=Paper=
{{Paper
|id=Vol-1830/Paper82
|storemode=property
|title=Energy Efficient Routing in Wireless Sensor Network Using Ant Colony Optimization and Firefly Algorithm
|pdfUrl=https://ceur-ws.org/Vol-1830/Paper82.pdf
|volume=Vol-1830
|authors=M. Okwori,M. E. Bima,O. C. Inalegwu,M. Saidu,W. M. Audu,U. Abdullahi
}}
==Energy Efficient Routing in Wireless Sensor Network Using Ant Colony Optimization and Firefly Algorithm==
<pdf width="1500px">https://ceur-ws.org/Vol-1830/Paper82.pdf</pdf>
<pre>
   Energy Efficient Routing in Wireless Sensor Network Using Ant Colony Optimization and

                                                      Firefly Algorithm

                    M. Okwori, M.E. Bima, O.C. Inalegwu, M. Saidu, W.M. Audu, U. Abdullahi
                                    Federal University of Technology, Minna
      Email{michaelokwori, bimamuhammad, ogbole.inalegwu, samuslim, audum, umarabdullahi}@futminna.edu.ng



   Abstract—Energy conservation in Wireless Sensor Networks             Routing in WSN is handled differently from what is
(WSN) is a crucial venture as their miniaturize nature limits        obtainable in traditional wireless networks. This is because
their power capabilities. An effective way of energy conservation    of the limited resources available in sensors, and as such any
is the adoption of efficient routing of data from source to sink.
This work investigates the performance of two meta-heuristic         routing technique deployed in WSNs should minimize energy
algorithms, Ant Colony Optimization (ACO) and Firefly Al-            consumption and ultimately maximize network lifetime [4].
gorithm (FA) on optimal route detection in a WSN routing             Generally the many WSN efficient routing schemes can be
management system. An adapted ACO was used to search for             categorized into network structure, communication models,
optimal routes between selected source and sink nodes, after         topology based and reliable routing schemes. The network
which a developed Discrete FA ran same search. Performance
of both were tested on sensor networks deployed randomly, in         structure protocols on which this paper is based takes into
a clustered pattern and finally randomly-clustered. Evaluators       consideration how the nodes are interconnected and routes
used were energy budget of reported routes. Results show that        used to send data to destination from source. They are
FA was able detect routes with less cost than those detected by      further classed into flat protocols, hierarchical protocols and
ACO for short routes while ACO performed better with longer          location based protocols [5]. This paper investigates energy
routes. Considering the enhanced speed of performance of ACO
in comparison to FA and the local search nature of FA, it would      optimization of a location based routing protocol using meta-
be beneficial for future work to explore a hybridized FA-ACO         heuristic algorithms.
algorithm.                                                              Meta-heuristic algorithms are designed to mimic natural
   Keywords—WSN, Firefly Algorithm, Ant Colony Optimiza-             phenomena as they randomly search through a space for
tion,                                                                the optimum solution subject to preconfigured constraints. In
                                                                     this paper we use two of such algorithms, Firefly algorithm
                      I. I NTRODUCTION                               and the Ant Colony algorithm, to find the optimal path that
                                                                     minimizes the total energy expended in sending a data packet
   Wireless Sensor Networks (WSN) are a collection of small          from source to sink. First, a review of related works is
devices working together to capture/monitor a particular             presented in section II. A description of the optimization
phenomenon of interest. They find useful applications in             problem and detailed report of two methods of route opti-
home automation, disasters and environmental monitoring,             mization based on each algorithm is outlined in section III.
military operations, multiple target tracking, security surveil-     A Vehicle Routing Problem with Time Windows (VRPTW)
lance, health services and other commercial purposes [1], [2].       dataset was used to test and evaluate the performance of the
Energy management in WSN is crucial as their usefulness is           algorithms, after which comparison is made between the two
dependent on how long they are alive and replacement is              algorithms in section IV. Section V presents the conclusions
difficult as deployment area usually is not easily accessible.       of the investigation
As such a lot of techniques are employed to prolong their                               II. R ELATED W ORKS
lifespan, these include topology management schemes (can
                                                                     A. Related Work on Routing Protocol in WSN
be location-driven or connection driven), power management
(sleep/wakeup protocols and MAC protocols), data reduc-                 A wireless sensor network (WSN) consists of sensor nodes
tion schemes (data compression and in-network process-               which are distributed around a given location. These sensors
ing), energy efficient data acquisition and sending (adaptive        have limited energy capability to stay alive for a long period
sampling, hierarchical sampling and efficient routing) and           of time [4]. Although, over the years, sensors have improved
mobility based schemes (such as mobile sink and mobile               in their computational capabilities, the batteries are still
relay) [3]. This work presents an investigation of efficient         highly inefficient in comparison. Consequently, in an effort
routing in WSN.                                                      to extend the life of a sensor node, research has been pointed


