energy optimization approaches in wireless sensor networks: a

A.BOUDHIR et al., International Journal of Networks and Systems, 1(1), August – September 2012, 43-50

43 @ 2012, IJNS All Rights Reserved

ABSTRACT Due to its importance like a restriction whitch affect the survivability and lifetime of devices in wireless commu-nication, the energy consumption attract the attention of researchers around the world. Because of this, several approches focuses their studies to the challenge of ener-gy consumption. In Fact, related to their axes of re-searches, the scientists are more specified in precise area traiting the energy which gives rise to several approaches that aim economization and optimization of energy con-sumption of wireless nodes. In this survey, we focus on the energy consumption in wireless sensor networks and multimedia sensor networks concerned by the heavy data like audio and video traffic. Key words: Energy Optimization, WSN, WMSN.

1. INTRODUCTION

The main concern in communication between nodes of WSNs is the energy consumption. In sensor networks, a sensor node is equipped with one or more integrated sensors, embedded processors with limited capability, and short-range radio communication ability. These sen-sor nodes are powered using batteries with limited ca-pacity. By contain to standard wireless networks, wire-less sensor nodes are often deployed in variable envi-ronments, making it difficult to change their batteries. Moreover, recharging sensor batteries is complicated and still impossible. These severe constraints have a direct impact on the lifetime of a sensor node. As a result, energy conservation becomes an important area in WSNs to prolong the lifetime of sensor nodes. On the one hand, low-power electronics is one approach to reducing ener-gy consumption at a sensor node. The integration of low-power chips in the design of sensor nodes is a ne-cessary step toward achieving high levels of power effi-ciency. Energy gains resulting from energy-efficient chip design, however, can easily be squandered if the processing and communication capabilities of the sensor node are not operated efficiently. Achieving this goal requires the design of energy-aware communication pro-tocols. On the other hand, other approach based on an important issues in the design of MAC protocol for wireless sensor nodes. Several sources contribute to energy inefficiency in MAC-layer protocols. The first

source of energy waste is collision, which occurs when two or more sensor nodes attempt to transmit simulta-neously. The need to retransmit a packet that has been corrupted by a collision increases energy consumption. The second source of energy waste is idle listening. A sensor node enters this mode when it is listening for a traffic that is not sent. This energy expended monitoring a silent channel can be high in several sensor network applications. The third source of energy waste is over-hearing which occurs when a sensor node receives pack-ets that are destined to other nodes. Due to their low transmitter output, receivers in sensor nodes may dissi-pate a large amount of power. The fourth major source of energy waste is caused by control packet overhead. Con-trol packets are required to regulate access to the trans-mission channel. A high number of control packets transmitted, relative to the number of data packets deli-vered indicates low energy efficiency. Finally, frequent switching between different operation modes may result in significant energy consumption. Limiting the number of transitions between sleep and active modes, for exam-ple, leads to considerable energy saving. Energy-efficient link-layer protocols achieve energy savings by control-ling the radio to eliminate, or at least reduce, energy waste caused by the sources noted above. Further energy gains can be achieved using comprehensive energy management schemes which focus not only on the sensor node radio, but equally important, on other sources of energy consumption. The Optimization of the network in terms of energy efficiency can be achieved by providing the following key steps named as efficiency to network dimensioning, efficiency in the network processes, effi-ciency to the access network, efficient electronic equip-ments, use of RES and remote monitoring of the network for better management of the equipments (Table.1). Wireless Multimedia Sensor Networks (WMSN) are sensors networks which have capabilities for dealing with multimedia information. They are composed of multimedia sensors which are able to capture and trans-mit multimedia information, e.g., sensors might typically be low-resolutions cameras in surveillance environments. MWSNs present some challenges that are common to wireless sensor networks, i.e., the existence of limited resources, like sensors memory, energy consumption, CPU performance, etc. Due to these limitations, it is es-

Energy Optimization Approaches In Wireless Sensor Networks: A Survey A.BOUDHIR1, Med.BOUHORMA2, Med.BENAHMED3

List Laboratoty, ERIT, Faculty of Sciences and Tehniques, Tangier, Morocco [email protected], 2bouhorma@gmail, [email protected]

ISSN 2319 - 5975 Volume 1, No.1, July August- September 2012

International Journal of Networks and Systems Available Online at http://warse.org/pdfs/ijns08112012.pdf



sential to maximize the lifetime of sensors by reducing the amount of information that traverses the network. In addition, MWSNs have special characteristics that make them different from traditional WSNs, i.e., they must be able to handle special quality of service requirements for multimedia traffic. This means that sensors should be able to adapt their transmission capabilities to the parti-cularities of multimedia information.

