Genetic Algorithm with Gene Regulatory Networks
based Optimization Method for Distributed Video
Analysis System
Seishiro Inoue

Masaaki Yamauchi

Daichi Kominami

Hideyuki Shimonishi

Masayuki Murata

Graduate School ofInformation Scienceand Technology,
Osaka University
Osaka, Japans-inoue@ist.osaka-u.ac.jp

Graduate School ofInformation Scienceand Technology,
Osaka University
Osaka, Japanm-yamauchi@ist.osaka-u.ac.jp

Graduate School ofInformation Scienceand Technology,
Osaka University
Osaka, Japand-kominami@ist.osaka-u.ac.jp

Cyber Media Center,
Osaka University
Osaka, Japanshimonishi.cmc@osaka-u.ac.jp

Graduate School ofInformation Scienceand Technology,
Osaka University
Osaka, Japan
murata@ist.osaka-u.ac.jp

Abstract—To construct a digital twin, we have to analyze
a large amount of video data obtained from the real worldin real-time to perceive an accurate current situation. The
increase in the video traffic flowing through networks and theaccompanying increase in power consumption are problems.
One solution is edge computing to distribute video analyzingtasks; it requires dynamic control of task distribution andselecting analyzing models according to the network status andapplication requirements. Our research group has formulated an
optimization problem for dynamic control of distributed video
analysis systems and proposed a method to optimize power
consumption using a genetic algorithm. However, as the scale ofthe problem expands, there are cases where the genetic algorithm
cannot solve the problem because it falls into the local solution.
Therefore, we focus on gene regulatory networks that map agenotype of an organism to its phenotype. The characteristics ofgene regulatory networks are to memorize specific phenotypes,
to mutate multiple phenotype bits from one-bit perturbation in
genotype simultaneously, and to generate new phenotypes similar
to the memorized ones by the network structure. In this study,
we propose a dynamic control method for distributed video
analysis systems by applying gene regulatory networks to genetic
algorithms. We used a mathematical model of gene regulatory
networks and made it memorized several optimal solutions as
phenotypes. We confirmed the escape from local solutions byrecalling the stored solutions and generating multiple phenotype
bits mutations. We also verified the adaptability improvement
to the dynamic network environment and a new application
requirement by using the gene regulatory network.
Index Terms—Adaptive evolution, digital twin, gene regulatory
network, genetic algorithm, optimization problem.

I. I NTRODUCTION
Digital twin technology, which highly integrates a real anda virtual world, is attracting attention. The digital twin reproduces the same environment as the real world in the digitalworld as if it were a twin by collecting data about objects
and environments using cameras or sensors. The digital twin
This work was supported by MIC under a grant entitled ”R&D of ICT
Priority Technology (JPMI00316).”

