  The emerging research paradigm coined as multitasking optimization aims to
solve multiple optimization tasks concurrently by means of a single search
process. For this purpose, the exploitation of complementarities among the
tasks to be solved is crucial, which is often achieved via the transfer of
genetic material, thereby forging the Transfer Optimization field. In this
context, Evolutionary Multitasking addresses this paradigm by resorting to
concepts from Evolutionary Computation. Within this specific branch, approaches
such as the Multifactorial Evolutionary Algorithm (MFEA) has lately gained a
notable momentum when tackling multiple optimization tasks. This work
contributes to this trend by proposing the first adaptation of the recently
introduced Multifactorial Evolutionary Algorithm II (MFEA-II) to
permutation-based discrete optimization environments. For modeling this
adaptation, some concepts cannot be directly applied to discrete search spaces,
such as parent-centric interactions. In this paper we entirely reformulate such
concepts, making them suited to deal with permutation-based search spaces
without loosing the inherent benefits of MFEA-II. The performance of the
proposed solver has been assessed over 5 different multitasking setups,
composed by 8 datasets of the well-known Traveling Salesman (TSP) and
Capacitated Vehicle Routing Problems (CVRP). The obtained results and their
comparison to those by the discrete version of the MFEA confirm the good
performance of the developed dMFEA-II, and concur with the insights drawn in
previous studies for continuous optimization.