Table 1: Main Factors for Energy Efficient Network

2. WIRELESS SENSOR NETWORKS

Sensor network is deployed with an objective of ga-thering information, for a given initial battery energy, it is desired that the network continues to function and provide data updates for as long as possible. This is referred to as the maximum lifetime problem in sensor networks. During each data gathering phase, nodes spend a part of their battery energy on transmitting, receiving and relaying packets. Hence the routing al-gorithm should be designed to maximize the time until the _rst battery expires, or a fraction of the nodes have their batteries expired. 2.1. Design and Architecture

A WSN, sensor nodes are organized into fields "sensor fields" (fig.1). Each of these nodes has the ability to collect data and transfer them to the gateway node (called "sink" in English or sink) via a multihop architecture. Well then transmits this data via the Internet or satellite to the central computer "Task Manager" to analyze and make these decisions.

Figure 1: Sensor field architecture

2.2. Challenges And Constraints

The main factors influencing the architecture and constraints of sensor networks can be summarized as follows: Fault Tolerance: Some nodes may generate errors or

stop working because of a lack of energy, a physical or interference. These problems do not affect the rest of the network; it is the principle of fault tolerance. Fault tolerance is the ability to maintain network functional-ity without interruptions due to a fault occurring on one or more sensors.

Scale: The number of nodes deployed for a project may reach one million. Such a large number of nodes generates a lot of transfers inter nodal and requires that the well "sink" is equipped with lots of memory to store the information received.

Production costs: Often, sensor networks are com-

posed of a very large number of nodes. The price of a node is critical in order to compete with a network of traditional surveillance. Currently a node does not of-ten costs much more than $ 1. For comparison, a Blu-etooth node, already known to be a low-cost system, costs about $ 10.

The environment: The sensors are often deployed en

masse in places such as battlefields beyond enemy lines, inside large machines, the bottom of an ocean, fields biologically or chemically contaminated. There-fore, they must operate unattended in remote geo-graphic areas.

Network topology: The deployment of a large number

of nodes requires maintenance of the topology. This maintenance consists of three phases: Deployment, Post-deployment, and Redeployment of additional nodes.

Material constraints: The main constraint is the phys-ical size of the sensor. Other constraints are that ener-gy consumption must be reduced so that the network will survive as long as possible, it adapts to different environments (extreme heat, water, ..), it is very dura-ble and autonomous since it is often deployed in hos-tile environments.

The media transmission: In a sensor network, nodes are connected by a wireless architecture. To allow op-erations on these networks worldwide, the transmis-sion medium must be normalized. We mostly use the infrared (which is license-free, robust to interference, and inexpensive), Bluetooth and ZigBee radio com-munications.

Energy consumption: A sensor, because of its size, is

Energy Efficient Network

Dimensioning (Planning)

Efficient Access

Network

Efficient Network Processes

Efficient Electronic

EquipementRemote

MonitoringRenewable

Energy



limited in energy (<1.2V). In most cases the battery re-placement is impossible. This means that the lifetime of a sensor depends greatly on the life of the battery. In a sensor network (multihop) each node collects data and transmits values. The failure of some nodes requires a change in network topology and a re-routing of packets. All these operations are energy intensive, it is for this reason that current research focuses primarily on ways to reduce consumption.

3. WIRELESS MULTIMEDIA SENSOR NET-

WORKS

The technology boom in electronics contributed to the availability of equipment miniaturized and low cost such as CMOS cameras and microphones which helped further the development of sensor networks wireless multimedia (WMSN), devices that are able to recover the ubiquitous multimedia content such as streaming audio and video, still images, and data from environ-mental sensors. Sensor networks Wireless multimedia will not only strengthen the networks of sensors such as monitoring, home automation and environmental monitoring, but they will also enable several new ap-plications such as:

Monitoring Networks Multimedia, Storage of potentially relevant Traffic Control Systems, Medical Surveillance Remote Environmental monitoring, Location Services, Industrial Process Control, Etc.

