Adaptive Whale Optimization Delays Initial Sensor Failures in Simulation Experiments

A simulated 200-node wireless sensor network running an adaptive discrete whale optimization algorithm delayed the onset of its first node failure by nearly four percent compared to standard whale-based clustering, while sustaining reliable data delivery across thousands of communication rounds. Developed to alleviate the heavy transmission burdens placed on energy-constrained Internet of Things hardware, the technique modifies swarm-intelligence equations to solve fixed-cardinality cluster head selection. In simulated trials across twenty paired network topologies, the adaptive method achieved an average first node death milestone of 1823.80 rounds, exceeding the 1755.00 rounds observed under original whale optimization. However, this delayed initial failure coincided with a modest reduction in terminal network duration, as the system reached complete exhaustion at 2511.80 rounds compared to 2557.10 rounds under the baseline. Statistical evaluations also indicated that the adaptive strategy yielded no significant differences when benchmarked against particle swarm optimization across twelve evaluated metrics, demonstrating that heuristic modifications shift system trade-offs rather than delivering uniform superiority.

Wireless sensor networks deployed in environmental monitoring, industrial automation, healthcare, and infrastructure oversight rely on widely scattered battery-powered sensing units that send local measurements to a central base station. Because radio communication consumes substantial energy, direct long-range transmission from peripheral sensors rapidly drains battery reserves, creating an operational bottleneck. Hierarchical clustering mitigates this energy expenditure by organizing local nodes around elected cluster heads. Under this topology, ordinary member sensors transmit observations over short distances to their respective cluster head, which aggregates the collected traffic and transmits a consolidated packet to the distant base station. In the first-order radio energy model adopted in the study, transmission energy scales quadratically with distance in the free-space regime below 87.71 meters and with the fourth power of distance in the multipath regime beyond that threshold. Consequently, selecting an effective cluster head subset directly dictates whether member devices operate efficiently or deplete their limited reserves prematurely through inefficient long-distance communication paths.

When a monitoring protocol requires selecting exactly fifteen cluster heads from two hundred active sensors, the combinatorial search space encompasses an enormous number of possible subset configurations. While randomized rotation protocols such as the Low-Energy Adaptive Clustering Hierarchy assign leadership responsibilities based on probabilistic thresholds, they struggle to adapt to uneven residual battery levels across the field. To navigate this discrete optimization problem, the authors adapted the continuous Whale Optimization Algorithm, which emulates humpback whale hunting through encircling, exploration, and spiral exploitation operators. Because raw swarm coordinates are continuous vectors within an N-dimensional space, they cannot directly designate a valid subset of distinct sensor units without generating redundant or invalid assignments. To bridge this structural divide, the researchers implemented a fixed-cardinality random-key decoder. Each candidate whale carries a continuous vector bounded between zero and one, where each dimension corresponds to a sensor node. The decoder filters out depleted nodes, extracts entries belonging to living nodes, and selects the fifteen nodes with the highest numerical keys.

To prevent the continuous search mechanism from stagnating in repetitive subset configurations, the engineering team introduced three complementary search controls: progress-adaptive mutation, one-swap discrete refinement, and stagnation-triggered population restoration. Standard whale algorithms typically reduce their exploration parameter linearly over iterations, but the adaptive formulation couples exploration intensity directly to the proportion of the computational evaluation budget consumed during reselection. The probability of applying Gaussian perturbation to candidate keys increases from fifteen to thirty-five percent as the evaluation budget elapses, while the perturbation magnitude contracts from eighteen to three percent, shifting search behavior from broad exploration toward fine-grained local refinement. Once an optimization cycle finishes, the algorithm applies a local search heuristic that randomly swaps one cluster head with an active non-head node, retaining the replacement only if it lowers the overall fitness penalty. Furthermore, if the global best solution remains unchanged across three consecutive optimizer generations, the algorithm triggers a diversity restoration mechanism that reinitializes thirty percent of the candidate population.

Every candidate cluster head subset generated by the optimizer is evaluated using a composite minimization objective that explicitly penalizes four operational risks: residual energy depletion, excessive intra-cluster member distance, extended cluster-head-to-sink distance, and unequal cluster workload. The residual energy term calculates the average fractional battery exhaustion among selected cluster heads, steering the algorithm away from fragile nodes nearing depletion. The intra-cluster distance component normalizes the average Euclidean separation between active member sensors and their assigned cluster heads against the field diagonal of 282.84 meters. Proximity to the central base station is scaled relative to the maximum possible central distance of 141.42 meters. To prevent individual cluster heads from suffering premature exhaustion due to disproportionate aggregation duties, the cluster load imbalance term computes the coefficient of variation among cluster sizes. Under the baseline testing configuration, the fitness weights assign thirty-five percent importance to residual energy protection, thirty percent to intra-cluster compaction, twenty percent to base station proximity, and fifteen percent to workload balance.

