## 1 Introduction  
Wireless sensor networks (WSNs) are deployed in monitoring regions equipped with a large number of sensor nodes with neither partition nor infrastructure support, through the wireless self-organized network in multi-hop communication mode [1]. As a kind of new intelligent fusion of multiple disciplines, such as computer science, network technology, embedded system, calculation of multiple fields, microelectronics, sensor information acquisition and processing technology, _etc._, wireless sensor networks can be used to sense and collect in real time all kinds of data for monitoring objects and information about the environment, through various integrated microsensors. In previous research, the sensor embedded system used to be in charge of dealing with the information, and sending the sensed information to the user terminal by multi-hop relay through a self-organized wireless communication network, so as to realize the \"ubiquitous computing\" concept. WSNs have created a new era for information acquisition and processing technology, and have promising application prospects in many fields, such as national defense, industry, smart city, Internet of things (IoT), cyber-physical system (CPS), radio frequency identification(RFID), _etc._[2]. In the mobile environment, sensor networks are robust and the topology may vary as the nodes move. Providing sensor computing is however still a challenging issue, especially in heterogeneous or mobile environments. Present studies on WSNs are mainly confined to isomorphic network fields. Isomorphism in WSNs is used to simplify all of the node sensors to be of the same structure, while ignoring the effect the heterogeneity of any node brings to the design of network and protocols [3]. At the beginning of the study, this simplified network model was used for convenience, but with the development of wireless sensors and their applications in the research fields of the depth and the promotion, the isomorphic WSN model has become competent to meet the demands of actual application scenarios. Especially in the areas of practical network application, monitoring and management of sensor nodes are mainly set for mixed environments, where two or more sensor nodes would be needed for monitoring. Therefore, in a heterogeneous world, a heterogeneous WSNs model and the actual application scenario is suitable. Heterogeneous sensor networks refer to wireless networks consisting of a variety of different types of sensor nodes. Node energies and communication capacity of heterogeneous characteristics are ubiquitous features of heterogeneous wireless sensor networks (HWSNs), this paper reports research on wireless sensor network energy optimization and a topology control algorithm appropriate for the energy and communication capacity of heterogeneous wireless sensor networks. At present the research on heterogeneous networks is still in the initial stages of exploration, and there are still a series of unsolved problems to be solved. For example, exploring the scientific meaning of heterogeneous wireless sensor networks, and the specific content of networks in heterogeneous forms. The heterogeneous network model is at present so simple that it cannot adequately describe the actual application scenarios, thus the problem of how to construct the heterogeneous network, that involves how to design energy efficient strategies in heterogeneous networks, and thereafter improve the energy efficiency of the heterogeneous network remains unresolved. Therefore, the utilization of a large number of isomorphic WSN theories in heterogeneous networks has a profound theoretical and practical significance. Sensor nodes organized in the form of clusters can effectively achieve energy savings in the network. Many energy-efficient routing protocols are designed based on the cluster structure [4]. In the cluster structure, throughout the network the algorithms are only executed in a cluster range without waiting for control messages.