3.1. Design and architecture

The problem of designing scalable network architecture (fig.2) is of great importance. Rates for most networks are wireless sensor architecture based on a flat, homo-geneous wherein each sensor has the same physical and can only to interact with adjacent sensors. Traditionally, research on algorithms and protocols for sensor networks has focused on adaptability, that is to say, How to design solutions whose applicability is not limited by the size before growth the network. The flat topology cannot always be agreed to handle the amount of traffic generated by multimedia applications includ-ing audio and video. Similarly, the processing power required for data processing and communications the power required to operate, may not be available on each node. In the pre-vious figure, reference architecture for WMSNS is pre-sented, which is illustrated three sensor networks with different characteristics, deployed in different physical locations. The first cloud on the left shows a sin-gle-level network of video sensors homogeneous. A subset of sensors deployed has the highest processing

capabilities and is thus referred to as the processing cen-ters. The union of treatment centers is a distributed processing architecture. Multimedia content gathered is relayed to a wireless gateway with a multi-step path. The gateway is connected to a storage center, which is re-sponsible for the content of multimedia storage locally for the next recovery. Clearly, more complex structures for distributed storage can be implemented when permit-ted by the environment and application needs, which can lead to energy savings since, by storing it locally, the

Figure 2: WMSN Architecture



media should not be (wireless) relayed to remote loca-tions.

3.2. Challenges And Constraints Sensor networks wireless multimedia derive from a con-vergence of communication and calculation of signal processing and several branches of control theory and embedded computing. This interdisciplinary research will distributed heterogeneous systems and devices em-bedded in this direction, to interact and control the phys-ical environment. There are several factors that mainly influences the design of a WMSN: Strong demand for QOS (Quality of Service) A wide variety of applications envisaged on WMSN have different requirements. In addition to the methods of de-livering digital data, sending real-time multimedia data containing triggered events and observations obtained in a short time is a critical factor. Therefore, a solid founda-tion is necessary in terms of hardware and support high-level algorithms to provide quality service and to consider the application specific requirements. These requirements include multiple domains and can be ex-pressed, among others, in terms of a combination of lim-its on energy consumption, delay, reliability, distortion. ....”

Application of high bandwidth: Multimedia data, particularly video, need bandwidth during transmission of magnitude higher than that sup-ported by currently available sensors. The following ta-ble (Tab.2) cites the transmission rate for some sensors:

Multimedia coding techniques:

Decompression of video streams requires excessive use of bandwidth for a multi-jump (Tab.3).

Table 2: Image and Video Compression rate

Format (QCIF, 176 x 120) 21Ko, 30 Images /s Video Stream plus de 5 Mbit / s

Therefore, it is evident that the effectiveness of treatment techniques is loss compression necessary for multimedia sensor networks.

Table 2. Transmission ratio of some sensors Sensor Standard Nominal rate

of Transmission Crossbow’s MICAz TelosB

IEEE 802.15.4

250 kbit/s.

Techniques of Energy Conservation

Energie Communication Energy Processing Energy Sensing

MAC Protocoles

Routing Protocoles

System Partitionnement DVS

Removing Sensing

Reducing the number of communications Topology Control

Data Aggregation CSIP Negotiation Hierarchisation Power Control

Figure 3: Techniques and Approaches for Energy Conservation



Data processing in multimedia networks The data processing can execute algorithms on the raw data extracted from the environment requires new archi-tectures for collaborative processing, distributed taking into account the resource constraint and taking into ac-count the filtering and extraction of information well field. This can increase the adaptability of the system by reducing the transmission of redundant. Energy consumption is a fundamental concern in WMSN, even more than in wireless sensor networks traditional. Made by the sensors are devices with con-strained battery, while multimedia applications produce large volumes of data requiring high transmission rate and treatment at the time or energy consumption of sen-sor nodes is dominated by traditional communications capabilities, and is introduced by minimal effect. 4. ENERGY OPTIMIZATION APPROCHES Several studies have been conducted and are based on techniques from the literature. Various approaches have been subjected to energy optimization focusing on the capture, computing and communication. In Fig. 3, an overview of various techniques is listed: The energy sensor can be saved either in capture, processing or in communication level: At capture: the only solution provided for minimizing energy consumption at the capture is to reduce duration of catches. At Processing: energy calculation can be optimized by using two techniques: The approach DVS (Dynamic Voltage Scaling),

which is to adaptively adjust the voltage and frequency of CPU to save computing power without performance degradation.

