Search Based Software Engineering (SBSE) is an approach to software engineering in which search based optimization algorithms are used to identify optimal or near optimal solutions and to yield insight. SBSE techniques can cater for multiple, possibly competing objectives and/ or constraints and applications where the potential solution space is large and complex. This paper will provide a brief overview of SBSE, explaining some of the ways in which it has already been applied to construction of predictive models. There is a mutually beneficial relationship between predictive models and SBSE. The paper sets out eleven open problem areas for Search Based Predictive Modeling and describes how predictive models also have role to play in improving SBSE.