## 1 Introduction
But even so, this will eventually lead to high control-traffic overhead, excessive use of energy, an increase in data network congestion and a high delay [17; 18]. Therefore, it is essential to make a balance or an adaptation in choosing the beacon interval time (BIT) value (i.e., beacon rate) according to the network's requirements and features. Hence, a higher beacon rate means higher routing overhead, interference, energy consumption, and congestion and an increase in the transmission delay. On the contrary, a lower beacon rate results in longer route discovery and energy consumption, limited support to mobility and increased route instability [20; 21]. With this criterion, instead of using fixed periodic beacons, an adaptive beaconing-strategy based on fuzzy logic (AFB) is modeled in this work to adjust the beacon frequency in MANET and improve GPSR protocol. The newly proposed \"AFB-GPSR\", an improved GPSR protocol based on the AFB strategy, can effectively reduce the routing overhead and increase the network reliability in terms of the packet-delivery ratio and transmission delay. To achieve this, a fuzzy inference algorithm is designed to control the beacon interval's time values based on the variation of three key parameters: (i) node speed (NS), (ii) one-hop neighbors' density (OHND), and (iii) link reliability (LR) between the node and its neighbors. In this regard, several studies have suggested different analytical models like [24; 25] or intelligent schemes like [26; 27; 28] in designing the adaptive beaconing strategy for wireless ad hoc networks. As is known, Artificial Intelligence (AI)-based decision-making systems, such as fuzzy logic, are powerful tools in classification, optimization, prediction and decision-making systems [29]. A fuzzy logic system is widely employed to improve the performance of the GPSR routing protocol. It is an efficient tool used to solve complex patterns or behavioral variations based on input membership functions and a group of fuzzy rules similar to the human brain's operation. More precisely, a fuzzy logic system provides a foundation for dealing with imprecision and ambiguity that use varying degrees of truth, such as the uncertainty inherent in the nature of ad hoc networks due to dynamic topology, node mobility, resource limitations and unsteady links, where an accurate model cannot be implemented [30]. The main contributions of this study are highlighted as follows:  
* An adaptive geographic routing protocol, namely AFB-GPSR, is proposed. To achieve this, an adaptive beaconing strategy based on fuzzy logic (AFB) is designed to optimize the update beacon intervals and improve the routing performance. * The optimal beacon interval time (OBIT) is adjusted dynamically with the variations of three key network parameters: mobility of nodes, one-hop neighbors' density, and link quality of the nodes. * Extensive simulations are carried out using OMNeT++ jointly with the INET framework to verify the AFB strategy with GPSR routing protocol. The results show that the AFB strategy reduces the routing cost and improves network reliability in terms of the packet-delivery ratio, throughput, normalized routing load and delay in comparison to traditional AODV and GPSR routing protocols. * Moreover, the AFB-GPSR protocol exhibits good performance versus the state-of-the-art protocols in MANET environment. * In conclusion, the AFB strategy is an effective solution in broadcasting beacons for geographical routing as it can maintain more information accuracy in the local topology. The rest of the article is organized as follows: Section 2 introduces an overview of the classifications of routing protocols in ad hoc networks. Section 3 presents a literature review of some recent related works. Section 4 briefly describes the mechanism of conventional Greedy Perimeter Stateless Routing. In Section 5, the architecture of the proposed AFB-GPSR and fuzzy logic composition are described in detail.