## 1 Introduction  
A Low-power and Lossy Network (LLN) [1] consists of a large number of nodes, often sensor nodes, connected by Lossy channels. The nodes are typically resource-constrained, with limited battery power, memory, and processing capabilities. The channels are unstable, with relatively high packet loss and low packet delivery. LLNs usually have complex traffic patterns that support point-point, point-multi-point, and multi-point-point communication. This means that each node in the network may receive/send packets from/to single or multiple nodes. The network topology can dynamically change over time owing to power depletion and/or node mobility. A typical LLN is shown in Figure 1.  
LLNs have several unique characteristics that differ from other types of networks, such as wired networks and ad hoc wireless networks [2; 3; 4; 5]. The characteristics of Lossy channels and nodes, namely their limited energy, memory, and processing capabilities, indicate that the routing solutions designed for non-LLNs may not be adequate in terms of optimising delivery reliability and routing efficiency. By delivery reliability, we mean the ability to successfully deliver data packets from a source node to a destination node with minimum loss and delay as possible. By routing efficiency, we refer to the ability of a routing protocol to transmit data packets between a source node and a destination node in a timely and resource-efficient manner. In other words, it is a measure of how effectively a routing protocol can find the best path to transmit data packets with minimum costs in terms of energy consumption and control overheads. Routing in LLNs poses a fundamental challenge: determining the optimal path to reach a destination. Over the years, various solutions have sought to address the intricate routing demands in LLNs. However, many of these endeavours often need to account for the full spectrum of factors that influence routing reliability. A routing protocol designed for LLNs should operate within the constraints of Lossy channels and limited node energy and effectively and efficiently achieve the routing function. In other words, all factors that may impact packet delivery reliability and routing efficiency should be considered when making routing decisions. In addition, the routing protocol should also support dynamic topology and link quality changes as caused by power depletion. In light of these considerations, this paper presents a comprehensive assessment of current solutions for LLNs against performance and security requirements to identify limitations and emphasise the need for a reliable and efficient path-finding solution within the complex network of LLNs. Our research provides a critical analysis of existing routing solutions for LLNs, particularly focusing on the gaps in RPL solutions. We examine the oversight of neglecting essential reliability-effecting factors such as node energy levels and link quality in the path selection process. We thoroughly examine generic routing protocols and RPL objective functions, covering non-malicious and malicious LLNs, to identify areas of improvement for reliable path-finding. Our paper highlights the importance of maximising PDRs by considering the most reliability-effecting factors, even in the presence of malicious nodes. We underscore the absence of solutions capable of making real-time, global optimum decisions that adapt to dynamic network changes. As part of our contribution, we outline a road map for future work that aims to design and implement a robust path-finding solution for LLNs in the presence of PDAs. This forthcoming research endeavours to elevate delivery reliability and enhance routing efficiency in LLNs, bridging the identified gaps in the current state of the art. In detail, the remainder of this paper is structured as follows. Section 2 illustrates the characteristics of LLNs. Section 3 surveys the generic routing solutions. Section 4 surveys RPL objective functions for non-malicious LLNs and RPL objective functions for malicious LLNs (MLLNs).