Battery-Efficient Routing (BER)

• Battery-Efficient Routing (BER) is a family of energy-aware routing strategies that minimize battery consumption while ensuring network feasibility and lifetime protection.
• BER techniques are applied in diverse domains such as underwater IoT, MANETs, EV eco-routing, and UAV delivery, each adapting specific energy models and optimization objectives.
• Studies on BER reveal trade-offs between energy savings, route stability, and delay, offering actionable insights for designing load-balanced and QoS-aware routing protocols.

Searching arXiv for the cited BER-related papers to ground the article in current records. Searching arXiv for underwater BER review and related routing work. Searching arXiv for BER-related identifiers and metadata. Battery-Efficient Routing (BER) denotes routing and route-selection strategies that explicitly minimize battery or energy expenditure while preserving lifetime, feasibility, and service constraints. Across the literature, the term functions as a generic label rather than a single standardized protocol: in underwater Internet of Things networks it refers to routing that reduces per-node and network-wide energy consumption so battery-powered nodes can operate longer; in MANETs it denotes route selection that avoids low-energy, unstable, congested, or overhearing-prone relays; in battery electric vehicle and electric fleet routing it becomes eco-routing or battery-constrained path planning; and in mobile energy storage and UAV delivery it extends to route-and-charge or route-and-return feasibility under operational uncertainty (Tarif et al., 2023, Lotfi et al., 2010, Ahn et al., 2020).

1. Conceptual scope and terminology

BER spans several distinct routing objects. In packet networks, the routing object is usually a next hop, a multi-hop path, or a forwarding tree. In transportation and cyber-physical systems, it may be a traffic assignment, an electric-vehicle tour with charging stations, a mobile energy storage relocation schedule, or an online flight path that must remain battery-feasible under uncertainty. Several of the cited papers state explicitly that they do not use the term “Battery-Efficient Routing”; the label is therefore best understood as an editorial umbrella for energy-aware, battery-conserving routing techniques rather than a canonical name fixed by one subfield (Lotfi et al., 2010, Fazeli et al., 2020).

The common thread is the deliberate coupling of routing with battery state, energy cost, or lifetime protection. Some works minimize total communication energy, some minimize the bottleneck node’s energy, some trade energy against delay or QoS, and some protect return feasibility or state-of-charge bounds. A plausible implication is that BER is more accurately described as a family of optimization principles than as a single protocol class.

Domain	Routing object	Representative BER mechanism
UIoT and UWSN	Next hop or multi-hop route	Depth/pressure forwarding, clustering, AUV-assisted collection
MANET and WSN	On-demand route or clustered path	Residual-energy-aware costs, node-disjoint alternates, DAG shortest path
LPWAN and LoRa mesh	Uplink tree or gateway-directed path	RL-based multi-hop, position learning, standby repeaters
Vehicular and EV routing	Path, tour, or traffic assignment	Eco-routing, charging-aware min-max routing
Microgrids and UAV delivery	Mobile-storage route or flight path	SoC-constrained co-optimization, budget-gated wind-aware planning

This breadth is visible in representative formulations ranging from underwater QoS-aware forwarding and clustered IoT routing to subterranean LoRa meshes, BEV traffic assignment, EV fleet routing, microgrid MESS relocation, discrete battery-time-space formulations for autonomous dial-a-ride, and wind-sensitive UAV planning (Udugampola et al., 4 Oct 2025, Bose et al., 2022, Zhao et al., 1 Jan 2026, Li et al., 15 Apr 2026).

2. Objective functions, energy models, and route costs

The mathematical form of BER varies sharply by domain. Some works are explicitly formula-driven. In the MANET algorithm “A New Energy Efficient Routing Algorithm Based on a New Cost Function in Wireless Ad hoc Networks,” the destination evaluates each candidate route by

$$Cost(R)=w_1\frac{unstableNodesCount}{hopCount-1}+w_2\frac{sumOfNeighbors}{hopCount-1}+w_3\frac{sumOfBufferedPackets}{hopCount-1},$$

with simulation weights $w_1=0.5$, $w_2=0.3$, and $w_3=0.2$. Relay admission is gated by remaining lifetime,

$$RLT_i=\frac{E_i}{DR_i}, \qquad DR_i=\alpha DR_{old}+(1-\alpha)DR_{sample},$$

so that nodes unlikely to sustain the announced session are excluded from route discovery (Lotfi et al., 2010).

MEA-DSR uses a different lifetime-oriented criterion. Its destination selects the primary path by maximizing the ratio between the path bottleneck residual energy and the route length,

$$P^{*}=arg\max_{1\le j\le n}\frac{min\_bat\_lev(P_j)}{route\_length(P_j)},$$

and then chooses an alternate route that is as node-disjoint as possible from the primary. This moves BER away from pure minimum-hop routing toward explicit protection of weak nodes and balanced consumption over time (0902.4572).

