The deployment of sensor nodes is an important aspect in mobile wireless sensor networks for increasing network performance. The longevity of the networks is mostly determined by the proportion of energy consumed and the sensor nodes’ access network. The optimal or ideal positioning of sensors improves the portable sensor networks effectiveness. Coverage and energy usage are mostly determined by successful sensor placement strategies. Nature-inspired algorithms are the most effective solution for short sensor lifetime. The primary objective of work is to conduct a comparative analysis of nature-inspired optimization for wireless sensor networks (WSNs’) maximum network coverage. Moreover, it identifies quantity of installed sensor nodes for the given area. Superiority of algorithm has been identified based on value of optimized energy. The first half of the paper’s literature on nature-inspired algorithms is discussed. Later six metaheuristics algorithms (Grey wolf, Ant lion, Dragonfly, Whale, Moth flame, Sine cosine optimizer) are compared for optimal coverage of WSNs. The simulation outcomes confirm that whale optimization algorithm (WOA) gives optimized Energy with improved network coverage with the least number of nodes. This comparison will be helpful for researchers who will use WSNs in their applications.

WSNs are ad hoc networks of widely scattered small wireless, affordable, and self-sufficient motes used for cooperative environment monitoring. Every sensor mote (network node) may gather sensory information, analyze it, and then broadcast the refined data to its associates via a wireless transmission medium. Monitoring, medical, pollution monitoring, medical diagnostics, and building automation are some of the applications for WSNs [

Several works have been proposed using NI Algorithms in WSN [

Different researchers uses wireless sensor networks for different applications [

PSO, GA, and ant colony optimizer (ACO) well address sensor deployment. Every new attempt toward this approach shows it improves results from previous. In continuation, this work compared six NI algorithms for optimal coverage. None of them offer a rigorous analysis, especially regarding maximizing coverage range while using minimal energy. Furthermore, it also identifies the required number of sensor nodes for given network coverage. moreover, if researcher is limited to design WSNs with limited number of sensor nodes. This piece of work will be helpful to pick algorithm which is giving optimal value of energy with increased network coverage and no larger percentage of sensor nodes. To determine the optimal optimization technique, the proposed work compares six currently used nature-inspired optimization algorithms. It is particularly applicable to applications that call for extensive network coverage with minimal energy consumption. Additionally, it offers comparison with identical sensor nodes but a larger coverage area.

None of them provide a critical review, particularly of maximizing coverage range with optimized energy. The proposed work compares six existing nature-inspired optimization algorithms to find the best-fitted optimization algorithm. Especially it can be applied to applications where large network coverage is required with optimum energy requirement. Furthermore, it also provides comparison by no variations in sensor nodes but increased coverage area.

Different researchers have compared different nature-inspired algorithms [

NI set of rules is classified into three major classes: bio-inspired, physics chemistry-based, and swarm intelligence algorithms, as shown in

The Foundation of evolutionary computation is Darwin’s theory [

Algorithm | Source | Inspiration | Reference and year |
---|---|---|---|

Bio-inspired | |||

Hunter spider algorithm | International Journal of Computer Mathematics | Hunting behavior spiders | [ |

Black widow optimization | Engg. Applications of Artificial Intelligence | Mating behavior of black widow spiders | [ |

Grey wolf approach | Knowledge and Information Systems | Hunting capabilities as a team | [ |

Bald eagle optimization | Artificial Intelligence Review | Fish searching behavior of bald eagle | [ |

Tiki-Taka algorithm | Engineering Computations | Football playing | [ |

Barnacles mating optimizer | Engg. Applications of Artificial Intelligence | Both male and female reproduction phenomenon | [ |

Wingsuit flying optimization | IEEE Volume 8 | Popular extreme sport | [ |

Salp swarm algorithm (SSOA) | Journals and magazines IEEE | Crawling behavior of salps in deep-sea | [ |

Butterfly optimization | Soft Computing | Search for food and breeding behavior of butterflies | [ |

Spotted hyena optimizer | Advances in Engineering Software | The public connection between spotted hyenas and their cooperative behavior | [ |

