One of the important research issues in wireless sensor networks (WSNs) is the optimal layout designing for the deployment of sensor nodes. It directly affects the quality of monitoring, cost, and detection capability of WSNs. Layout optimization is an NP-hard combinatorial problem, which requires optimization of multiple competing objectives like cost, coverage, connectivity, lifetime, load balancing, and energy consumption of sensor nodes. In the last decade, several meta-heuristic optimization techniques have been proposed to solve this problem, such as genetic algorithms (GA) and particle swarm optimization (PSO). However, these approaches either provided computationally expensive solutions or covered a limited number of objectives, which are combinations of area coverage, the number of sensor nodes, energy consumption, and lifetime. In this study, a meta-heuristic multi-objective firefly algorithm (MOFA) is presented to solve the layout optimization problem. Here, the main goal is to cover a number of objectives related to optimal layouts of homogeneous WSNs, which includes coverage, connectivity, lifetime, energy consumption and the number of sensor nodes. Simulation results showed that MOFA created optimal Pareto front of non-dominated solutions with better hyper-volumes and spread of solutions, in comparison to multi-objective genetic algorithms (IBEA, NSGA-II) and particle swarm optimizers (OMOPSO, SMOPSO). Therefore, MOFA can be used in real-time deployment applications of large-scale WSNs to enhance their detection capability and quality of monitoring.

A wireless sensor network (WSN) comprises of a large number of small, autonomous and spatially distributed sensor nodes [_{Sense}_{Comm}

The embedded processors of sensor nodes transform the collected data into electrical signals and radio transceivers transmit these electrical signals to the data sink. Some sensor nodes may be unable to connect directly with a data sink because of limitations in their communication ranges and power sources. So, they use special intermediate nodes, the high energy communication nodes (HECN) as the gateways and send all of the monitored data to them. HECNs are directly connected with data sinks and provide external access to the network. The WSNs administrators collects the monitored data and send commands to the network through the HECN. In a WSN, every sensor node must connect to the HECN but all sensor nodes cannot establish direct communication links with HECN due to the communication range of nodes being small in comparison to the WSN size. Therefore, all those nodes, which are unable to directly communicate with HECN, establish multi-hop communication paths with HECN using intermediate nodes called relays. In this way, all nodes in a WSN can send data to the HECN by, at least, one of the two ways; directly, by using the direct communication path, or indirectly, by using the multi-hop communication paths [

In the last two decades, several meta-hubristic techniques have been used to solve the WSN layout optimization problem, such as genetic algorithms (GA), particle swarm optimization (PSO), ant colony optimization (ACO), fish swarm optimization (FSO) and artificial bee colony algorithm (ABC). These meta-heuristic algorithms provide fast results to problems, but do not guarantee the provision of fully optimized and accurate solutions.

Real world applications mostly depend on more than one objective functions. The solutions to such problems need simultaneous optimizations of these objective functions. This process is called multi-objective (MO) optimization, and it involves the optimization of a vector of solutions with more than one competing objectives. MO problems can be mapped in a vector form as a family of points known as a Pareto optimal set, where objectives are often conflicting. The optimal solution of one objective will not necessarily be the best solution for other objectives. Therefore, different solutions will produce trade-offs between different objectives and a non-dominated set of solutions is produced to represent the optimal solutions of all objectives. They provide output in the form of vectors, which contain Pareto in front of non-dominated solutions.

The genetic algorithms which can find non-dominating points from the population of solutions in parallel are categorized as multi-objective genetic algorithms (MOGA). Various MOGAs have been designed in the past and the literature review of these meta-heuristic techniques is presented in

Author/Year | Algorithm | Approach | Problem | Cover | Node type | Objectives | |
---|---|---|---|---|---|---|---|

Maximized | Minimized | ||||||

[ |
NSGA-II | Centralized | 1-Cover | Area | Heterogeneous | Coverage, mean-weightage of sensor nodes | Nodes count, proximity of target |

[ |
MOEA, NSGA-II, IBEA, IBEAHD | Centralized | 1-Cover | Area | Homogeneous | Coverage, lifetime | Nodes count |

[ |
SGA | Centralized | 1-Cover | Point | Heterogeneous | Coverage | Nodes count |

[ |
NSGA-II | Distributed | 1-Cover | Point | Heterogeneous | Coverage | Nodes count, energy consumption |

