Downstream purification yields and costs can be significantly improved by genetically modifying a product protein to alter its physical properties. Purification tags, or sequences of amino acids which are genetically fused onto the product protein, have been extensively researched and used for this purpose. However, all of the work in this area has involved specific purification tags, which have advantages in certain situations but are not generically optimal. In this work we describe the development and application of a combinatorial approach which can generate the best sequence of amino acids for a particular product protein. The aim of the work is to develop an algorithm which generates sequences of amino acids (i.e. purification tags) which may be fused onto a specific product protein and used to aid in subsequent purification steps. The work is integrated into a previously developed bioprocess synthesis algorithm, which enables us to compare the flowsheets generated with and without purification tags for a case study system. The results show that the approach allows us to synthesise flowsheets with fewer units, higher yields and lower costs.