Most of the current attempts for business process optimisation are manual without involving any formal automated methodology. This paper proposes a framework for multi-objective optimisation of business processes. The framework uses a generic business process model that is formally defined and specifies process cost and duration as objective functions. The business process model is programmed and incorporated into a software platform where a selection of multi-objective optimisation algorithms is applied to five test problems. The test problems are business process designs of varying complexities and are optimised with three popular optimisation techniques (NSGA2, SPEA2 and MOPSO algorithms). The results indicate that although the business process optimisation is a highly constrained problem with fragmented search space, multi-objective optimisation algorithms such as NSGA2 and SPEA2 produce a satisfactory number of alternative optimised business processes. However, the performance of the optimisation algorithms drops sharply with even a slight increase in problem complexity. This paper also discusses the directions for future research in this area.