Optimization and Computational Fluid Dynamics - Department of ...

8 Multi-objective Optimization in Convective Heat Transfer 253
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Fig. 8.15 Fabricability check
ing performances of the second set, as it comes out from a comparison between
Figs. 8.13(a) and 8.13(b). As already anticipated the MOGA algorithm is well
suited for truly multi-objective problems. It is robust, albeit somehow slow
for increasing number of objective functions or design variables.
Once a high quality Pareto front has been obtained, one can choose slightly
different strategies in order to improve the fitness of the channels. One way
is to transform the multi-objective problem into a single-objective one by
means of a weighted function, involving objectives. The mono-objective optimization,
performed using MOGA-II and Simplex [45] algorithms, makes the
process faster. Having two starting objectives, imposing different relations
between designs, a different weight distribution on f and Nu could be given
and a different ranking to each alternative would be assigned. Using MCDM,
two kind of utility functions were created: the first privileges the increase of
Nusselt number, whereas the other is more focused toward the reduction of
the friction factor. In this way, the results summarized in Fig. 8.14 have been
obtained after evaluating 2,500 designs.
In the same figure two sequences of three channels, each one having almost
the same performance metrics, are marked. They represent different
arrangements of geometries in the Pareto front. After the NURBS optimization
process it has been recognized that two different families of channel
shapes belong to the part of the Pareto front characterized by high values of
f and Nu, and they are shuffled.
Although various kind of corrugations are present, the main difference
between the two types, the one called S for short (ID a, ID c, ID e), the
other L for long (ID b, ID d, ID f), is the length of the module. The average
length of S-channels is 1, while for L-channels it is 2, so the ratio between
length of channels S and channels L is 0.5. This is an important feature of the
optimization because it shows the non-univocity of the solution, i.e., similar
performances can be reached by very different geometries [41]. In Fig. 8.16,
the design database has been filtered and divided into two categories. Pareto