[ |
MOGA | Centralized | 1-Cover | Area | Heterogeneous | Differentiated detection levels, coverage, | Energy consumption |

[ |
FD-MOGA | Centralized | 1-Cover | Area | Heterogeneous | Differentiated detection levels, coverage, | Energy consumption |

[ |
SGA | Centralized | 1-Cover | Area | Heterogeneous | Coverage, sensors per cluster in charge | Energy consumption, overlap per cluster in charge error, sensors out of range error |

[ |
NSGA-II, MOEA/D-RH | Centralized | 1-Cover | Area | Heterogeneous | Coverage, lifetime, connectivity | |

[ |
SGA | Centralized | 1-Cover | Area | Heterogeneous | Connectivity, mean relative deviation of sensor nodes, | Active/inactive nodes, transmission ranges, energy consumption |

[ |
NSGA-II | Centralized | 1-Cover | Point | Homogeneous | Coverage, accuracy constraint | Nodes count |

[ |
MOEA/D-ED |
Centralized | 1-Cover |
Point | Homogeneous | Coverage constraint, connectivity, Lifetime | Energy consumption, nodes count |

[ |
MOEA/D |
Centralized | 1-Cover | Point | Homogeneous | Coverage, lifetime | |

[ |
VEGA | Centralized | 1-Cover | Area | Heterogeneous | Coverage, connectivity | |

[ |
GA | Centralized | K-Cover | Area | Heterogeneous | Coverage, connectivity | Nodes count |

[ |
MOGA |
Centralized | K-Cover Dis/set | Point | Homogeneous | Coverage as quality of service, lifetime | Energy consumption |

The literature review of PSO is presented in

Author/Year | Algorithm | Approach | Problem | Cover | Node type | Objectives | |
---|---|---|---|---|---|---|---|

Maximized | Minimized | ||||||

[ |
PSO, VFPSO |
Centralized | 1-Cover | Point | Homogeneous | Coverage, detection capability | |

[ |
PSO | Centralized | 1-Connect | Area | Heterogeneous | Connectivity | Energy consumption |

[ |
PSO | Distributed | 1-Cover | Point | Homogeneous | Coverage | Nodes count |

[ |
MOPSO | Centralized | 1-Cover | Area | Homogeneous | Coverage, life time | |

[ |
IPO |
Distributed | 1-Cover | Area | Homogeneous | Coverage | |

[ |
PSO | Distributed | 1-Cover | Point | Homogeneous | Coverage | |

[ |
PSO | Distributed | 1-Cover | Point | Homogeneous | Coverage | Sensor movement |

[ |
MOPSO | Centralized | 1-Cover | Area | Homogeneous | Coverage, life time | |

[ |
Hybrid Immune-PSO | Centralized | 1-Connect | Area | Heterogeneous | Coverage, mean relative density | Energy consumption, overlap per cluster in charge error, sensors out of range error |

[ |
Consensus PSO | Centralized distributed | 1-Cover | Area | Homogeneous | Coverage | Energy consumption |

[ |
PSO | Centralized | Minimal k-Cover | Area | Homogeneous | Coverage | Nodes count |

[ |
PSO, hybrid PSO-DE | Centralized | 1-Connect | Point | Homogeneous | Coverage | Energy consumption |

[ |
PSO, GA, hybrid PSO | Centralized | 1-Connect | Area | Homogeneous | Coverage |

In this research, a multi-objective firefly algorithm (MOFA) is proposed and applied for the layout optimization of WSNs.

The firefly algorithm (FA) approach is inspired by the natural light flashing behavior of fireflies, which they use to attract prey or their mating partners in the swarm. In this algorithm, the authors assume that all fireflies are unisexual [

The luminance intensity or brightness of a firefly is controlled by the values of an objective function f(x). The luminance intensity (I) of a firefly at a particular location x in the solution space can be represented as I(x), which is directly proportional to the value of objective function f(x). The light in nature follows the inverse square law; when the distance from the light emitting source increases, the intensity decreases due to absorption in the environment. This principle is used in the algorithm to update the luminance intensity of fireflies.

The luminance intensity I(r) of a firefly at a distance r can be expressed as in _{0} is the original light intensity of the firefly at a distance (r = 0), and γ is the fixed light absorption coefficient.