enables continuous monitoring and optimization of objects
and systems in the real world. The digital twin technology
is expected to bring new value to a variety of industries [1].
To construct the digital twin, accurate and real-time recognition of the real-world situation is necessary. Therefore, wehave to collect and analyze a large amount of video andsensor data in a short time. A large amount of video datais generated from multiple cameras or LiDAR sensors andcollected on a cloud server via the network. Then, AI video
analysis technologies, such as YOLO [2], process the datato construct the digital twin. Users can view the analyzed
results from the digital twin [3]. Research of beyond 5G
and 6G is now actively conducted; it is expected that highspeed, high-capacity communications with low latency will
be realized. It causes development of applications including
high-capacity communication in a short time; we can expect
the rapid increase of traffic flow through network in the
future. The traffic increase is expected to significantly increase
power consumption in the network [4]. Then reducing power
consumption of the entire network system is a major challenge
in the utilization of the digital twin in beyond 5G and 6G era.
Edge computing technology is one of the solutions for thecommunication delay and power consumption by the increasein video traffic. Edge computing is that places servers, namededge servers, closer to the data source than the cloud servers
and allocates part of the data processing of the cloud servers to
the edge servers [5]. The power consumption of the networkand communication delays are reduced because the amount oftraffic in the entire network is reduced. The processing latencyof the video data is also reduced because the edge servers areclose to the terminals of users [6].
When we operate edge servers, we have to dynamicallydetermine how processing is distributed according to the network status and types of applications. Network status includes
network congestion and usage amount of edge and cloudservers. The required processing latency and accuracy of analysis vary depending on the applications. To achieve efficient
distributed processing for lower power consumption, we haveto monitor network status regularly and dynamically optimize
the distribution of processing depending on the applications.
Our research group has formulated a power consumption
optimization of a distributed video analysis system as a combinatorial optimization problem and proposed an optimization
method using Genetic Algorithm (GA) [7]. The system consists of three types of computational resources, terminal, edge
server, and cloud server, which are connected by networks.
When a camera attached to the terminal acquires video data,
an application on the terminal sends a request to analyze thevideo data to the optimization module with a maximum latency
requirement and a minimum accuracy requirement. The optimization module determines the processing distribution ratio
and video analysis AI model for each computing resource
so that the power consumption is minimized while satisfying
the two requirements. Note that, since the video analysis AI
models have a trade-off between processing speed and analysis
accuracy, we have to set appropriate AI models according to
the requirements. Because the system has multiple computational resources and networks and the complexity increases
exponentially concerning the size of the system, our group has
solved it with GA. In addition, it has been proposed to use theBayesian Attractor Model (BAM). The BAM stores multiple
attractors of network status information with corresponding
solutions to the problem. When the BAM judges a current
network status as similar to the stored one, GA uses thecorresponding solution to improve adaptation speed [8].
However, as the scale of the problem expands, GA cannot
achieve optimal solutions and falls into local ones in somecases. This is because, while GA mutates one bit in manycases, the mutation is too small to escape from the local
optima; and the mutated individuals are eliminated in theevolution process. In addition, as the problem scale and theinformation on the network status increases, it takes time to
get all the information and judge the similarity of the network
status. It may also be possible to misjudge if the network stateis partially similar. Therefore, it is necessary to be able tomemorize and recall past optimal solutions, independent fromthe information on the network state.
We focus on Gene Regulatory Networks (GRN), a mechanism in living organisms that maps the genotype of anorganism onto a phenotype of a cell. One of the characteristics
of GRN is that mapping from a wide genotypic space to anarrow phenotypic space facilitates the expression of specificphenotypes. It is also known that mutation on a particulargene in the genotype called a sensitive node, causes multiple changes of phenotypes simultaneously [9]. The modular
structure of GRN also allows only a particular module tochange, leading to generate new phenotypic combinations ofpast phenotypes.
In this paper, we propose a method to utilize GRN in GA
for optimizing distributed video analysis systems against fluc-tuations in network conditions and application requirements.
We confirm that GRN, an adaptive evolutionary mechanismof living organisms, improves the adaptive capability towards
environmental changes surrounding the system. Specifically,by using the mathematical model of GRN that pre-learned
optimal solutions for several requirements as phenotypes,
we verify whether genotypic and phenotypic mutations improve the adaptability. We verify whether the GRN-based
method can find the optimal solution in less time than GA
by recalling the memorized phenotype without grasping theentire system state when the system state changes. Also, by
simultaneously changing multiple phenotypes with a small
number of genotypic mutations, it will be verified whether it
is possible to escape from local solutions and quickly find an
optimal solution. In addition, we evaluate whether the GRNbased method can adapt to inexperienced network status andapplication requests by utilizing memorized phenotypes or new
phenotypes generated from the network structure of GRN.

II. R ELATED WORK
A. Gene Regulatory Networks (GRN)
GRN is a network of gene interactions. The interactions
can either promote or suppress activity. When genes regulate
other’s activity, various cells are expressed and vital organs are
generated. By setting different initial genes, i.e., genotypes,
it is possible to generate multiple types of cells and organs
from the same GRN. The expression pattern of a gene that is
generated by GRN is called phenotype.
In biological evolution, only mutations that are advantageous for survival are retained by natural selection. Thus, GRN
may be biased in the distribution of phenotypes through theevolutionary process. Such biases are reported to have threecharacteristics in [10]. (1) Distributed associative memory
capable of storing and recalling past phenotypes. (2) Associative memory that accurately represents a complete phenotype
from a partial embryo. (3) Generalization that generates new
combinations of phenotypic features. In addition, it is possible
to mutate multiple phenotypes simultaneously by mutating
specific genes of the genotype, called a sensitive node, to givea large variation in the phenotype; this character is verified
using boolean networks, one of the models of GRN [9]. In
a combinatorial optimization problem for a system subject toenvironmental variation such as the one targeted in this paper,
adaptability may be enhanced by recalling past memories frompartial environmental conditions. Furthermore, if phenotypic
generalization is utilized, it is expected to generate appropriate
phenotypes for unknown environmental conditions.
We use a mathematical n × n adjacency matrix model [11]as GRN. The n bit phenotype is calculated by multiplying
the n bit genotype for multiple times. Since the distributionof phenotypes is biased according to the matrix, the specificphenotypes can be expressed multiple times as memory.

