Ubuntu is moving away from the old /etc/network/interfaces or /etc/network/interfaces.d/*.cfg style of configuration towards netplan. Unfortunately nobody seems to have thought about dummy network interface support. There seems to be a workaround with a bridge device without attached interfaces, but I could not get netplan to assign IP addresses to that bridge interface and it furthermore leads to the boot-up process hanging for a few minutes.
I therefore stick with the old /etc/network/interfaces for now and work around a bug with the dummy module initialization in 18.04 like this:
auto dummy0 iface dummy0 inet static address 10.0.0.1 netmask 255.255.255.0 pre-up rmmod dummy; modprobe dummy numdummies=4
The last line did the trick.