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   towards reducing the energy demand of the nodes. This            same discrete algorithm was also applied by the authors to
is obviously because the core design aspects in a WSN are           solve the manufacturing cell formation problem [17].
Energy Efficiency and Reliability [6]. Energy Efficient (EE)           Firefly algorithm was used for routing optimization in
Routing has been mentioned in the literature as a means             WSN in [18]. A novel fitness function depending on residual
of extending the life of a sensor node[7]. Since energy is          energy, node degree and distance was proposed, and then
expended during transmission, the most energyefficient route        optimized. Results showed superior performance to some
during transmission will consume the least energy. This has         stated existing routing algorithms.
engendered EE routing protocol for WSNs.                               Another interesting work combined firefly algorithm with
   Basically, routing protocols for WSN are classified into flat    the gossip algorithm and applied it to WSN to investigate
protocol, hierarchical protocol and location based Protocol         time of sensor synchronization and data convergence rate
[5]. In Flat protocol routing scheme, nodes are distributed         [18]. The impact of hybrid algorithm was investigated on
uniformly; with none performing a leading role; to transmit         a live network to find out how simulation results correlate
data in a cooperative manner i.e. transmitting to the next          with live field applications. Conclusion drawn from results
neighbor. In the case of the hierarchical scheme, nodes are         obtained indicate that assumptions such as fireflies commu-
given varying roles and groups known as clusters [8]. Each          nicating at the speed of light and the low latency due to fast
cluster must have a Cluster Head (CH) which is a node that          processing speed is not applicable in a live networks where
has higher capabilities than other nodes and is used to relay       much higher latency is expected. A wide range of application
data to the sink node. Within a distribution of nodes, there        in diverse fields are presented in [14], [19].
may be many possible routes to get to a particular destination.
Mathematical models were developed in [9] to determine the          C. Review of Ant Colony Optimization Related Work
most energy efficient route to use in a WSN under resource             An Adaptive Ant Colony Optimization (ACO) algorithm
restriction. The task of determining the most energy efficient      is proposed in [20] for clustering based dynamic routing in a
route is a hard optimization problem [10]. Consequently,            WSN. This was designed to take into consideration the unpre-
many meta-heuristic techniques have been developed to find          dictable nature of a Wireless Sensor Network. Sensors nodes
the most optimal energy efficient route.                            can be deployed in either a sparse or dense nature. The ACO
   Artificial Bee Colony meta-heuristics algorithm [11] and         finds the optimal network setting in order to improve data
improved harmony search algorithm [12] were used to de-             aggregation thereby reducing data redundancy. An adaptive
termine the optimal energy efficient route in a WSN. An             routing scheme based on ACO was also developed in [10].
Improved Genetic Algorithm was developed to eliminate the           Route selection is based on the residue energy inn the nodes
possibility of choosing an invalid note for routing in a WSN        as well as the location of nodes. In this case, clusters were
[13]. Parameters used in the node selection include nodes           not used in the grouping of nodes.
position in relation to sink, neighboring nodes, remaining             Fuzzy logic was used in addition to ACO in [21] in a cross-
energy and energy requirement. Since this research work             layer WSN protocol stack to optimize routing in a WSN. To
was based on using Firefly and Ant Colony optimization              improve EE of the routing protocol, a multilayer approach
algorithms for route optimization, the literature will be based     was adopted. Nodes were grouped into clusters with cluster
on them.                                                            heads which are closest to the sink. Fuzzy logic was used
                                                                    in the cluster head selection using metrics such as residual
                                                                    energy, number of neighbors and quality of communication
B. Review of Firefly Related Work
                                                                    link for the selection. However, ACO was used for reliable
   Firefly optimization algorithm, which is presented in more       and energy efficient inter-cluster routing from cluster heads
detail in section III have been used to solve several research      to sinks.
optimizations in literature. These work include, but not               ACO was further used to determine a multi-objective
limited to a wide range of issues in the field of engineering       optimization i.e. energy efficiency and security of transmitted
design problems, image processing, identification and clus-         data [22] in a WSN. The factors used to carry out this include
tering, and software testing [14]. A review of some of its          the time delay, bandwidth and the energy consumption.
application is hereby presented.                                    Neural Network was used together with ACO to for the
   In [15], the authors modified the original firefly algorithm     purpose of routing in [23]. The neural network is used to
by discretizing it and applying several novel route operators       select the cluster head while ACO was used to determine
to solve the Vehicle Routing Problem with Time Windows              best route. An ACO was used to develop an enhanced routing
(VRPTW). Results presented showed that the developed                protocol for WSN [24] with mobility as the metric.
Evolutionary Discrete Firefly Algorithm (EDFA) is promising
compared to other versions of EDFAs. Another discrete                                     III. M ETHODOLOGY
firefly algorithm, using the sigmoidal logistic function is            This section presents details about how the Firefly al-
presented in [16], is used to find the optimal solution to per-     gorithm (FA) and Ant Colony optimization (ACO) algo-
mutation flow shop minimizing the makespan. The problem             rithms are used to optimize the selection of energy efficient
is NP-hard and formulated as a mixed integer programming.           route between two nodes. The objective function used for
Results revealed superior performance to the ant colony. This       optimization was derived from [9]. It requires finding the