The approach of partitioning system, which involves transferring a calculation prohibitive computation time to a base station that has no energy constraints and has a high computational capacity.

At communication Level: the minimization of the energy consumption during communication is closely related to protocols developed for the network layer and the MAC layer. These protocols are based on several techniques: data aggregation, trading and CSIP (Collaborative Signal and Information Processing). This last technique is a discipline that combines several areas: communication and low power computing, signal processing, distributed algorithms and fault

tolerance, adaptive systems and sensor fusion theory and decisions. These techniques aim to reduce the number of transmit / receive messages. By cons, the topology control allows adjustment of the transmission power and clustering of sensor nodes (hierarchisation).

The control of transmission power not only affects the

life of the battery of a sensor node, but also on the capacity of the traffic that is characterized by the number of packets successfully transmitted to a destination. In addition, it affects the connectivity and management of the density (the number of neighboring nodes). Thus, it can conserve energy in two ways: explicitly by the application of low power emission and implicitly by reducing contention with other nodes transmitters. The control module of the power is often integrated in the protocols or network layer or the MAC layer.

The hierarchy is to organize the network structure at several levels. This is the case, for example, clustering algorithms (clustering), which organize the network into groups (clusters) with group leaders (Cluster Head) and member nodes.

4.1. Routing protocols and energy optimization In the literature, various classified hierarchical routing protocols for sensor networks are based on energy, the location and quality of service (QoS). Of data-centric protocols such as SPIN, broadcast live, consolidate re-dundant data when routing from source to destination. On the other hand, QoS protocols such as SPEED meets the diverse needs such as energy efficiency and reliabili-ty as well as real-time requirements. Finally, hierarchical protocols such as LEACH, APTEEN Pegasis form clus-ters (Cluster Head) CH minimize the energy consump-tion for both processing and data transmission. MECN, in turn based on the minimization of network graph nodes el limit, therefore, the maintenance and the num-ber of links and the power in the field of graph limits. Other studies use OEDR (energy-delay optimized routing) which is similar to OLSR (optimized link state routing) based on the concept of MPR (Multipoint Re-lays) and periodically sends messages with a view to determine the energy transmission and the delay between the source node and its neighbor. LEACH (Low-Energy Adaptive Clustering Hierarchy)

o LEACH protocol is based on a distributed clustering

algorithm. It involves randomly selecting nodes cluster-heads and assigns this role to the various nodes according to management policy round-robin ie turn to ensure fairness of energy dissipation among nodes. In order to reduce the amount of in-



formation transmitted to the base station, the clus-ter-heads aggregate the data captured by nodes that belong to members of their own cluster, and send an aggregated packet to the base station.

PEGASIS (Power-Efficient Gathering in Sensor In-

formation Systems) o The basic idea of this protocol is to prolong the life-

time of the network, nodes only communicate with their nearest neighbors and in turn the communica-tion with the base station. When the round of all nodes communicate with the base station completes, a new cycle begins and so on. This reduces the power required to transmit data per turn because the power is evenly distributed principally made drain-ing nodes. Thus, Pegasis has two main objectives: To increase the lifetime of each node using col-

laboration techniques and thereby increase the lifetime of the network;

To allow local coordination between nodes that are close so that the bandwidth consumed in communication is reduced.

APTEEN And TEEN (Threshold-Sensitive Ener-

gy-Efficient Protocols) o TEEN and APTEEN are two hierarchical routing

protocols. TEEN protocol in the sensor node senses the environment continuously, but data transmission is done less often. The cluster node sends its mem-bers a threshold called 'hard' (HT) with the threshold value of the attribute is detected, and a software threshold (ST) is a small change in the value of the attribute that triggers node to switch on its transmit-ter and transmit. Thus, the threshold is trying to re-duce the number of transmissions by allowing nodes to transmit only when the attribute is detected in the interval of interest. On the other hand, APTEEN is a hybrid protocol that changes the periodicity or thre-shold values used in the protocol TEEN according to the needs of users and the type of application. AP-TEEN in the cluster broadcasts the following para-meters: Attributes (A): A set of physical parameters on

which the user is interested in obtaining informa-tion.

Thresholds: Includes hard threshold (HT) and soft threshold (ST).

Schedule: Time multiplexing that assigns a slot to each node.

Count time (CT) maximum time between two successive reports sent by a node.