Clustered IoT routing in MINEN is organized around a radio energy model and a load-balancing edge weight. Its transmit and receive costs follow

$$E_{t(ij)}=(E_{elec}+\epsilon_{FS} d_{ij}^{2})l_{ij}$$

or

$$E_{t(ij)}=(E_{elec}+\epsilon_{MP} d_{ij}^{4})l_{ij},$$

depending on the propagation regime, with

$E_{r(ij)}=E_{elec}l_{ij}.$

Routing then uses

$e_{ij}=w_1 e_{r(ij)}+w_2 e_{t(ij)}+w_3 E_{sf(ij)},$

where $w_1=0.5$0, thereby combining transmission, reception, and “energy spent so far” in a single Dijkstra-compatible path metric (Vashishth et al., 2018).

Transportation-oriented BER adopts generalized path costs rather than per-hop radio costs. In multi-objective BEV eco-routing, the generalized link cost is

$w_1=0.5$1

which allows the routing policy to trade off travel time and battery energy in a multi-class user-equilibrium assignment. This formulation is explicitly tied to BEV-specific energy behavior such as regenerative braking and speed sensitivity on arterials versus highways (Ahn et al., 2020).

Risk-sensitive BER for UAV delivery introduces time-dependent edge costs driven by wind: $w_1=0.5$2 with a continuously enforced return-feasibility condition

$w_1=0.5$3

Here BER is not merely a shortest-path problem; it is an online safety filter that prunes energy-infeasible edges and triggers abort when conservative return energy exceeds the remaining battery margin (Li et al., 15 Apr 2026).

By contrast, the UIoT review explicitly states that it does not provide closed-form acoustic energy or channel-loss equations. Its metric combinations are conceptual rather than formulaic, built from residual energy, hop count, data size, path diversity, depth, angle, throughput, freshness, and reliability (Tarif et al., 2023).

3. Protocol families and mechanisms in communication networks

In underwater Internet of Things research, BER is shaped by acoustic-channel costs, node mobility, sparse three-dimensional topologies, GPS unavailability, and the practical impossibility of battery recharge. The review groups recent energy-efficient routing methods into depth-/pressure-/geographic/opportunistic forwarding, cluster-based routing, AUV/ROV-assisted data collection, cross-layer and multi-modal routing, flooding- and hole-aware routing, and self-organizing or adaptive clustering. Representative mechanisms include depth- and angle-aware selective power control in DSPR, clustering and aggregation in CUWSN, residual-energy- and distance-aware cluster-head election in k-means routing, residual-energy and heterogeneous-path balancing in multi-modal routing, Bayesian MDS-based localization for hybrid magnetic/optical/acoustic links, and guard-based flooding for routing holes (Tarif et al., 2023).

MANET BER papers emphasize route fragility and control overhead. The new cost-function algorithm avoids nodes with low expected remaining lifetime, unstable neighbor sets, large neighborhoods, and long queues, thereby reducing route breaks, overhearing, and retransmissions. MEA-DSR instead combines destination-only replies, controlled duplicate RREQ forwarding, a bottleneck-energy-to-hop-count metric, and a maximally node-disjoint alternate path. PC-AODV modifies AODV differently: it scales HELLO periodicity by neighbor count,

$w_1=0.5$4

and infers neighbor energy from the timing of HELLO acknowledgments, using $w_1=0.5$5 and $w_1=0.5$6, so that low-energy relays can be avoided without changing packet formats (Lotfi et al., 2010, 0902.4572, Heni et al., 2012).

Wireless IoT sensor-network BER often couples clustering, aggregation, and route selection. MINEN forms clusters using distance to the base station, message length, and sensed data, elects cluster heads by residual energy, constructs a DAG over the cluster heads, and runs Dijkstra with an energy-and-load-balancing edge weight. In event-driven agricultural sensing, energy-aware routing is combined with directionally constrained flooding, max–min residual-energy path selection, in-network aggregation of minima or local averages, coordinator-based deployment, and threshold-triggered reporting for low battery or abnormal water level (Vashishth et al., 2018, Pai et al., 2014).

LPWAN and multi-interface networks introduce additional BER mechanisms. EMH treats uplink multi-hop topology selection as a centralized multi-armed bandit problem and uses an $w_1=0.5$7-greedy policy, with payoff defined as the inverse of the average bottleneck energy over $w_1=0.5$8 cycles. Cooperative short-range relaying in multi-interface wireless networks instead minimizes energy per bit by combining Wi-Fi short-range forwarding with superior long-range infrastructure links, achieving a reported maximum energy-efficiency gain of up to $w_1=0.5$9 in simulation (Barrachina-Muñoz et al., 2018, Fedrizzi et al., 2013).

