## 1 Introduction  
In recent years, the wireless sensor network routing protocol has been studied in widely. Many excellent routing protocols have been proposed, such as AODV [1], DSR [2], DSDV [3], _etc._ However, as the research moves along, more and more researchers realize that the traditional Open System Interconnect Reference Model (OSI) cannot meet the current quality of service (QoS) requirements of a wireless sensor network; even the OSI model simplifies the network design and improves the robustness. The reasons for this issue are, firstly, the wireless sensor network is a serious resource-constrained network [4], e.g., the limited bandwidth, the limited energy, the limited data processing capability, _etc._ Secondly, the OSI model only allows the communication between the adjacent layers, which cannot adapt to the dynamic changing of the wireless environment flexibly. Recently, the research proposes a cross-layer method for wireless sensor network communication protocol design, and many cross-layer methods have been proposed [5, 6]. The cross-layer design allows the different layers to communicate with each other to coordinate the resource allocation between different layers, and allows the routing protocols to adapt to the wireless environment and the various applications. The core idea of the cross-layer design is to achieve the optimal resource allocation automatically in different layers. The cross-layer design is flexible due to its adaptive ability to adjust to meet the QoS requirements and the network constraints at the same time. Among various different developed policies, two important methods are the optimization-based routing algorithm and the fuzzy logic-based routing algorithm. For the optimization-based routing algorithm, e.g., in [7], the authors propose the Delay-Aware cross-layer design for network utility maximization in multi-hop networks; in [8], the authors introduce a new cross-layer design framework which join the scheduling and power control together; in [9], the authors show the optimization method in a cross-layer design of the wireless network; in [10], the authors present a survey of cross-layer solutions based on the nature of the adaptation using a systematic evaluation of existing approaches and identify critical criteria applicable to generic cross-layer framework design. In [11, 12, 13, 14], the authors research the layering as optimization decomposition, in detail, including the problems, the current status, the open issues, the mathematics, the network architectures, and the framework; more recent works can be seen in [15, 16, 17, 18]. For the fuzzy logic-based routing algorithm, e.g., in [19], the authors take the remaining battery reserve capacity, the link quality, and transmission power into consideration, by using the fuzzy logic inference system to determine the next hop relay node. In [20], the authors use the number of link breaks, the interface queue length, and the type of application as the inputs of the fuzzy logic system to enable each mobile node to separately switch between a reactive routing mode and a proactive routing mode. In [21], the authors use a fuzzy logic system to coordinate the physical layer, data-link layer, and application layer for cross-layer design; the ground speed, average delay, and packets successful transmission ratio are selected as antecedents for the fuzzy logic system. More related works can be found in [22, 23, 24, 25, 26]. However, the recent works also have some disadvantages. First, both of the two types of routing algorithms mentioned above will become extremely complex when the number of constraints increases, which is unacceptable in a wireless sensor network as the computation capability of a node is limited. Second, due to the complexity, they have limited ability to deal with the issue of multiple constraints.