SMECN (Small Minimum Energy Communication Network)

The essential property of the subnet constructed by MECN is based on the property of minimum energy. Given a graph G representing the network nodes, MECN ensures that between each pair (u, v) of nodes that are connected in G, the subgraph has a minimum energy path between these nodes, this allows messages to be transmitted with minimal use of energy compared to all possible paths. Characterization used to construct a pro-tocol called SMECN (communication network for small minimum energy) lies in the construction of subnets SMECN probably smaller than one constructed by MECN. If emissions to a given power setting are able to reach all nodes in a circular area around the diffuser SMECN allows for him to reduce maintenance costs associated with MECN and can achieve significant sav-ings in energy consumption. SMECN provides calcula-tion and processing easier than MECN. In [1], A.V. Et al, all propose an energy efficient adap-tive Multipath routing technique using multiple paths between source and the sink. They proposed an energy efficient protocol for WMSN's which is capable of searching multiple paths and allocating the traffic on each path optimally. The focused here work on distri-buting the load to the nodes significantly impacts the system lifetime. The results show that the energy effi-cient adaptive multipath routing scheme achieves much higher performance than the classical routing protocols, even in the presence of high node density and overcomes simultaneous packet forwarding. [2] is another work which is dedicated to save energy in WSN, whitch can be used in WMSN, proposed an approach which consists of three components: a middle-ware to handle the heterogeneity of data and applica-tions, called SemanticMidd, an ontology to give a formal semantics to data and a reconfiguration module to com-municate with ontology and middleware and process queries. The proposed ontology uses inference rules as a basis for their results from the information captured, and thus proposes a automatic sensor reconfiguration so smart. 4.2. MAC protocols and energy optimization In [3], C.U Et. al, the authors proposes an adaptive radio low-power sleep modes based on current traffic condi-tions in the network. This mode provides an analytical model to conduct a comparative study of different MAC protocols (BMAC, TMAC, SMAC, DMAC) suitable for reduction of energy consumption in wireless environment. This technique exposes the energy trade-offs of different MAC protocols. It first introduces a comprehensive node energy model, which includes



energy components for radio switching, transmission, reception, listening, and sleeping for determining the optimal sleep mode and MAC protocol to use for given traffic scenarios. The study focuses on energy consump-tion during a single sampling period (Figure.4):

Figure 4: Energy consumption during a sample period In [4], authors based their work on explicit cooperation among nodes which is clearly impractical in WSNs as it causes additional energy and bandwidth consumption. They presented a concept of incompletely cooperative game theory to improve the performance of MAC pro-tocols in WSNs without any explicit cooperation among nodes. The problem of energy-efficient MAC protocols for WSNs is modeled as game-theoretic constraint opti-mization with multiple objectives, energy consumption and QoS metrics. This work focuses on a simple method of the sleeping probability based on analytical model. Z. CHEN Et al. [5] presents a WSN access control al-gorithm based on slotted ALOHA protocol, this algo-rithm incorporates the power control of physical layer, the transmitting probability of MAC layer, and the ARQ of link layer. In this algorithm, a cross-layer optimization is preformed to minimizing the energy consuming (E) and power (ρ) per bit, in the equations (1) and (2) where N is the number of nodes, B is the bandwidth and R present the ratio.

(1)

(2)

In [6], the energy consumption for physical and MAC layer is analyzed, the analysis is based on a linear networks, so the conclusion may not be practical in realistic scenarios. A cross-layer solution among MAC layer, physical phenomenon, and the application layer for WSNs is proposed. In many works, the receiver-based routing is exploited for MAC and routing cross-layer