Requests of video analysis• Maximum latency requirements• Minimum accuracy requirements ( mAP )Optimaization Module
Genetic Algorithm using GRN• AI model• Processing portion

System• AI model• Processing portion• AI model• Processing portion

Access network(6G, WiFi, fixed, etc.)
Backbone network

Network status• Bandwidth• Propagation delay
CameraTerminal

Edge server

Cloud server

Fig. 1. System model.

B. Energy optimization of distributed video processing systemwith BAM [8]Our research group formulated the energy optimization of a
distributed video analysis system as a combinatorial optimization problem and proposed a method to solve it by a GA with
BAM. The method with BAM assesses the similarity of the
network environment using all the network state information.
However, it is likely to make misjudgments when the network
state is partially similar as the system scale becomes large. In
this study, we propose an optimization method that does notuse network state information for similarity judgments. We
use GRN, which can generate similar phenotypes as solutions
without network state information.
III. OVERVIEW OF THE SYSTEM MODELS AND THE
PROPOSED METHOD

A. System overview
We describe the system overview in Fig. 1. The system has
three computation resources, terminals connected to cameras,edge servers, and cloud servers. The terminals and the edge
servers are connected by access networks. The edge servers
and the cloud servers are connected by backbone networks. An
application on a terminal sends a request to the system withrequirements of latency and accuracy. An optimization module
monitors the information of each network, such as bandwidthand propagation delay. When the module receives the video
processing request, it creates a session on the path via theterminal, an edge server, and a cloud server. Then, the module
allocates the appropriate processing ratio and AI model foreach computing resource using our proposed method, “Genetic
Algorithm using GRN” in Fig. 1. After the allocation, video
data is sent from the camera to the terminal and the edge server
according to the processing ratio; the cloud server processes
the remaining data. Note that, the optimization module does
not supply the video analysis task until it finds a solution thatsatisfies the requirements of the request.
B. Definition of optimization problem
The energy optimization of the distributed video analysis
system is defined as a combinatorial optimization problem.

We use the almost same definition of previous work [8] of ourresearch group. The proposed method optimizes the processing
ratio and AI model that satisfies the application requirement
and reduces the power consumption of the entire system. The
processing ratio is the ratio of allocated video analysis tasks
for each computing resource. The AI model is the model ofthe video analyzer to be used in each computing resource. Two
requirements are processing delay requirements and accuracy
requirements of video analysis. Note that, since the video
processing AI models have a trade-off between processing
speed and analysis accuracy, we have to set appropriate models
according to the requirements.
1) Optimized variables: The two types of control information are processing ratio Wsd and AI model Msd , where s denotes session and d denotes device. The optimal combinationof these variables considering all sessions and the entire power
consumption in the system is searched.
2) Constraints: The constraints in this optimization problem are the end-to-end (E2E) delay and analysis accuracy ofthe processing request.
The E2E delay is defined as
XX
Ts (t) =Tsd (t) +Tsn (t) ≤ Tsmax , ∀s ∈ S,
s
d∈D
n∈N s
(1)
where S is the set of all sessions. Ds and N s are theset of devices and networks used by session s, respectively.
Tsd (t) is the processing delay for video analysis on device dof session s, and Tsn (t) is the processing delay and thetransmission delay in network n of session s. The constraintof the processing delay is Ts (t) < Tsmax ∀s ∈ S, where Tsmax isthe upper limit of processing delay sent from the application.
The analysis accuracy is defined as.
X
dAs =AMs Wsd /|Ds | ≥ Amin(2)s , ∀s ∈ S,
s
d∈D

d

where As is the video analysis accuracy in session s, AMs
is the analysis accuracy when using model Msd on device d,Pdand d∈Ds AMs Wsd /|Ds | is a weighted average of analysis
accuracy. The constraint of the analysis accuracy is As (t) >min
Aminis the lower limit of analysis accuracys ∀s ∈ S, the As
sent by the application.
3) Objective function: The overall system power consumption E(t) at time t is an objective function. It is defined as
the sum of the power consumption of devices E d (t) and of
network E n (t) of each device d and network n as
XX
E(t) =E d (t) +E n (t).
(3)
s
s
d∈D

n∈N

C. Optimization method
1) Encoding: To solve the optimization problem, the control information for distributed processing needs to be encoded.
The phenotype is represented in a bit string as [Wsd ∀s ∈S, ∀d ∈ Ds , Msd ∀s ∈ S, ∀d ∈ Ds ], where session s andcomputing resource d.

