This invention relates to methods and systems for searching. It is particularly applicable to methods of searching which enable efficient identification of compatible portfolios. Embodiments of the invention propose methods of searching which address the huge search space issue associated with identifying compatible portfolios. In particular, embodiments of the invention start their search operations simultaneously from both sides by both trying to form valid portfolios from candidate products until a valid solution is found and trying to find conflicts from the defined compatibility rules until a conflict is found which leads to the conclusion that no valid solution exists. A conclusion from either process will stop the whole searching process which can significantly reduce blind and unnecessary searching in the whole search space. In embodiments of the invention, the two sides of the search process are also connected in a way which permits two-way communications between the processes to share information about invalid search branches during the execution of the search. The shared information is then used to direct the current and later stage of search execution. Such exchange of information can also significantly reduce the search space and create more efficient searching systems and methods, particularly by stopping search agents from carrying out invalid future searches in branches that another agent has already identified as invalid.