Bat algorithm | International Journal of Swarm | Echo-sounding mechanism of bats | [ |

Black hole mechanics optimization | Asian Journal of Civil Engineering | Mechanics of black hole | [ |

Whale optimizer | Advances in engineering software, Elsevier | Feeding behavior of whales | [ |

Sine cosine algorithm | Knowledge-based systems, Elsevier | Trigonometric behavior of sine and cosine wave | [ |

Dragon fly algorithm | Neural Computing and Applications Springer | Swarming behavior | [ |

Ant lion optimizer | Advances in engineering software, Elsevier | Foraging behavior of ants | [ |

Moth flame optimizer | Knowledge-based systems, Elsevier | Special navigation methods at night | [ |

Nature’s physical and chemical phenomena the resource of these algorithms like electrical charges, gravity, etc. Illustrations of these algorithms are simulated annealing SA [

These algorithms are a trace of inspiration for social insects, how they interact with each other and maintain social life like ants, cuckoos, bees, etc., make societies. Nature-inspired algorithms are gaining massive attention from researchers from every field.

A recently huge number of NI algorithms have been established. This work draws a performance comparison between six NI algorithms Grey Wolf (GWO), Ant Lion (ALO), Sine Cosine Optimizer (SCO), Moth Flame (MFO), Dragonfly (DA), Whale Optimization (WOA) based on their optimum value. The following subsections provide a short introduction to these algorithms.

The way ants hunt served as an inspiration for this. It adopts the antlion’s five-step hunting process. Building traps, taking a random trip, being stung by ants, and catching and rebuilding traps [

The haphazard walk of an ant can be analyzed through

A random walk can be represented as below stated equations is taken from [

^{−})1.

Antlion’s Pit trapping: A mathematical model of this pit trapping is given by

Sliding ants towards antlion: Antlion’s trap building is proportional to their fitness. This behavior 1 is shown in mathematical models

Catching-prey and pit re-building: When an ant is in the antlion’s jaw by the time it reaches the bottom of the pit, the hunt has reached its conclusion.

It can be mathematically as

It is a result of the navigation method of moths. It maintains a fixed angle concerning the moon, very feasible for traveling in a straight line [

It is a source of inspiration for social interaction of dragonflies routing, food-finding, and preventing enemies [

These two behaviors are based on 5 main factors of individuals in groups. These factors can be mathematically modeled in the given equations [

Separation:

_{k} is the recent position and Shows the position of the kth individual and y is the current position.

Alignment:

_{k} Shows K_{T} velocity of the individual, N is the amount of localities.

Cohesion:

_{k} Is the position of the kT h individual.

Attraction toward food source:

^{+} Shows the food source position.

Distraction:

^{−} Is the enemy’s position.

It is an inspiration for the bubble net shooting approach of whales. The mathematical model of whale optimization consists of encircling prey, a bubble-net feeding mechanism, and a search for a target [

Bubble net hunting mechanism: Humpback whales shrink the circle around prey by swimming in a spiral-shaped path. The given mathematical model with fifty percent probability chooses the shrinking process or spiral model as shown in

Prey Search: Humpback whales explore arbitrarily according to the location of other whales. The math-magical

The Development of this algorithm is an inspiration by grey wolve’s hunting and leadership behavior [

It is founded on the hunting mechanism of grey wolves. The mathematical model of the Gray Wolf optimizer shows that Alpha α is the fittest solution. The 2nd and the 3rd best solution is represented by β and δ. The leftover answers are characterized by ω. Grey wolves surround prey during hunting.

Mathematical equations of hunting behavior [

_{p} is the position vector of prey.

It is developed by inspiring sine and cosine mathematical models [

The test had been led on a laptop (intel core i5, 3 GHZ CPU, 3 MB cache, MATLAB 2020b). The analysis of six NI algorithms (Grey wolf, Ant lion, Dragon fly, Whale, Moth flame, Sine cosine optimizers) been done on the basis’s optimum of four composite benchmark functions. These benchmark functions offer significant variants in the form of shifting, rotation, and expansion. It provides excellent complexity among current benchmark functions.

