With the advent of Mobile Edge Computing (MEC) that shifts powerful computing resource from remote data centers to the network edge, Digital Twins (DTs) have emerged as a promising technology to provide comprehensive descriptions of physical objects in cyberspace with real-time interactions. Recent advancements of the Internet of Things (IoT) have contributed abundant and continuous data to the explosion of DTs, spurring the need to address the freshness of DTs through timely synchronizations. In this paper, we investigate innovative methodologies to improve the freshness of DTs while minimizing the cost of diverse resources consumed for improving freshness. Specifically, we first formulate a novel optimization problem: the DT freshness optimization problem. Next, we provide an Integer Linear Program (ILP) solution for the DT freshness optimization problem when the problem size is small; and devise a randomized algorithm at the expense of bounded resource violations, otherwise. We finally evaluate the performance of our algorithm through simulations. The simulation results show that our algorithm is promising.