2) Genetic Algorithm (GA): GA is an optimization methodthat performs genetic manipulations such as crossover andmutation on a population containing N individuals and conserves the individuals suitable to the environment for the
next generation. The suitability is calculated by the fitness
function, defined in (4). Each individual has a genotype andphenotype; and in GA, the phenotype is mapped directoryfrom the genotype. Individuals are selected according to theirfitness, and individuals similar to them are generated throughgenetic manipulation to search the solution space around thesimilar one. The procedure of a simple model of GA, called
Simple GA (SGA) is below.
i To initialize genotypes of N individuals to random values.
ii To generate new individuals by crossover and mutation.
iii According to the fitness of the phenotype mapped by the
genotype, selecting N individuals remaining in the next
generation, and repeat i) and ii).
3) Fitness function: The fitness function indicating adaptability of individual is defined asXX
F (t) = −E(t) − α(Ts (t)max − Ts ) − β(As (t) − Amin
s ).
s∈S

s∈S

(4)
The fitness is high with the reduction of the power consumption E(t). The second and third terms are penalties of delay
and accuracy respectively, where α and β are coefficients.
D. Proposed method to use GRN for GA
We embed GRN in GA. We deploy an adjacency matrix as
GRN in each individual and map the phenotype through the
GRN.
1) Calculation of phenotype: We calculate the phenotype
array by multiplying the genotype array and the adjacency
matrix of GRN multiple times. The phenotype represented by
P (t) = [p0 (t), p1 (t), . . . , pn (t)] at k-th step is calculated as Xn
bij pj (k) − τ2 pi (k), (5)pi (k + 1) = pi (k) + τ1 σ
j=0where genotype vector is G = [g0 , g1 , . . . , gn ](−1 ≤ gk ≤ 1),
GRN matrix is B = [bij ](0 ≤ i, j ≤ n), and pi (0) = gi . The
fitness of an individual is calculated by pi (k ∗ ), where k ∗ is aparameter of calculation steps. τ1 and τ2 are coefficients of aneffect of interaction between genes and a decay ratio of theexpression pattern respectively. σ is a sigmoid function andwe set a hyperbolic tangent function.
2) Algorithms: We introduce phenotype mutation in addition to the genotype mutation. The phenotype produced by
GRN is biased. Therefore, individuals biased by GRN with
only genotype mutation cannot generate every phenotype in
the phenotypic space. By adding the phenotype mutation, theproposed method can achieve every solution. The balanceof each mutation is configured by the parameter N2 . The
algorithm of the proposed method works in the following steps
and repeats ii), iii), and iv).
i To initialize genotypes of N individuals to random values.

ii To calculate the fitness from the phenotype of individuals
and save the best N1 ones as elite.
iii By phenotypic mutation, generating N2 individuals for the
next generation from the current population.
a) Selecting one individual by selection method, such as
roulette selection.
b) To generate a new individual by applying mutation andcrossover to the phenotype of the selected one.
c) To repeat a) and b) until N2 individuals are generated.
iv By genotypic mutation, generating N −N1 −N2 individuals
for the next generation from the current population.
a) To select one individual by the selection method.
b) Generating a new individual by applying mutationand crossover to the genotype of the selected one andcalculating its phenotype.
c) To repeat a) and b) until N − N1 − N2 individuals are
generated.
3) Memorizing phenotypes by GRN: We refer [10] to design
an adjacency matrix of GRN to express specific phenotypes.
We evolve GRN by selection pressure in the direction closer
to the target phenotypes to be memorized. First, we initialize
the genotype vector G and the GRN adjacency matrix B withzero. Second, we select one target phenotype and mutate G and
B to minimize the hamming distance between the generated
phenotype by GRN and the target one. Third, we switch thetarget phenotype and continue mutations. Switching the target
phenotype multiple times creates a bias in the expression of
the phenotype, i.e., GRN memorizes the phenotypes.
IV. E VALUATION
We confirm that the GRN-based proposed method improves
adaptability to the dynamic environment and how the characteristics of GRN affect it. The adaptability is measured by
the fitness function F (t) defined as (4) and power consumption E(t) in time t defined as (3).
The environmental changes in this distributed video analysis
system include two cases: switching applications that use thesystem and fluctuating network status. The applications are
divided into two types: applications that have used the system
multiple times and applications that have never used the systemor used the system a few times. GRN can memorize optimal
solutions that can satisfy the requirements of the former, calling it a known application, and achieving a reduction of power
consumption. When the known application sends a request, thememory stored in the GRN can make the adaptability high.
Optimal solution of the latter, calling it a new application,
is not memorized in GRN. In addition, it is considered the
network status, such as the available bandwidth for this system,changes more frequently than the application switching. Thus,
we simulate three cases to evaluate the adaptability of the
GRN-based proposed method: the application switches to the
known ones, the known application and dynamic network
bandwidth, and switching to the new application in dynamical
network bandwidth.