The experimental validation evaluated the proposed clustering architecture within a simulated environment representing a static sensing field spanning two hundred meters by two hundred meters. The simulated network contained exactly two hundred sensor nodes, each equipped with an initial energy supply of one joule, yielding a total network capacity of two hundred joules. A stationary base station was placed at the field center with coordinates of one hundred meters by one hundred meters. To ensure experimental fairness, population-based optimizers—including standard whale optimization, particle swarm optimization, and the proposed adaptive method—were restricted to a fixed population size of thirty candidates and an identical computational budget of three hundred fitness evaluations per reselection event. Reselection was scheduled every ten communication rounds or triggered immediately if a serving cluster head depleted its battery. The full evaluation framework comprised three hundred simulation runs across three planned stages: fitness-weight sensitivity, cluster head density, and comparative executions across five distinct clustering protocols using twenty paired topology seeds.

The comparative executions demonstrated noticeable shifts in network operational milestones between the proposed framework and baseline approaches. Compared to original whale optimization, the adaptive discrete algorithm extended the first node death milestone by 3.92 percent, moving the average onset of node failure from 1755.00 rounds to 1823.80 rounds, a statistically significant improvement confirmed by Holm-adjusted pairwise testing with an adjusted p-value of 0.0041. However, the terminal lifetime milestone showed an opposing trend: last node death occurred at 2511.80 rounds under the adaptive technique, representing a 1.77 percent decrease from the 2557.10 rounds achieved by original whale optimization. By balancing cluster loads and distributing energy expenditure more evenly during early operation, the adaptive method delayed initial node attrition but left fewer residual energy reserves to sustain an extended terminal tail once node depletion accelerated.

When evaluated against the classical Low-Energy Adaptive Clustering Hierarchy, the adaptive algorithm delivered substantial gains across absolute endurance and delivery metrics. The adaptive model increased total operational lifetime to last node death by 7.84 percent, raised cumulative packet delivery to the central base station by 4.52 percent, and retained 18.30 joules of residual network energy at round 2000 compared to 11.17 joules under the randomized protocol, representing a 63.80 percent energy advantage. This discrepancy stems from how rate-based metrics normalize performance across different network lifetimes, as compressing packet deliveries into an earlier, shorter operating period mechanically inflates delivery metrics calculated on a per-round basis.

A critical finding emerged from the direct head-to-head comparison between the adaptive whale optimization algorithm and particle swarm optimization. While the adaptive method achieved slightly higher sample means in initial failure delay, cumulative data throughput, and cumulative alive-node availability, none of the twelve Holm-adjusted pairwise statistical tests detected a statistically significant difference between the two metaheuristics. The researchers cautioned that this lack of statistical significance must not be interpreted as evidence of operational equivalence, as no formal equivalence testing or predefined margins were incorporated into the experimental design. Instead, the finding indicates that within the tested budget of three hundred fitness calculations, both population-based search mechanisms achieved comparable effectiveness in locating high-quality cluster head subsets. Sensitivity investigations into alternative fitness weights further revealed that weighting residual energy heavily extended first node death to 1890.55 rounds at the expense of terminal endurance, whereas prioritizing load balancing extended terminal survival to 2806.95 rounds while accelerating initial node failures.

The study authors highlighted several structural constraints inherent to their experimental modeling that define the practical boundaries of their findings. The simulation assumed idealized centralized control, wherein node coordinates and exact residual energy states were available to the central optimizer without modeling the uplink packet overhead, channel contention, transmission delays, or battery depletion required to collect that telemetry in physical deployments. Furthermore, the communication architecture relied entirely on direct, single-hop transmissions from cluster heads to the central base station, omitting multi-hop routing and relay hierarchies to isolate cluster selection dynamics. The evaluation framework also omitted physical wireless phenomena such as signal fading, packet collisions, environmental obstacles, node mobility, and energy harvesting. Additionally, the algorithm incorporates no cryptographic authentication or malicious node detection mechanisms, leaving it vulnerable to compromised nodes advertising false energy levels. The researchers concluded that establishing real-world viability will require validating the adaptive algorithm on physical hardware testbeds with multi-hop forwarding and empirical state-reporting overhead.

Subject of Research: Adaptive metaheuristic cluster head selection in wireless sensor networks

Article Title: Adaptive discrete clustering based whale optimization for energy efficient cluster head selection in internet of things-enabled wireless sensor networks

Article References: Bhardwaj, S., Srivastava, J. N., & Sanghi, A. (2026). Adaptive discrete clustering based whale optimization for energy efficient cluster head selection in internet of things-enabled wireless sensor networks. Discover Electronics, 3(1), Article 159. https://doi.org/10.1007/s44291-026-00317-5

Image Credits: AI Generated

DOI: 10.1007/s44291-026-00317-5

Keywords: wireless sensor networks, cluster head selection, whale optimization algorithm, particle swarm optimization, LEACH protocol, network lifetime, first node death, last node death, random-key decoding, energy efficiency, Internet of Things, first-order radio model, intra-cluster distance, cluster load imbalance, stagnation-triggered restart, progress-adaptive mutation, combinatorial optimization