## 2 Related Works  
Opportunistic routing (OR) has undergone significant advancements since the introduction of ExOR by [PERSON] [PERSON] in 2005 [1]. While ExOR demonstrated improved throughput and reliability over traditional fixed-path routing, its impact on energy consumption remained largely unexplored. This limitation prompted extensive research into energy-efficient OR protocols for wireless sensor networks (WSNs), leading to the development of several OR-based solutions [17, 18, 19, 20, 21, 22]. Early protocols were designed for always-on networks, but later adaptations incorporated duty-cycled medium access control (MAC) mechanisms to reduce power consumption [3, 7, 8, 9, 23, 24, 25, 26]. To optimize forwarder selection, researchers introduced various routing metrics, including hop count [27, 28, 29, 30, 31], geographical distance [32, 33, 34, 35, 36], expected transmission count (ETX) [1, 18, 20, 37, 38], expected transmission time (ETT) [39, 40, 41] and coding gain [42]. For duty-cycled WSNs, a new metric called expected duty cycle (EDC) [3] was proposed to measure the number of wake-up cycles required for successful packet delivery. Further refinements led to expected any-path transmission count (EAX) [17, 43, 44, 45] and expected any-path transmission time (EATT) [46], both designed to enhance OR efficiency under duty-cycled conditions. Additional metrics, such as dynamic forwarding delay [47], incorporated parameters like link quality, node mobility, and directionality to improve routing performance. Many OR protocols aimed to maximize energy efficiency and prolong network lifetime by integrating residual energy awareness into routing metrics [3, 7, 8, 9, 19, 23, 24, 48, 49, 50]. Notable approaches include OAPF [17], which employs EAX-based prioritization, and MORE [18], SOAR [20], and OMNC [22], which extend ExOR's ETX-based selection strategy. Conversely, OPRAH [28] focused on link quality, contradicting OR principles by restricting forwarder choices to high-quality links. EFFORT [21] introduced an end-to-end cost metric that balances multiple factors to optimize routing decisions. A significant advancement in OR was introduced with ORW [3], which utilized EDC for forwarder selection while implementing duty cycling to reduce energy consumption. However, ORW suffers from several limitations: (i) high computational overhead due to recursive EDC calculations; (ii) poor load balancing, as the lowest-EDC node is frequently selected, leading to rapid energy depletion; (iii) the lack of a forwarder limit, resulting in redundant transmissions and routing loops. Building on ORW, ORD [8] and ORR [7] introduced modifications to improve efficiency. ORD reduces transmissions by aggregating multiple packets, but this increases latency. ORR introduced the forwarder score, incorporating residual energy into forwarder selection, but heavily favoring high-energy nodes may lead to congestion and uneven energy depletion. Further advancements include MOR [51], which integrates multi-channel transmission into ORW, allowing the first node that wakes on the correct channel to forward packets. However, frequent channel switching incurs excessive energy costs. LEOR [24] mitigates this by restricting forwarder selection zones and prioritizing nodes based on distance, residual energy, and connectivity, although at the expense of increased overhead due to RTS/CTS/ACK mechanisms. MORR [9] extends ORR by addressing channel interference and forwarder load balancing, but its transmitter regulation mechanism lacks adaptability. Geometric-based OR techniques, such as LORA [23], introduced candidate zones (CZs) to define spatially constrained forwarder selection areas based on factors like directionality, transmission distance, and residual energy. However, high computational costs and inconsistencies in randomly deployed networks limit its practicality.