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route with the least energy consumption and maintaining                B. Ant Colony Optimization Algorithm
the energy limitation of the nodes. Consequently, the next                In this section, we present the use of ant colony optimiza-
section provides details about the input parameters for the            tion (ACO) algorithm for the selection of the optimal energy
developed algorithm i.e. the objective function and defined            efficient route. The pheromone secreted along the selected
constraints. When a node wants to transmit, it searches for            path is based on the equation (5) which shows the inverse
the most optimal route to use for the transmission. Fig. 1             relationship between the deposited pheromone and the cost.
shows an overview of the link between source and sink nodes.
Subsequent sections provide details on the FA and the ACO                                                         Q
techniques adopted.                                                                     ϕ(i, j) = ϕ(i, j) +                            (5)
                                                                                                                cost(k)
                                                                         Where ϕ is the deposited pheromone, i= source node, j
                                                                       = destination node, k = selected ant and Q is a constant.
                                                                       Subsequent ants are most likely going to select the path with
                                                                       the most pheromone along its trail. This is represented in the
                     Figure 1. Schematic of WSN
                                                                       equation (6)
                                                                                                           [ϕ(i,j) ]α
                                                                                       P (i, j) =                                      (6)
A. Input Parameters                                                                                 [ϕ(i,j) ]α + [ϕ(i,k) ]α
   The model considers multi-period transmissions from                 A colony of ants (P) is generated to find possible solutions
nodes and aims at prolonging the lifetime of the WSN. It               subject to the condition of least energy consumption along
is assumed that there are n number of nodes distributed                a selected path. The decision at each node on which path to
randomly around an area with each node having a limited                select next is made using a Roulette Wheel Selection algo-
energy with an initial value of ei0. The equation for the              rithm. The pseudocode for the ACO is shown in Algorithm
optimization process is represented in equation 1 where ej             1.
is the energy at the next hop node.
                                                                       Algorithm 1 Ant Colony Optimization Algorithm
                          X       X
                      min(  ei0 −   ej )                         (1)   While termination condition is not met
                                                                         For each ant k=1 to P,
   Equation 2 is used to determine the amount of energy                         Move ant(k) until it gets to destination
consumed during transmission from source to destination                          Compute the cost of the route using the objective
node. Where cw is the energy used to wake nodes for                    function
transmission and ct is the energy expended by a node to                         Compare cost with best route
transmit to the next hop node i.e. a node directly linked.                            If lower,
This direct transmission is constrained by a a linking distance                          overwrite best route with new route,
which is a maximum distance (ld) within which nodes can                               Else
transmit. Therefore, two nodes i and j that are dij distance                             maintain best route
away from each other can only communicate directly if                                 End If
dij<ld. Such nodes will be considered to be linked where Xij             End For
represents the connect between node i and j. Xij= 1 means              Use best route to transmit data
there is a link between i and j otherwise, Xij = 0 this is shown       Update pheromone trail
in equations 3 and 4.                                                  Perform evaporation
                                                                       End While
                           X                X
      Eit − Eit−1 + cw          Xijt + ct         dij Xijt = 0   (2)
                                                                       C. Firefly Related Algorithm
               p                                                           The firefly algorithm is a highly efficient algorithm that
       dij =       (Dx[i] − Dx[j])2 − (Dy[i] − Dy[j])2           (3)   mimics the social behavior of fireflies and was introduced
   where Dx is the x coordinate of the node (i or j) while Dy          in 2009 [25]. The original algorithm was formulated to
is the y coordinate of the node (i or j).                              solve continuous optimization problems and works based on
                                                                       three assumptions of the behaviors of the fireflies stated in
                          (
                            1 dij < ld                                 [14]. A population of fireflies is randomly generated and
                  Xij =                                    (4)         each generation evaluates its fitness based on a set objective
                            0 Otherwise
                                                                       function. The fitter fireflies attract other less fit in close
   Furthermore, nodes are required to have enough energy for           proximity to it. The movement of each firefly towards the
transmission to the next hop neighbor Ei < Eij where Ei is             fitter fly is guided by equation 7.
the remaining energy in node i and Eij is the energy required                                              2
to transmit from node i to next hop node j.                                       xt+1
                                                                                   i   = xti + β0 e−γrij (xtj − xti ) + αti           (7)