In this optimization problem, the structure of the optimal
solution can be clustered into several patterns. Concretely, thedistribution ratio of tasks is distinctive, such as processing allvideo analysis tasks in the cloud server or processing sometasks at the edge and most tasks at the terminal. The switchingof the application requirements tends to reform the structure of
the solution, i.e., requiring large-scale phenotypic mutations,such as changes in the processing proportions and deployed AI
models. On the other hand, differences in network bandwidth
rarely vary the structure of the solution greatly. The changes
affect mainly the AI model selection and some processing
proportions. In other words, it causes smaller changes than
the application switching. Based on these characteristics, we
discuss the utilization of GRN with environmental changes.
A. Simulation settings
We use three types of devices (Ds = {t, e, c}): terminal,edge server, and cloud server, and two types of communication
networks (N s = {naccess , nbackborn }): access network andbackbone network. We assume that one terminal executes
one application and constitutes one session. The simulation
environment is configured for the cases with one, two, andfour sessions. In this paper, we focus on cases of four sessions
due to page restriction. The number of computing resources
and structure of the network is shown in Fig. 1.
1) Device setting: Table I shows the configures of eachdevice. We use an estimation model based on actual measurements [8] to define the value of the processing latency andpower consumption model.
GPU processing load rate Ld (t) is estimated as
 
X

d
d
d
O
(t)
/
C
Eff
Ld (t) =
,
(6)
s
d
s∈S

where d and t are the device and the time respectively.
Processing load Osd (t) on session s is calculated asd
Osd (t) = (OMs (t) + OA )Wsd (t) + OB (FPS).
(7)
By using (7), processing latency Tsd (t) and power consumption E d (t) is calculated as

 

d
Tsd (t) = OMs (t) + OA + OB / C d Effd Ld (t) ,
(8)
d
d
d
E d (t) = EIDLE+ αE ECPU-TDP+ β E EGPU-TDP
Ld (t).

(9)2) Network settings: We set the network of simulations asshown in table II unless there is an environmental change.
Calculations formula and models are based on the previous
work [8]. The network transmission delay Tsn (t) and network
power consumption E n (t) are defined as


X
n
d
n
Ts (t) = R 1 −Ws (t) /B n (t) + Tprop, (10)
s,nd∈DpassE n (t) =



X
s∈S

R 1−

X


d
W
(t)
Ebit ,ss,nd∈Dpass(11)

s,nwhere Dpass
is the set of devices that a session s has passed before reaching network n and B n (t) is the available bandwidthnon network n at time t satisfying B n (t) ≤ Bmax.

TABLE ID EVICE SPECIFICATIONS AND ESTIMATED PARAMETERS .
Spec and variablesCPUd
TDP ECPU-TDPGPUFP32 C dd
TDP EGPU-TDP
Efficiency Effdd
IDLE power EIDLEFLOPS A and B(OA , OB )(αE , β E )Terminal t
Core i78700T
35W
GeForce
GTX1070
6.463Tflops
150W
0.4

Edge server e
Xeon GOLD
6226R ×2
150W ×2
Tesla T4 ×2
8.141Tflops×2
70W ×2
0.39

Cloud server cCore i910940X
165W
RTX
A5000
27.77Tflops
230W
0.48

55.236W(1.5, 0.1)

334W
(2.2, 0.1)

258.3176W(8.1, 0.4)

(0.97, 0.78)(0.97, 0.67)(0.29, 0.81)