modularity. The performance evaluations of all these propositions present the advantages of cross-layer approach at the routing and MAC layer. In [7] the authors propose a position based cross layer resource allocation approach to achieve optimal image transmission quality while assuring energy efficiency in WMSNs.The work traits the image-pixel-position information and image-pixel-value information is with an optimized across PHY, MAC and APP layers regarding p-data and v-data distortion reduction correlations. The important p-data segments containing structure and position information are more reliably protected and transmitted to improve image quality, and the relatively unimportant v-data segments containing image pixel value information are less protected during transmission to improve energy efficiency. In [8], Wu proposed an FEC(forward error correction) based UEP (unequal error protection) approach for energy efficient image transmission in WMSN, and studied the energy-quality tradeoff. In that approach, the wireless channel was modeled using a two consideration of energy resources in WMSN, and layer oriented optimization without considering position-value diversity in the image bit stream. Unfortunately, the approaches for delay constrained distortion minimization cannot be directly applied to WMSN due to the high priority of energy efficiency, and the quality gain of the layer based UEP schemes is very limited. In [9], The uncertain energy consumption in each sensor nodes is modeled as a polyhedral set. The lifetime maximization problem is formulated as a robust optimization problem, the counterpart of which is showed to be a convex problem with linear constraints. The authors solve the robust counterpart problem in its dual domain with dual decomposition and subgradient method. A partially distributed algorithm is proposed, based on the solution of the problem. The algorithm is proposed to be implemented in small scale WMSNs with sink node responsible for partially central calculation function.

4.3. Processing and energy optimization

Wireless sensor network is an exclusively typical low power system according to the energy limited application environment, which is directly embodied in both the hardware and software design. The processor obviously acts as the headquarters for the whole system. The optimized low power processor design will contribute to efficient power controlling of the whole system. Dynamic Voltage Scaling (DVS) is another emerging technology used to reduce the power consumption of handheld and mobile devices. The displays, disks and CPU are the most power consuming components of a

• Listening Energy

• Sleeping Energy

• Overall Energy

• Delay Considerations

• Receiving Energy

• Transmission Energy

Sam

ple

Peri

od



computer system. Reducing the energy consumption of display and hard disk mainly depends on new technology invention or by turning them off after a period of idle time. There has to be a system that would reduce the CPU power at times when there is no CPU usage and will clock at full speed when there is heavy processor load. DVS is the technique of dynamically reducing the processor speed and thereby reducing the voltage and power consumption. The authors of [10], presented a novel WSN-Oriented low-power processor (WO-LPP) design scheme. The processor has an 8-bit simple 3-stage pipeline event-driven RISC ISA core and 4k SRAM, 64K on-chip program Flash connected by Harvard bus. The hardware architecture separate memories and buses for program and data, in order to maximize performance and parallelism. In [11], Authors propose a cooperative power-saving technique that applies DVS and DMS (Dynamic Modulation Scaling) to sensor nodes for minimizing energy consumption. This technique uses a prediction mechanism that estimates the load of the processor and the radio communication device based on the log data to realize proper cooperation. 4.4. Energy sensing and energy optimization

The sensing is a local operation, e.g. temperature, radiation, humidity or similar physical measurement. There are a lot of applications, civilian or military alike, which implement some remote discovery, localization or tracking activities. In this case, the active sensing is performed mainly by emitting light, electromagnetic or sound waves. Obviously this imposes a heavy burden on the limited energy resources available to the mote, shortening his life and consequently the life of the WSN itself. Sensing coverage and network connectivity can be viewed as a measure of quality of service in a WSN. Maximizing coverage and ensuring network connectivity is a difficult task and many solutions were proposed. Authors in[12], proposes a more energyefficient sensing model, based on circular sectors withvariable angles and radii, negotiated between the motes, as a function of their current energy capabilities. In [13], authors propose the practical energy-sensitive approach exploiting such a trade-off, where sensing rate can be changed dynamically depending on coverage statistics and event detection utility. They formulate energy efficient problem under Markovian assumptions, where the objective is to provide a certain degree of coverage capacity and probability so as to maximize the network lifetime.

Another method is proposed by [14] to optimize the sensor life by organizing the sensors into a maximal number of non-disjoint set covers with non-uniform sensing ranges. Sensors available in one set cover remain active at any instant of time while other sensors are in sleep mode to consume negligible energy. Each set cover is activated successively, thereby increasing the total lifetime of the network 5. CONCLUSION In this article, the state of the art that we discussed focuses on an overview of some recent work on energy optimization in WSN and WMSN that inherit a lot of characteristics of Ad hoc networks with some limitations. These sensor networks are very limited in energy, when energy efficiency is important at all layers of the protocol stack. In this work, we focused our attention on three important aspects for optimizing energy, namely routing, energy capture and processing. In this context, we reported some work on energy efficiency aimed to maximize the life of the system. Several tools of the theory have been used to address these optimization problems. REFERENCES 1. A. V. Sutagundar, S. S. Manvi, Kirankumar. B. and

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energy optimization approaches in wireless sensor networks: a

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