This paper presents a survey of work on Search Based Software Engineering (SBSE) for Software Product Lines (SPLs). We have attempted to be comprehensive, in the sense that we have sought to include all papers that apply computational search techniques to problems in software product line engineering. Having surveyed the recent explosion in SBSE for SPL research activity, we highlight some directions for future work. We focus on suggestions for the development of recent advances in genetic improvement, showing how these might be exploited by SPL researchers and practitioners: Genetic improvement may grow new products with new functional and non-functional features and graft these into SPLs. It may also merge and parameterise multiple branches to cope with SPL branchmania.