TABLE IIN ETWORK PARAMETERS AND SET VALUES IN THE SIMULATIONS .
Network typen
Bandwidth: Bmaxn
Propagation delay: Tprop
Power consumption per bit: Ebit
Bit per frame: Rnaccess
25 Mbps
10 ms
193 × 10−9 W
470 Kbitnbackborn
250 Mbps
10 ms
60 × 10−9 W

3) Predefined application performance requirements: We
set three types of requirements as the known applications.
Their optimal solutions are memorized as phenotypes by GRN.
Table III shows the predefined performance requirements andthe phenotypes. The phenotypes are obtained by multiple
searches using SGA because the computation of all bit-string
combinations requires an enormous time. In this search, thenetwork bandwidth is fixed to the value in Table II, which isan almost mean value of the network bandwidth variation.
4) Settings of parameter, etc.: In the proposed method,
unless we specified, N = 100, N1 = 5, and N2 = 50. In otherwords, the population has 100 individuals and the number ofindividuals generated by the proposed method is 5 : 45 : 50
for elite individuals, generated by genotypic mutation, andgenerated by phenotypic mutation.
In genetic algorithm, we introduce roulette selection and

TABLE IIIP REDEFINED PERFORMANCE REQUIREMENTS AND ITS SOLUTIONS .
App. requirement for eachsession
A1
A2
A3
A4
B1
B2
B3
B4
C1
C2
C3
C4

LatencyTsmax
0.04238 s
0.12856 s
0.11831 s
0.10322 s
0.06481 s
0.05974 s
0.04144 s
0.09141 s
0.12314 s
0.03937 s
0.12405 s
0.11723 s

Accuracy
Amin
s
(mAP)
26.855 %20.926 %27.375 %22.440 %34.535 %41.178 %26.532 %37.337 %48.583 %31.529 %33.166 %23.430 %Memorized
phenotype

Fitness[0,0,6,4,6,2,
0,0,3,2,2,4,
0,0,6,7,6,6,
0,0,5,1,3,7][0,0,5,6,7,5,
0,0,6,7,0,5,
6,0,0,0,7,3,
0,0,5,1,2,4][0,0,7,0,0,4,
7,0,0,0,0,2,
0,0,5,3,7,4,
0,0,5,1,3,0]-365.696-389.289-379.944

TABLE IV
S PECIFICATIONS OF VIDEO PROCESSING AI MODELS [12].

0

Model
YOLOv3-tiny
YOLOv3
YOLOv3-sppdAccuracy: AMs
33.1 %
55.3 %
60.6 %dFLOPS: OMs (t)5.6 B
65.9 B
141.5 B

Msd
{0, 1, 2}{3, 4, 5}{6, 7}

elite survival strategy, two-point crossover with crossover rateof 0.2, and point mutation. SGA also stores 5 % of elites.
We set the range of Wsd and Msd as 0–7, the latter’s
corresponding models are described in Table IV. We also set(α, β) = (105 , 105 ), (τ1 , τ2 ) = (1.0, 0.2) and k ∗ = 10.
B. Simulation of application switching to the known ones
1) Evaluation procedures: We set the application requirements from the predefined set shown in the table III as
follows: requirement A→B→C→A→.... and set it to change
periodically every 60 s. We perform 10 trials with 10 application changes, in other words, 90 switches excluding the firstone of each trial. We compare the actual computation time toadapt to the environmental change and power consumption forboth the proposed method and SGA.
2) Results: We show the transition of fitness in Fig. 2.
The proposed method can find the optimal solution ina shorter time than SGA after environmental changes. The
average computation time and generation of GRN is 0.56 s and25, and of SGA is 45 s and 2,897 respectively. This is because
GRN recalls the memorized phenotypes in a few generations.
GRN achieves shorter computation times, although it requires
a longer computation time of one generation than SGA due
to the phenotype computation. Also, out of 90 environmental
changes, SGA found the optimal solution 28 times, whereas
GRN found it in all cases. In the proposed method, a single
genotype mutation allows the simultaneous mutation of multiple phenotype bits and avoids falling into a local solution.
When the number of sessions is 1, we confirm that the
SGA also can reach the optimal solutions in a short time forall environmental changes. This is because the bit length of
the genotype is short and the optimal solution can be reachedwith a relatively small number of mutations in the case. We
have checked that the increase in sessions makes the problem
difficult and SGA could not solve it.
To evaluate the power consumption, we first compare theunavailable time that the system cannot provide the video
analysis service because the performance requirements are notsatisfied. As an average time for 10 trials, the total unavailable
time was 171 s in SGA, whereas it was 1.27 s in the proposed
method. We can confirm that the stability of the service
was greatly improved. A comparison of the average power
consumption while the performance requirements are satisfied
shows that SGA is 505 W while the proposed method is 378 W.
It indicates a significant reduction in power consumption.
We also focus on the parameter N, the number of 2
individuals generated by the phenotypic mutation. When theN2 is small, such as 15, the search time is shorter than N2 =fitness