Ackley’s Function

Sphere Function

Rastrigin Function

Griewank Function

Results are analyzed based on the different optimum values obtained. The minimum optimum value shows convergence on a small value near zero. The optimum energy value varies as the number of network coverage varies.

Algorithms | Network coverage = 50 |
Network coverage = 100 |
Network coverage = 100 |
Network coverage = 200 |
---|---|---|---|---|

Rastrigin function (objective function) | ||||

GWO | 0.15 | 3.14 | 0 | 0.0084 |

ALO | 6.96 | 5.96 | 1.98 | 0.0764 |

DA | 12.99 | 11.319 | 8.955 | 0.0478 |

MFO | 2.42 | 3.61 | 1.99 | 0.0591 |

SCA | 0.236 | 9.5 | 2.22e−6 | 0.0493 |

WOA | 5.79e−5 | 5.9e−6 | 0 | 0.2835 |

Gramwick’s function (objective function) | ||||

GWO | 0.02 | 0.01 | 0.007 | 9.9496 |

ALO | 0.13 | 0.027 | 0.106 | 3.4210 |

DA | 0.431 | 0 | 0 | 1.9943 |

MFO | 0.183 | 0.09 | 0.009 | 0.0052 |

SCA | 0.17 | 0.05 | 1.33e−05 | 6.9647 |

WOA | 0.26 | 0.24 | 0.1455 | 3.5527e−14 |

Ackley’s function (objective function) | ||||

GWO | −8.88e−16 | 2.6e-15 | −8.88e−16 | 1.3897e-27 |

ALO | 1.001e−4 | 4.8e-5 | 1.45e-5 | 9.1820e−11 |

DA | −8.88e−16 | −8.88e−16 | −8.88e−16 | 0.0046 |

MFO | 1.19 e−4 | 9.8e-5 | 9.05e−11 | 1.6315e−08 |

SCA | 5.5e−5 | 1.25e−4 | 1.90e−10 | 1.8297e−12 |

WOA | 5.81e−9 | 1.739e−13 | 2.66e−15 | 1.2680e−29 |

Sphere function (objective function) | ||||

GWO | 9.4e−4 | 8.55e−20 | 4.6e−36 | 1.897e−20 |

ALO | 2.04e−8 | 1.136e−8 | 9.7e−10 | 9.1820e−10 |

DA | 0 | 0 | 0 | 0.002 |

MFO | 0.044 | 0.0031 | 5.69e−9 | 1.315e−04 |

SCA | 0.0013 | 1.98e−6 | 1.723e−9 | 1.7e−10 |

WOA | 8.69e−9 | 5.22e−12 | 2.30e−25 | 1.80e−31 |

This part shows the effect of search agents and iterations on the objective function. Search agents = network coverage area, iterations = no of nodes. The testing has been performed on four composite benchmark functions. The size of the network coverage area varies from 50–200

The convergence curves of six compared algorithm for composite test function is illustrated in

The extreme left convergence curve is of extensive network coverage with a few nodes. The middle has the same no of nodes but increased network coverage. The severe right convergence curve is slight in-network coverage with a small no of nodes.

Each curve shows that if coverage areas increase, then the global minimum does not converge to Most algorithms converge to a global minimum if the coverage area grows with increased nodes.

Nature-inspired algorithms are most efficient in producing an optimal solution for several optimization problems.

This paper compares six NI algorithms for optimal coverage in WSNs that are analyzed based on their objective function. This shows that increasing coverage area and a small number of nodes performance of algorithms becomes low. If the number of nodes increases with an improved coverage area, the algorithm gives fast convergence toward the global optimum. However, many algorithms analyzed did not perform well by growing coverage areas with small nodes. On the other hand, WOA (whale optimization algorithm) converges towards global optima for most of the benchmark functions among these six algorithms. To conclude, WOA can be chosen for optimal network coverage of WSNs without increasing nodes.

The authors would like to acknowledge Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2023R193), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2023R193), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

The authors declare that they have no conflicts of interest to report regarding the present study.