![](bg6.png)
lem to be applicable on another problem, where the
two problems are connected by a gadget. An exist-
ing gadget between Vertex Cover and Hamiltonian
Circuit was detailed, after which constraint families
were covered. These constraint families are vital to
the “translatability” between IP formulations of prob-
lems. Subsequently, our proposed approach was in-
troduced, using specifically the detailed gadget to re-
fine the constraints from Vertex Cover to Hamiltonian
Circuit. This then applies naturally to the optimisa-
tion versions of these two problems: Minimum Ver-
tex Cover and the TSP. This clearly suggests further
avenues of research with respect to implementation of
the approach, experimentation and future generalisa-
tions.
What we are proposing here is a way to transfer
between algorithms in order to bring about meaning-
ful comparisons. Constraint classes and their respec-
tive gadgets allow us to translate from one problem to
another and preserve underlying problem structure. It
is this preserved problem structure we wish the new
algorithm to be able to exploit. By representing prob-
lems as IPs, we can see which constraints need to be
modified when transforming between problems. They
also show us how to modify algorithms for solving
one problem into algorithms to solve another. This
observation is fundamental to our argument. The ap-
proach is useful since we can use it to modify exist-
ing algorithms intended for one domain, and therefore
design “new” heuristics which are applied to a differ-
ent domain (see Figure 1 for a graphical interpreta-
tion). This approach goes some way to addressing
the concerns of (S
¨
orensen, 2015). Our outlook, then,
is a framework in which we can take algorithms de-
signed for one problem, and meaningfully compare
them with algorithms designed for another problem.
ACKNOWLEDGEMENTS
The authors should like to thank Queen Mary Uni-
versity of London and the University of Plymouth for
their generous hospitality when writing this paper. Fi-
nally, the authors thank the anonymous referees for
their suggestions which helped improve the work.
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