Abstract: Topology optimization solves the basic engineering design problem of distributing a limited amount of material in a design space in order to form a structure or a mechanism that works in an optimal way. One of the most interesting applications is the synthesis of compliant mechanisms. A compliant mechanism is a structure with the following features: i) the external load is transformed to motion along specific direction at a given point of the structure (different to the ones where the loading is applied), ii) it is a monolithic, single-piece structure without any joints and hidges, iii) the structure is flexible enough to deliver motion, iv) the strucure is stiff enough to bear the applied load. Several multi-objective topology optimization problems are first formulated in this paper. Due to local minima that arise iterative local search methods may not be effective. Therefore, a hybrid algorithm utilizing elements of global optimization techniques such as Differential Evolution and Particle Swarms Optimization, is proposed. The hybrid scheme uses iterative local search methods as the evaluation tool of the previously mentioned global optimization algorithms.