In nature, attractiveness among the fireflies depends on the intensity of light they emit, and it is directly proportional to the brightness of fireflies. Therefore, for any two flashing fireflies, the less bright always has a tendency to move towards the brighter one. According to the principle of inverse square law, the values of attractiveness decrease among fireflies as the distance among them increases. The attractiveness β varies with the distance r between any two fireflies. As the attractiveness is proportional to the light intensity, so the attractiveness β is calculated according to _{0} is the attractiveness at a distance (r = 0) from a firefly.

In the FA approach, as shown in _{0} in

In [_{o} is the initial value of the random factor, and α^{t} is the value of alpha for iteration number (t).

A multi-objective firefly algorithm (MOFA) [

The optimal layout designing problem is related to the selection of physical positions of sensor nodes in a way that they entirely cover a geographical area or a set of targets [

The layouts directly affect the efficiency and monitoring capability of WSNs, and if layout optimization is not considered while deploying the sensor nodes, then WSNs behavior may become unpredictable with high network failure rates, bad area coverage, and frequent disconnections. This degradation in WSNs drastically influences the functionality and performance of real-time applications.

In this solution, a two-dimensional plane is used for the representation of monitoring area to be covered by the deployed sensor nodes. A distance vector (DV) is used to represent a single solution of each problem, and the size of this vector depends on the total number of sensor nodes as in

When the position coordinates of the monitoring area (length × width) are taken as 100 × 100, then for all single and multi-objective problems, two vectors X = {0, 1, 2……100} and Y = {0, 1, 2……100} are used to represent (x, y) coordinates of the two-dimensional area points. A third vector contains the information of active and inactive sensor nodes in the case of homogeneous WSNs and the size of this vector is set to “n”. This vector is used for the calculation of the maximum and the minimum number of sensor nodes for all problems. For heterogeneous WSNs, this third vector is used to represent the various sensing ranges of nodes (RSense). In all of our experiments, complete solutions of optimization problems are encoded in the form of firefly chromosomes.

In homogeneous WSNs, all of the nodes are considered identical with the same sensing range (R_{Sense}) and no encoding is required for representing the node properties. Each firefly is encoded as a complete layout solution of a WSN. The sensor nodes are encoded as genes of a chromosome, and information about their positions and active and inactive modes is included. In the encoding of each chromosome, an active-inactive (A/I) mode bit is used, which is set when a node is considered active and could take part in the fitness calculation of the designed solution, as shown in

The fitness calculation of each solution is performed by taking the weighted sum of all objective functions. The fitness calculation methods for coverage, number of nodes, connectivity, lifetime, and energy consumption of WSNs are presented here.

The number of nodes for each solution is calculated using the number of active-inactive (A/I) mode bits. In solutions of homogeneous WSNs, a single active-inactive (A/I) mode bit is used to calculate active nodes while set to one.

There are two methods available for the calculation of coverage; one is grid-based, and the second is area-based. In both of the techniques, a binary sensing model is used where the sensing area of a node is considered as a circular disk with a fixed sensing range (R_{Sense}). An object present at a distance less than the sensory range can be sensed by a node. Here the detection probability _{Sense} according to

In the area-based method, the sensor nodes are randomly distributed in the monitoring area. The area covered by an individual sensor node is measured depending on its sensing radius (R_{Sense}), which is the same for all sensor nodes in a homogeneous WSN. The total area covered by these nodes is calculated, and the overlap among sensor nodes is subtracted to get full area coverage according to

In the grid-based method, the whole monitoring region is divided in square grids of equal sizes. Euclidean distance of sensor nodes from the center point of each grid is calculated to determine if a grid is completely covered by some of the nodes or not. The maximum area covered by any sensor node i at position (xi, yi) is calculated by using the sensing radius (RSense). The total covered grid points of the grid are then normalized by the total points in the area according to

The grid-based method is fast when the number of sensor nodes and the monitoring area or points are small, but it becomes slow when the WSNs size grows due to the presence of a large number of nodes. To avoid the performance degradation of the algorithm, the area-based coverage calculation method is used for area coverage and the grid-based method is used for point coverage.

