Hugh Everett's many-worlds interpretation, attempts to avoid the problem by suggesting there is only one wavefunction, the superposition of the entire universe, and it never collapses--so there is no measurement problem.
Hugh Everett's relative state interpretation, also referred to as the many-worlds interpretation, attempts to avoid the problem by suggesting it is an illusion. Under this system there is only one wavefunction, the superposition of the entire universe, and it never collapses--so there is no measurement problem.