The distribution of edge resources in the edge computing environment has an important impact on the Quality of Service (QoS) of edge services. Unreasonable server placement will inevitably lead to problems such as server overload or underload, deteriorating workload balancing and service wait time. Therefore, the key issue to be addressed in server placement is how to enhance the QoS of edge services through efficient edge server placement strategies under multiple requirements such as average task wait time and data privacy. Edge computing (EC) assisted with blockchain technology was argued to be the most potential solution. In this paper, we propose a blockchain-assisted secure ES placement algorithm named ETS_GA. ETS_GA is based on the elite-preserving genetic algorithm (EGA), which is proven to converge. The premature problem of traditional genetic algorithm (GA) is effectively solved by using tabu search (TS) and niche sharing (NS). In addition, we construct an adaptive state supervising machine (ASM) to realize real-time algorithm supervision and adaptively iterate the optimization strategy. Blockchain-based privacy protection methods are also deployed in the placed servers to provide real-time privacy protection. Finally, our proposed method is experimentally compared with four baselines using the real Shanghai Telecom base station data set, whose results demonstrate the superiority of ETS_GA in terms of convergence and global search capability.