase it is an obvious idea to combine the EA with the describedVND or VNS. In our rst approach, we do this asin the MA of the previous section: The VND is always onlyapplied to new best solutions as a strong local improvement.This EA/VND hybrid will be denoted by HybB.Another combination possibility is to run the EA and theVNS in a pure sequential way: The EA's nally best solutionis used as the starting point for the VNS. We term thisalgorithmic setting as HybS.A re nement of this approach is the intertwined executionof the EA and the VNS, as it is shown in Algorithm 3: Aprespeci ed total execution time T is divided into 2 slotsand both algorithms are alternately applied. The EA startsand retains its population during its pauses. When the VNStakes over, it always begins with the EA's so far best solutionand with its rst neighborhood. Of course, each nalsolution of the VNS at the end of its slots is also insertedinto the EA's population, replacing the worst solution andrejecting solutions having the same TreeRank scores as alreadyexisting ones. We denote such an intertwined settingwith EA/VNS phases by HybI .One might think it is even better to use the MA instead ofthe EA in the hybrid variants, but this is not true in general.Preliminary tests have clearly shown a worse performance ofa sequential MA/VNS combination. This is probably due tothe MA already focusing too strongly on local optima andthus seeding the VNS with a solution less suitable for furtherimprovement. In the following, we therefore only considerin more detail an intertwined MA/VNS hybrid which wedenote by HybI .
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