Subterranean LoRa mesh BER is built around a lightweight position learning phase, gateway-directed minimum-hop forwarding, passive standby repeaters for hidden-node loss recovery, and coarse-grained battery-aware route switching. Repeaters report battery level only when it drops by one unit, while route changes are throttled to multiples of ten battery levels to limit oscillation and signaling overhead (Udugampola et al., 4 Oct 2025).

4. Vehicular, mobile-storage, and aerial formulations

In road-transport systems, BER frequently appears as eco-routing. The BEV study formulates a multi-objective, multi-class, stochastic user-equilibrium assignment in which BEV routes are chosen using a joint time-energy cost. Its central claim is that BEVs do not share the same eco-routing logic as ICEVs: BEVs are more energy efficient on low-speed arterial trips, partly because regenerative braking recuperates energy, whereas ICEVs tend to favor steadier freeway operation. As a result, BER in this setting is congestion-aware and vehicle-class specific rather than merely distance minimizing (Ahn et al., 2020).

Fleet-level EV routing adds explicit charging-station structure. The min-max electric vehicle routing problem minimizes the maximum distance or energy traveled by any EV while ensuring battery-feasible movement between customers and charging stations. The branch-and-cut model uses arc variables, charging-station visitation variables, and energy-flow variables, while the associated three-phase heuristic combines a load-balancing assignment, feasibility-preserving charging insertion, variable-neighborhood search, and a genetic algorithm. The data block further states that minimizing the maximum route energy and balancing routes reduces worst-case charge throughput and depth of discharge, thereby mitigating degradation, although degradation is not explicitly modeled (Fazeli et al., 2020).

Battery-coupled routing also appears in infrastructure restoration. In the microgrid MESS formulation, routing decisions for mobile energy storage systems are co-optimized with charging, discharging, and load restoration in a mixed-integer second-order cone program. BER is implicit rather than explicitly named: the model values restored load, penalizes generation and transport cost, and moves SoC bounds over a transport graph so that mobile storage can be repositioned where it most improves restoration under network and converter constraints (Bose et al., 2022).

Discrete battery-aware routing becomes still more explicit in the battery-time-space fragment-based formulation for the Electric Autonomous Dial-a-Ride Problem. BTSFF discretizes both time and battery, represents a state as $w_2=0.3$0, and treats a fragment as a feasible subpath whose cost combines travel cost and excess user ride time. Partial charging and battery-swap variants are both supported, and time-discretization errors in the swap case are corrected with lazy constraints that eliminate infeasible fragment chains (Zhao et al., 1 Jan 2026).

Vehicle assistance can also lower energy in ad hoc communications. In the reliable energy-efficient routing algorithm for vehicle-assisted wireless ad hoc networks, a moving vehicle acts as a relay between two sets of battery-powered IoT nodes in the presence of jammers. The optimization minimizes the sum transmit energy of battery-equipped nodes subject to an end-to-end outage constraint and per-node transmit-power limits, using a three-step dynamic-programming method with equal per-hop outage allocation (Huang et al., 2017).

Aerial BER under environmental uncertainty takes the most explicitly safety-critical form. The wind-sensitive truck-assisted UAV framework models delivery on a time-dependent energy graph whose edge costs evolve with wind-induced changes in ground speed and traversal time. BER continuously recomputes risk-aware edge costs, evaluates conservative return energy, and aborts missions when the Budget Gate fails. This formulation couples task allocation, routing, and decentralized trajectory execution rather than treating energy as a post hoc validation step (Li et al., 15 Apr 2026).

5. Trade-offs, evaluation practices, and reported performance

A recurrent result across BER studies is that battery savings are purchased through nontrivial trade-offs. In UIoT, clustering lowers energy by aggregation and shorter hops but can introduce cluster-head bottlenecks and control overhead; AUV collection balances energy well but can increase collection delay; opportunistic forwarding reduces retransmissions and latency but must control listening overhead; guard-based flooding improves reachability but must bound duplicate rebroadcasts; and reliability-oriented multi-copy forwarding can improve packet delivery ratio while harming energy unless duplication is tightly controlled (Tarif et al., 2023).

The same pattern appears elsewhere. The new MANET cost-function algorithm reduces control overhead and total energy relative to MMPR but does not report packet delivery ratio, delay, lifetime in time-to-first-node-death, or statistical significance. MEA-DSR reduces consumed energy per packet and energy imbalance relative to DSR in most mobility scenarios, but its delivery ratio can be lower than DSR under low mobility. In BEV eco-routing, pure energy minimization can sharply increase travel time, and the multi-objective formulation is expressly designed to moderate that penalty (Lotfi et al., 2010, 0902.4572, Ahn et al., 2020).