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   The first term is the position of the firefly in the subsequent      Algorithm 2 Pseudocode for Firefly Algorithm
round, the second term (due to attraction) is the movement              Initial population of n fireflies x(t)=[x 1,x 2. . . . . . ..x d]
towards a better firefly dependent on the distance, rij , of            Divide population into 3 clusters
firefly xi to xj, the coefficient of absorption, β0 and the             Generate objective function fn(x),
attraction coefficient γ. The last term is the randomization            Generate objective function g(x)
parameter which determines the degree of exploitation of                Light intensity Ii determined by g(x)
the search space. Detailed explanation of each parameter and            Define light absorption coefficient
setting is presented in [26].                                           For k=1:n
   In this work, the Firefly Algorithm was modified to handle              While (t<MaxGeneration),
the discrete problem of route selection. First, the fireflies                 If g(k ) = inf
search for feasible routes by using incremental dimensions                      Mutate k to new k using β0=0, and β0=1,
(d) until a feasible route is found. This is then used to                     for invalid and valid nodes for each x (i ) respectively.
generate three initial population C1, C2, and C3 shown in                       Each x (i )moves probabilistically towards the valid
equations 8, 9 and 10.                                                  nodes closest to it.
                                                                                 If g(new k) < g(best k)
                  
                   Pij           j
                               Pi+1       ···    j
                                                Pd−2
                                                                                   best k = new k
                 P j+1         j+1              j+1                               End If
                 i            Pi+1       ···   Pd−2
           C1 =  .              ..
                                                     
                                                  ..            (8)             End If
                 ..              .       ···      .                      End While
                       Pin          n
                                   Pi+1   ···    n
                                                Pd−2                    End for k
                                                                        Report best k as final route
                                                                        Post process results and visualization
                   Pij           j               j
                                                    
                               Pi+1       ···   Pd−1
                 P j+1         j+1
                               Pi+1       ···    j+1 
                                                Pd−1
                 i
           C2 =  .                                              (9)
                                                     
