Mutation breeding refers to the process by which the seed is exposed to radiation or chemicals in order to develop an improved mutant variant. It can help to improve individual plants' yield and resistance properties.
Conventional breeding is the development of new varieties (cultivars) of plants by using natural processes and traditional methods such as selection and breeding of high yielding varieties. Since potato and tomato belong to two different species and thus cannot be hybridized by conventional breeding methods.
A pollination technique in which the desired pollen grains are used for pollination by artificial means is known as artificial pollination. Since potato and tomato are incompatible, even artificial pollination cannot be used as the pollen grains will not germinate to form the pollen tube on incompatible species.
The fusion of the protoplasm of two different plant cells in order to produce a hybrid variety is called somatic hybridization. The protoplasts of two plants can be made to fuse with a chemical called Polyethylene glycol (PEG). Thus, somatic hybridization would be the best suitable method in developing the hybridized variety between potato and tomato.