Setting	BER outcome	Comparator
UIoT DSPR	about 30% lower energy; higher delivery ratio	DR and VDBR
Subterranean LoRa mesh	185% higher maximum throughput; 75% lower energy; 54% lower latency; PDR from 88.7% to 96.7%	optimized flooding
MINEN IoT-WSN	150 alive nodes up to ~2800 rounds; total energy reaches 0 after ~3000 rounds	LEACH ~1700/~2100; FCM ~2600/~2600
BEV multi-class MO-routing 1	BEV energy reductions of 13.5%, 14.2%, 12.9%, and 10.7%; average travel time reduced by up to 10.1% in highly congested conditions	standard user-equilibrium TT-routing
Wind-aware UAV BER	SUC 93.8±1.1% at $w_2=0.3$1 and 61.5±1.3% at $w_2=0.3$2 under 4 wind classes; FAIL 0.0% in the first case	SER, RER, GER

Several studies report more granular effects. In subterranean LoRa meshes, energy-aware switching increased network lifetime from about $w_2=0.3$3 minutes to over $w_2=0.3$4 minutes in a two-end-device scenario by evening out repeater depletion. In MINEN with GSO sleep scheduling, operational duration increased to approximately $w_2=0.3$5 rounds, compared with approximately $w_2=0.3$6 for EECA, approximately $w_2=0.3$7 for GA, and approximately $w_2=0.3$8 for PSO. In BEV eco-routing, energy-only routing reduced BEV energy by $w_2=0.3$9, $w_3=0.2$0, $w_3=0.2$1, and $w_3=0.2$2 across four congestion levels, but travel time could increase by up to $w_3=0.2$3; the multi-objective version reduced those penalties substantially (Udugampola et al., 4 Oct 2025, Vashishth et al., 2018, Ahn et al., 2020).

Evaluation practices are uneven. The UIoT review explicitly notes that it does not provide unified simulation settings across protocols. Some MANET papers offer trends but no numeric tables for core metrics; others omit idle and sleep energy. Transportation papers are typically richer in optimization structure, but may not model SOC feasibility, charging availability, or degradation explicitly. A plausible implication is that BER results are often strong within a local benchmark regime but difficult to compare directly across protocols, hardware, or environments (Tarif et al., 2023, Lotfi et al., 2010, Fazeli et al., 2020).

6. Open problems and recurrent misconceptions

One common misconception is that BER names a single, settled protocol family. The surveyed papers show the opposite: some use the term explicitly, many do not, and the underlying methods range from HELLO-timing adaptations and node-disjoint source routing to reinforcement learning, stochastic traffic assignment, mixed-integer conic co-optimization, and online risk-sensitive planning. In that sense, BER is a cross-domain descriptor for routing under battery-aware objectives rather than a unique standard (Lotfi et al., 2010, Li et al., 15 Apr 2026).

A second misconception is that BER simply means shortest-path or minimum-hop routing. Many formulations reject that equivalence. MANET cost functions penalize instability, congestion, and overhearing even when the resulting route is longer. MEA-DSR explicitly optimizes bottleneck battery level relative to hop count rather than hop count alone. BEV eco-routing may prefer arterials over highways. Wind-aware UAV BER may choose a longer geometric route because favorable winds reduce traversal energy and preserve return feasibility (0902.4572, Ahn et al., 2020, Li et al., 15 Apr 2026).

Open problems are similarly domain-specific but structurally related. In UIoT, the review highlights energy-aware AUV trajectory planning, smarter clustering and cluster-head selection under environmental dynamics, learning-based routing, cross-layer hybrid communications, reliability with low energy overhead, and standardization under limited real-time configurability. PC-AODV identifies robust timing inference for HELLO acknowledgments and collision-aware parameter setting as unresolved. MINEN points to mobile IoT-WSNs and alternative clustering schemes. MEVRP suggests stochastic energy variation, charger queues, time windows, and richer degradation models. BTSFF identifies adaptive discretization and decomposition as natural extensions. The microgrid MESS model leaves transport uncertainty and explicit travel-energy usage to future work. The UAV framework itself notes limited wind discretization, simplified propulsion, and the absence of richer stochastic risk measures (Tarif et al., 2023, Heni et al., 2012, Vashishth et al., 2018, Fazeli et al., 2020, Zhao et al., 1 Jan 2026, Bose et al., 2022).

Taken together, these directions suggest that the enduring research problem in BER is not merely lowering energy consumption on a static graph. It is the design of routing policies that remain battery-feasible, load-balanced, and QoS-aware when energy state, channel quality, traffic, mobility, charging opportunity, and environmental uncertainty all evolve during operation.