                 ..             ..               ..                                  IV. R ESULTS AND D ISCUSSION
                                  .       ···      . 
                       Pin          n
                                   Pi+1   ···    n
                                                Pd−1                       The developed algorithms were tested using VRPTW
                                                                        dataset with 100 nodes being considered. Source and sink
                                                                        nodes were selected at random and the algorithms are tasked
                   Pij           j
                                                 Pdj
                                                     
                               Pi+1       ···
                 P j+1         j+1                                     with finding a route with the least possible energy consump-
                 i            Pi+1       ···   Pdj+1                  tion i.e. Cost. The number of iterations for the algorithm were
           C3 =  .                                             (10)
                                                      
                 ..             ..                .. 
                                  .       ···       .                  set at 200, 150, 100 and 50. The results were observed to
                       Pin          n
                                   Pi+1   ···   Pdn                     determine which algorithm performed best as the number of
                                                                        iterations increased. Furthermore, 1000 individuals were con-
   In the matrices, n i s the number of fireflied, each value           sidered for both Algorithms and 3 different VRPTW datasets
P∈{1,2......N} and N is the number of sensors. Luster C1                were considered namely: the Random (R1), Clustered (C1)
and C2 search for routes shorter and longer than the feasible           and Random-Clustered (RC1). The values for the constraints
route while C3 searches for route of same length. The three             of the objective function are shown in Table I. The results
clusters were the fed to the firefly algorithm for final test, with     obtained are shown in Tables II, III and IV.
a retest of teh C1 and C2 for a feasible route. Two fitness
functions were then used to initiate movement in fireflies and                                      Table I
                                                                                      C ONSTRAINTS OF O BJECTIVE F UNCTION
perform the search for the best firefly, f{} n(x) and g(x). See
equations 11and 12.                                                                              Parameter   Value
                                                                                                    e0        10
                                                                                                   ct         0.1
                    fi (x) = E(Pi → Pi+1 )                      (11)                               cw          1
                                                                                                   ld         15


                             d−1
                             X                                             For the randomly distributed sensors, the results show that
                  g(x) =           E(Pi → Pi+1 )                (12)    as the number of iterations increased, the performance of Ant
                             i=1                                        Colony Optimization (ACO) increased while that of Firefly
                                                                        Algorithm (FA) remained same (See Table II). FA performed
   where i=1,2,......No. of iterations and is set not less than         better than ACO in finding routes under the random dataset.
the dimension of each population                                        It therefore can be inferred that for problems where the
   f i(x) is the energy expended by Pi in sending data to Pi+1 for      solutions are randomly distributed in a search space, FA
iteration i. and                                                        would be the recommended algorithm to use.
   g(x) is the total energy expended along a route.                        In the clustered scenario, it was observed that as the
   The pseudocode of the modified firefly and parameter                 number of iterations increased, FA quickly converged towards
setting is shown in Algorithm 2.                                        the best observed route while ACO converges slowly towards



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                                                             Table II
                                          R ESULTS FROM R1 SENSOR DEPLOYMENT DATASET

