This paper presents a constructive solid geometry based representation scheme for structural topology optimization. The proposed scheme encodes the topology using position of few joints and width of segments connecting them. Union of overlapping rectangular primitives is calculated using constructive solid geometry technique to obtain the topology. A valid topology in the design domain is ensured by representing the topology as a connected simple graph of nodes. A graph repair operator is applied to ensure a physically meaningful connected structure. The algorithm is integrated with single and multi-objective genetic algorithm and its performance is compared with those of other methods like SIMP. The multi-objective analysis provides the trade-off front between compliance and material availability, unveiling common design principles among optimized solutions. The proposed method is generic and can be easily extended to any two or three-dimensional topology optimization problem by using different shape primitives.