## 1 Introduction
This comes from using mesh clients as routers, thus compensating for the bad performance of some space directions; bad flow or connection failures produced by obstacles (buildings, trees, _etc._). Further, for implementing WMNs, already available components, coming from other technologies, can be used such as: _Ad Hoc_ network routing protocols [5, 14, 15], IEEE 802.11 MAC protocol, wired equivalent privacy (WEP) security, _etc._ Unfortunately, these solutions can offer some but not all of the necessary performance needed to satisfy final subscribers. As one of the main problems, optimal routing which considers all important parameters of WNM topology stands out [14, 15]. The advantages of WMNs are: (1) Reliability--the ability of the protocol to fulfill quick rerouting in the case of link failure between nodes in overall route; mobile user connectivity--protocol should enable fast hand-offs; (2) Scalability: in the case of overloading, the number of nodes and QoS in the network cannot be expanded, so various categories of traffic should be delivered to the optimal routes which can satisfy needed quality of service [11]. On the other hand, wireless routers in WMNs are expected to be unstable. Apart from routers, wireless links can be unstable. The quality of data transmission can be weakened by multi-path fading effects, external interference and weather conditions. The potential instability of routers and links can appear after determining the optimal route, during transmission of data, which brings us additional requirements related to the protocol. Existing routing protocols applied to WMNs do not have enough scalability [14, 16]. Some protocols perform an additional check after finding an optimal route, but it is certain that the conditions can changed over time [16]. Usually, the changes are detected only when the link fails or if some of the routers do not respond [17, 18]. The authors of [19, 20] suggested some solutions, where the route testing is done periodically, but the testing interval is not small enough to follow current network monitoring. Besides, the protocol should obtain adaptability in a sense of topology change, as well as adaptability of routers and links, which is quite often in WMNs. In addition to the problem of defining the optimal routing protocol, while designing the WMN, the problem of the quality of wireless transmissions has to be considered. Several authors have provided suggestions for solving the transmission problem and making optimal use of the available spectrum [21, 22, 23]. In this paper, one solution for optimal routing in WMNs is proposed, more specifically, the one emphasizing the management of network resources. Taking into consideration all particularities of WMNs, the proposed solution provides, in the Pareto sense, the optimal route selection, in the shortest time interval, taking into account the current state of the network and optimal use of all network resources. In that way, it is necessary to choose the route in accordance with the needs of future subscribers and their traffic, with as small as possible number of rerouting and the optimal loading balance of the entire network. The rest of this paper is organized as follows. The brief view of related work is given in Section 2. Section 3 describes the methodology including network deployments and protocol description. The used artificial neural network model is explained in Section 4, while new routing metric based on Hopfield neural network is given in Section 5. Section 6 provides our simulation results. At the end we summarize our work and give future plans in the Conclusions.