  Iterations   Source     Sink     ACO Route Detected                   Cost of ACO     Firefly Route Detected        Cost of Firefly
                Node      Node                                             Route                                          Route
                49         65      [49,11,90,32,66,65]                    10.813        [49,11,90,32,66,65]              10.8132
                71         46      [71,20,70,62,48,46]                     11.18        [71,20,70,88,48,46]               11.082
     200        72         36      [72,26,27,88,7,19,36]                  13.379        [72,58,89,18,48,36]              11.3624
                22         20      [22,21,53,28,69,70,20]                 12.262        [22,21,26,76,81,20]              11.0932
                16         67      [16,91,42,15,41,23,67]                 12.304        [16,37,57,41,23,67]              11.0755
                49         65      [49,11,90,32,66,65]                    10.813        [49,11,90,32,66,65]              10.8132
                71         46      [71,20,30,10,62,48,46]                   12          [71,20,70,88,48,46]               11.082
     150        72         36      [72,21,40,58,89,18,48,36]              13.442        [72,58,89,18,48,36]              11.3624
                22         20      [22,74,21,26,76,50,51,20]              12.751        [22,21,26,76,81,20]              11.0932
                16         67      [16,100,87,57,41,23,67]                12.179        [16,37,57,41,23,67]              11.0755
                49         65      [49,11,90,32,66,65]                    10.813        [49,11,90,32,66,65]              10.8132
                71         46      [71,20,90,11,48,46]                    11.416        [71,20,70,88,48,46]               11.082
     100        72         36      [72,73,2,13,89,18,48,36]               13.767        [72,58,89,18,48,36]              11.3624
                22         20      [22,21,53,27,31,70,20]                 12.472        [22,21,26,76,81,20]              11.0932
                16         67      [16,100,42,57,41,23,67]                12.106        [16,37,57,41,23,67]              11.0755
                49         65      [49,11,90,32,66,65]                    10.813        [49,11,90,32,66,65]              10.8132
                71         46      [71,20,30,10,62,48,46]                   12          [71,20,70,88,48,46]               11.082
     50         72         36      [72,40,53,89,83,8,46,36]               14.063        [72,58,89,18,48,36]              11.3624
                22         20      [22,4,54,68,50,51,20]                   12.47        [22,73,26,76,81,20]              11.1041
                16         67      [16,91,42,57,41,23,67]                 12.083        [16,37,57,41,23,67]              11.0755


                                                             Table III
                                          R ESULTS FROM C1 SENSOR DEPLOYMENT DATASET

  Iterations   Source     Sink     ACO Route Detected                   Cost of ACO     Firefly Route Detected        Cost of Firefly
                Node      Node                                             Route                                          Route
                64         10      [64,68,43,47,20,21,10]                 11.087        [64,41,47,20,21,10]               10.085
                52         97      [52,24,23,10,2,99,97]                  12.585        [52,24,23,10,2,99,97]            12.5853
     200        10         66      [10,21,20,47,69,66]                    9.8866        [10,21,20,47,43,66]              9.8866
                32         92      [32,33,34,29,23,10,2,99,92]            16.038        [32,29,27,23,10,2,98,92]         14.4769
                35          2      [35,31,32,29,23,10,2]                  11.738        [35,32,29,26,10,2]               10.3921
                64         10      [64,68,43,47,20,21,10]                 11.087        [64,41,47,20,21,10]               10.085
                52         97      [52,49,47,20,21,10,2,99,97]            14.885        [52,24,21,10,2,99,97]            12.7235
     150        10         66      [10,21,20,47,69,66]                    9.8866        [10,21,20,47,43,66]              9.8866
                32         92      [32,29,27,24,25,23,10,1,2,99,92]        17.92        [32,29,23,10,6,2,99,92]          14.4687
                35          2      [35,32,29,23,10,3,2]                   11.569        [35,32,29,26,10,2]               10.3921
                64         10      [64,68,43,47,20,21,10]                 11.087        [64,41,47,20,21,10]               10.085
                52         97      [52,24,23,10,5,75,2,99,97]             15.015        [52,24,23,10,2,99,97]            12.5853
     100        10         66      [10,21,20,47,69,66]                    9.8866        [10,21,20,47,43,66]              9.8866
                32         92      [32,29,28,23,10,9,6,2,99,100,92]       18.149        [32,29,23,10,2,98,94,92]         14.4818
                35          2      [35,32,29,22,23,10,2]                  11.627        [35,32,29,26,10,2]               10.3921
                64         10      [64,69,47,20,21,10]                     10.27        [64,41,47,20,21,10]               10.085
                52         97      [52,49,47,20,23,10,2,99,97]            15.041        [52,24,23,10,2,98,97]            12.8766
     50         10         66      [10,21,20,47,43,66]                    9.8866        [10,21,20,47,43,66]               9.8866
                32         92      [32,33,34,29,23,10,2,98,96,94,92]      18.155        [32,29,23,10,2,98,95,92]         14.4787
                35          2      [35,34,29,21,10,2]                     10.927        [35,32,29,26,10,2]               10.3921



