"Some of the greatest opportunities provided by free improvisation are in the exploration of relationships between players. In this respect solo improvisation doesn't make any sense."
said Derek Bailey in his book "Improvisation: Its nature and practice in Music" (1st edition: Moorland publishing, Ashbourne, UK, 1982).
Derek Bailey was himself a solo improviser (among other musical activities).
Most of the time, improvisation is done by several musicians, influencing each other during their play, combining their actions to create balance and shapes.
Solo improvisation actually comes first, when, as beginners, we simply enjoy touching an instrument and explore it. Then comes reason, we want to play songs, pieces, and for many of us, play with others. Here comes improvisation again when trying to just have fun together.
In my opinion, solo improvisation as a style occurs when a skilled musician decides to establish a new relationship with the instrument, with music.
The most difficult, at this moment, is to get back to the simplicity of our first musical experience, to get back to a discovery mood.