Permission Set Assignments are data in the org. The DML operation cannot be performed by a Change Set - but this sample code might help you in automating the assignments.
// the user reference
User u = new User();
// the names of the permission sets you need to assign
List<String> permissionSets = new List<String>{'permission_set_name_1','permission_set_name_2'};
// the assignment records for DML
List<PermissionSetAssignment> psAssignments = new List<PermissionSetAssignment>();
// query for the sets and assign to the user
for (PermissionSet ps : [SELECT Id, Name
FROM PermissionSet
WHERE Name IN :permissionSets]) {
psAssignments.add(
new PermissionSetAssignment(
AssigneeId = u.Id,
PermissionSetId = ps.Id
)
);
}
// insert the assignments
insert psAssignments;