Beautiful Memories of a Deserted Island

The protagonist is exiled to a deserted island, where he falls in love with several heroines and faces off against savages and pirates. Rescue never comes. Three months later, he learns that nuclear war has broken out on the mainland, and the survivors have fled to islands in the ocean in search of somewhere to live. The island where the protagonist is stranded will become the only place left on Earth where people can survive, and he naturally becomes its ruler.