A WSN is considered connected when there exists at least one single or multi-hop communication path between all of the sensor nodes and the data sink. The main goal of the optimization algorithms is to minimize the number of disconnected nodes in the network, so that a fully connected network is attained. The connectivity of each layout solution is tested by creating a graph with nodes as its vertices, and a minimal spanning tree is developed with the data sink as the root node. Two nodes i and j are considered connected if the distance (dij) between them is less than their communication radius (R_{Comm}) and the edge weight (EWij) is set to the distance (dij) between them as in

Every node in a WSN may perform several different tasks such as maintenance, sensing, processing, transmission and reception of data to and from other sensor nodes. These operations consume energy and for an optimal layout, the minimum data transmission path must be used to conserve this energy. For the calculation of energy consumption (EC_{i}) at each node _{i}_{i}) from which data can be received are calculated and the node maintenance energy (M_{i}), the transmission energy (Tra_{i}), and the reception energy (Rec_{i}) are summed up according to

The life time of a WSN depends on the failure of the first node in the network. The life time of a single node (LT_{i}) is calculated using the initial energy (IE_{i}) and the consumed energy estimate (EC_{i}) of each node. The time until which a node can work is calculated as in

The performance of MOFA is tested by comparing it with the multi-objective genetic algorithms (IBEA, NSGA-II) and the particle swarm optimizers (SMPSO, OMOPSO) according to the parameter settings presented in

Sensing radius RSense | 10 m | Energy consumption | Maintenance = 15 mA, |

Communication radius | 20 m | ||

Node type | Homogeneous | Population size | 20 |

Points | 100 points | Archive size | 10 |

Initial energy | 1000 mA | Maximum iterations | 1000 |

Deployment dimensions | 2-D | NSGAII parameters | Crossover Rate CR = 0.9, |

Area | 100 × 100 m^{2} |
IBEA parameters | Crossover Rate CR = 0.9, |

Nodes count | 20, 30, 40, 50, 60, 70 | SMPSO parameters | Mutation Rate MR = 0.05 |

Deployment scheme | Random | OMOPSO parameters | Mutation Rate MR = 0.05 |

Sensing model | Binary | MOFA parameters | Alpha (α) = 0.53, Gemma (γ) = 0.96, (delta) δ = 1.15 |

The results for best non-dominated solutions are obtained by varying the number of homogeneous sensor nodes in the range (20–70) with a swarm size of 20. For all the experiments, 1000 iterations are run to find the Pareto optimal solutions.

A solution with five competing objective is designed for the multi-objective point coverage problem. It involves the maximization of point coverage, lifetime and connectivity of sensor nodes, along with the minimization of energy consumption and the number of sensor nodes. The results are presented in

Algorithms | Node count | Optimization objectives | ||||
---|---|---|---|---|---|---|

Coverage % | Nodes count | Disconnected nodes | Energy consumption | Lifetime | ||

NSGAII | 40 | 85 | 37 | 0 | 690 | 11 |

50 | 89 | 44 | 0 | 933 | 9 | |

60 | 90 | 50 | 0 | 963 | 8 | |

70 | 93 | 59 | 0 | 6582 | 0 | |

IBEA | 40 | 81 | 34 | 0 | 647 | 11 |

50 | 89 | 39 | 0 | 779 | 9 | |

60 | 81 | 56 | 0 | 18369 | 0 | |

70 | 87 | 69 | 0 | 6774 | 0 | |

SMPSO | 40 | 91 | 34 | 0 | 13053 | 0 |

50 | 91 | 44 | 0 | 4663 | 0 | |

60 | 96 | 51 | 0 | 11352 | 0 | |

70 | 98 | 60 | 0 | 1023 | 7 | |

OMPOSO | 40 | 83 | 34 | 0 | 5207 | 0 |

50 | 89 | 47 | 0 | 27762 | 0 | |

60 | 97 | 53 | 0 | 1014 | 8 | |

70 | 99 | 60 | 0 | 9303 | 0 | |

MOFA | 40 | 91 | 40 | 0 | 4563 | 0 |

50 | 95 | 50 | 0 | 10527 | 0 | |

60 | 97 | 60 | 0 | 11425 | 0 | |

70 | 98 | 70 | 0 | 13125 | 0 |

The solution for the multi-objective area coverage problem is formed with the simultaneous optimization of six objectives. These objectives are the maximization of area coverage, lifetime and connectivity of sensor nodes and the minimization of energy consumption, overlapped region and the number of deployed sensor nodes for homogeneous WSNs. The results of this experiment are presented in

Algorithms | Node count | Optimization objectives | |||||
---|---|---|---|---|---|---|---|

