Elastic optical networks (EONs) are considered as very promising architectures for future optical transport networks, since they efficiently use the spectrum resources and provide high bandwidth scalability and granularity. In this paper, the virtual topology design (VTD) problem on EON is considered. Given the physical network and the traffic demand matrix, the goal of VTD is to find the routing paths and the allocated frequency slots of the demand so that the objective cost can be minimized. In this paper, multiple- path routing is allowed and delay-variation between lightpaths for same demand is considered. In this paper, an integer linear programming (ILP) model is used to define the VTD problem on EONs. Moreover, a genetic algorithm (GA) and two heuristic al- gorithms are proposed to solve this problem. Simulations show that the proposed algo- rithms can achieve good results.