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A Connected Dominating Set (CDS) is used as a virtual backbone for efficient routing and broadcasting in Wireless Sensor Networks (WSNs). Most existing works focus on constructing a Minimum CDS (MCDS), a k-connect m-dominating CDS, a minimum routing cost CDS or a bounded-diameter CDS. However, no work considers the load-balance factor of CDSs in WSNs. In this paper, we propose a novel problem - the Load-Balanced CDS (LBCDS) problem, in which constructing an LBCDS and load-balancedly allocating dominatees to dominators are investigated simultaneously. A Genetic Algorithm (GA) based strategy called LBCDS-GA is proposed to construct an LBCDS in a WSN. As a matter of fact, constructing a CDS as a virtual backbone in a WSN is an efficient way to extend network lifetime through reducing the number of the nodes involved in communication, while building an LBCDS and load-balancedly allocating dominatees to dominators can further prolong network lifetime through balancing the workloads of all the dominators. Through extensive simulations, we demonstrate that our proposed methods extend network lifetime by 65% on average compared with the best and latest MCDS construction algorithm.