Researchers have applied genetic algorithms (GAs) and other heuristic optimization methods to perform truss optimization in recent years. Although a substantial amount of research has been performed on the optimization of truss member sizes, nodal coordinates, and member connections, research that seeks to simultaneously optimize the topology, geometry, and member sizes of trusses is still uncommon. In addition, most of the previous research is focused on the problem domains that are limited to a structured domain, which is defined by a fixed number of nodes, members, load locations, and load magnitudes. The objective of this research is to develop a computational method that can design efficient roof truss systems. This method provides an engineer with a set of near-optimal trusses for a specific unstructured problem domain. The unstructured domain only prescribes the magnitude of loading and the support locations. No other structural information concerning the number or locations of nodes and the connectivity of members is defined. An implicit redundant representation (IRR) GA (Raich 1999) is used in this research to evolve a diverse set of near-optimal truss designs within the specified domain that have varying topology, geometry, and sizes. IRR GA allows a Pareto-optimal set to be identified within a single trial. These truss designs reflect the tradeoffs that occur between the multiple objectives optimized. Finally, the obtained Pareto-optimal curve will be used to provide design engineers with a range of highly fit conceptual designs from which they can select their final design. The quality of the designs obtained by the proposed multi-objective IRR GA method will be evaluated by comparing the trusses evolved with trusses that were optimized using local perturbation methods and by trusses designed by engineers using a trial and error approach. The results presented show that the method developed is very effective in simultaneously optimizing the topology, geometry, and size of trusses for multiple objectives.