Coverage % | Nodes count | Disconnected nodes | Energy consumption | Lifetime | Overlap | ||

NSGAII | 20 | 55 | 18 | 0 | 255 | 67 | 0 |

40 | 86 | 34 | 0 | 8085 | 0.7 | 19 | |

60 | 95 | 51 | 0 | 43914 | 0.4 | 37 | |

70 | 96 | 54 | 0 | 40791 | 0.3 | 44 | |

IBEA | 20 | 53 | 20 | 0 | 5003 | 0.5 | 8 |

40 | 85 | 39 | 0 | 25982 | 0.4 | 35 | |

60 | 73 | 56 | 0 | 47757 | 0.2 | 100 | |

70 | 66 | 66 | 0 | 57431 | 0.2 | 106 | |

SMPSO | 20 | 48 | 16 | 0 | 225 | 66 | 1 |

40 | 83 | 32 | 0 | 11919 | 0.4 | 15 | |

60 | 91 | 36 | 0 | 14413 | 0.3 | 19 | |

70 | 85 | 41 | 0 | 21798 | 0.3 | 21 | |

OMPOSO | 20 | 54 | 19 | 0 | 270 | 66.7 | 4 |

40 | 82 | 35 | 0 | 31074 | 0.3 | 26 | |

60 | 98 | 42 | 0 | 64717 | 0.1 | 31 | |

70 | 100 | 41 | 0 | 41184 | 0.1 | 24 | |

MOFA | 20 | 62 | 20 | 0 | 5997 | 0.3 | 0 |

40 | 88 | 40 | 0 | 21715 | 0.2 | 35 | |

60 | 98 | 60 | 0 | 54879 | 0.3 | 87 | |

70 | 100 | 70 | 0 | 91555 | 0.1 | 114 |

WSNs layouts obtained by plotting the best solutions of multi-objective area coverage problem are shown in the

The results show that MOFA and OMOPSO found near optimal solutions and provided the best solutions with 100% point and area coverage with full connectivity of the network. SMPSO and NSGAII found better results than IBEA with 100% connectivity. The closeness of the non-dominated solutions generated by the multi-objective algorithms to the true Pareto Front can be determined if the true Pareto Front is known. In the absence of the information about the true front, the values of spread is a quality indicator of solutions. For the performance comparison of multi-objective algorithms, we use the hyper volume quality indicator, and its value is maximized to gain good quality non-dominated solutions. The algorithm with a high hyper volume value of non-dominated solutions is considered superior to those with low hyper volume values. The comparison of the hyper volume and spread indicators for non-dominated solutions generated by multi-objective algorithms MOFA, NSGA-II, IBEA, SMPSO and OMOPSO are shown in

The spread values of solutions generated by MOFA are low when the number of nodes is small, but they improve with increments in nodes. The solution spread values of MOFA are better than SMPSO and OMOPSO with 50, 60 and 70 nodes. NSGA-II and IBEA show high spread values with a small number of nodes but provide a zero spread of solutions with 60 and 70 nodes, as shown in

The hyper volumes of solutions generated by MOFA are lower than values provided by OMOPSO and SMPSO but higher than NSGA-II and IBEA values. This shows that solutions generated by MOFA are dominated by SMPSO and OMOPSO but better than solutions of NSGA-II and IBEA, as shown in

Our experiments show that the multi-objective firefly algorithm efficiently optimizes the layout schemes for homogeneous WSNs by providing Pareto optimal front of non-dominated solutions. The algorithm well utilizes the exploration and exploitation capabilities associated with meta-heuristic algorithms. Our results show that MOFA maximizes the area coverage to 100% and the point coverage to 99%. It is also noticeable that the layout diagrams obtained from our simulations show improvement in energy consumption and lifetime of the network, which leads to ideal layouts of WSNs. Moreover, MOFA is scalable for large-scale wireless sensor networks. Comparative analysis with SMPSO, OMOPSO, NSGAII and IBEA show that MOFA provides near optimal results with a better convergence speed.

This study can be further extended for the optimization of heterogeneous WSNs with probabilistic sensing models. MOFA can also be applied to other multi-objective optimization problems, such as localization, energy-aware routing, clustering and scheduling of WSNs.

The authors extend their appreciation to the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University for funding this work through Research Group No. RG-21-07-09.

This research has been funded by the

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