the same route. This is shown in Table III. The performance            performed generally better than ACO, it should be noted that
of FA was therefore, better than ACO in finding routes in the          there were also numerous instances where ACO performed
clustered dataset.                                                     better than FA in discovering an energy efficient route.
   The performance of ACO improved in the Random-
Clustered dataset and even performed better than FA in                                        V. C ONCLUSION
finding long routes. It can also be seen from Table IV that               In this paper, an investigation into the performance of two
both ACO and FA have improved performance as the number                meta-heuristic algorithms for energy efficient route discovery
of iteration increases.                                                was presented. These algorithms are the Firefly Algorithm
   Furthermore, it should be noted that both ACO and FA                (FA) and the Ant Colony Optimization (ACO) Algorithm.
algorithms are statistical in nature thus they often provide           VRPTW dataset was used to generate nodes to be deployed in
different results after a number of runs. Therefore, the algo-         a Wireless Sensor Network (WSN) setting and the algorithms
rithms were subjected to multiple iterations. Even though FA           are to find the best route that costs the least amount of energy



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                                                                    Table IV
                                                 R ESULTS FROM RC1 SENSOR DEPLOYMENT DATASET

  Iterations     Source        Sink       ACO Route Detected                      Cost of ACO      Firefly Route Detected               Cost of Firefly
                  Node         Node                                                  Route                                                  Route
                   16            56       [16,12,53,69,90,66,56]                    12.141         [16,13,87,52,83,56]                      11.007
                   6             18       [6,7,60,53,82,99,57,22,24,18]             17.572         [6,79,60,53,82,99,57,22,18]             17.0759
     200           96            77       [96,80,65,52,74,58,77]                    13.166         [96,80,65,52,74,58,77]                  13.1656
                   75            31       [75,58,77,25,20,51,85,50,34,31]           18.965         [75,58,87,52,65,91,67,50,34,31]          19.973
                   12            44       [12,53,69,68,54,96,72,41,44]              16.962         [12,53,69,68,54,72,41,44]               14.9452
                   16            56       [16,13,87,86,57,83,56]                    12.099         [16,13,87,52,83,56]                      11.007
                   6             18       [6,7,60,53,82,99,52,57,24,18]             17.378         [6,79,78,53,82,52,57,22,18]              17.451
     150           96            77       [96,80,66,83,57,74,58,77]                 14.171         [96,80,65,52,74,58,77]                  13.1656
                   75            31       [75,58,74,57,83,56,62,50,34,31]           18.436         [75,97,87,52,65,91,67,50,34,29,31]      21.1271
                   12            44       [12,53,98,55,68,54,72,41,42,44]           17.171         [12,53,55,68,54,72,41,44]               15.0372
                   16            56       [16,13,87,52,57,83,56]                    12.432         [16,13,87,52,83,56]                      11.007
                   6             18       [6,7,60,53,82,99,57,24,18]                16.238         [6, 7,60,98,65,64, 51,20,18]            16.9509
     100           96            77       [96,80,65,52,74,58,77]                    13.166         [96,80,65,52,74,58,77]                  13.1656
                   75            31       [75,58,74,57,83,56,62,50,34,31]           18.436         [75,97,59,86,99,65,91,67,50,34,31]      20.9219
                   12            44       [12,53,88,100,61,54,72,41,44]              16.69         [12,78,53,69,68,54,72,41,44]            17.0868
                   16            56       [16,15,12,53,82,65,66,56]                 12.718         [16,13,87,52,83,56]                      11.007
                   6             18       [6,7,60,53,82,99,52,57,24,18]             17.378         [6,7,60,98,82,52,57,22,19,18]           17.5793
      50           96            77       [96,80,66,83,57,74,58,77]                 14.171         [96,80,65,52,74,58,77]                  13.1656
                   75            31       [75,58,74,57,83,56,95,62,50,34,31]        19.491         [75,58,77,25,20,51,76,85,50,34,31]      21.1947
                   12            44       [12,53,82,90,68,54,72,41,44]              17.024         [12,53,55,68,54,72,41,44]               15.0372



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