500
1000
1500
2000
25000

60

120

180

240
300
time[s]

360

420

480

SGA
GRN
540

Fig. 2. Fitness transition when the requirement changes every 60 seconds.
We show results of 10 trials of the proposed method (GRN) and SGA.

50 case because many individuals are generated by genotypic
mutations, i.e., recall. On the other hand, in N2 = 85, it
takes longer time to find the optimal solution than in N2 =50 case because few individuals are generated by recalling.
We confirmed that phenotype switching requires changing
the solution structure and genotypic mutation, which changes
multiple phenotype bits simultaneously, is effective.
C. Simulation of dynamic network bandwidth with the known
application
We confirm the adaptability of GRN in dynamic network
bandwidth fixing the applications to known ones. Although achange in network bandwidth does not require a significant
change in the structure of the optimal solution, it does requirechanges in some parts of the solution. Namely, in this section,
we evaluate the adaptability in similar environments to theones that GRN memorized.
1) Evaluation settings: We randomly select the bandwidthof the access network and the backbone network in therange of 10–50 Mbps and 10–500 Mbps respectively to make
50 patterns. We deploy in order of the patterns each 180 s. We
perform it in 10 trials. Thus, the 500 environment is simulated
in each requirement. The application requirement is fixed ineach trial selected from the known ones shown in Table III.
2) Results: Fig. 3 shows the time transition of the fitness
when the application requirement is set to requirements A, B,
and C in Table III, respectively.
In each requirement, SGA and GRN show different transitions. This is because the magnitude of changes in solution space by the bandwidth fluctuations depends on theconstraints. When the constraint is less strict, the solution
space change tends to be small and the transition tends tobe stable. In requirement A with less strictness of accuracy
constraints, there are less susceptible to network fluctuations
because the tasks tend to be processed by the terminals. In
requirement C with less strictness of delay constraints, because
the bandwidth changes are tolerated, the solution space is
not changed largely. On the other hand, when the application
requires strict constraints, such as requirement B, the solution
space sensitively changes. This is because tasks need to beprocessed in high-performance servers, like the cloud, due
to the accuracy constraints, thus the effect of bandwidth
becomes large. Moreover, the solution tends to violate thedelay constraints when the bandwidth changes.

0500

fitness

1000
1500
GRN N2=15
GRN N2=50
GRN N2=85
SGA

2000
2500

0

2000

4000

time[s]

6000

8000

(a) Performance requirement is fixed at requirement A.
0500

fitness

1000
1500
GRN N2=15
GRN N2=50
GRN N2=85
SGA

2000
2500

0

2000

4000

time[s]

6000

8000

(b) Performance requirement is fixed at requirement B.
0500

fitness

1000
1500
GRN N2=15
GRN N2=50
GRN N2=85
SGA

2000
2500

0

2000

4000

time[s]

6000

8000

(c) Performance requirement is fixed at requirement C.
Fig. 3. The fitness transitions of the proposed method (GRN) and SGA withchanging bandwidth in 50 patterns. The vertical dotted line is changed time.
New phenotype 0 0 7 3 1 3 7 0 3 2 2 3 0 0 5 4 6 6 0 0 5 1 3 0
Requirement A

006462003224006766005137

Requirement C

007004700002005374005130

One bit differenceSame bits with colored ones

Fig. 4. New phenotype generated by the combination of memories.

In the case of requirement A, 10 s after the environmental
change, GRN, where N2 = 50, satisfies the requirement 489
times out of 500, and SGA satisfies it 453 times. GRN achieves
higher fitness 334 times, SGA achieves higher fitness 39 times,
and the same fitness 163 times. The GRN achieves higher
adaptability than SGA. In particular, GRN, where N2 = 50,
reaches an adaptable solution to most network bandwidths in
8 out of 10 trials, such as the solution of 12 th environment in
Fig. 3(a). However, SGA cannot reach it. This solution might
be a local one, but no better solution was found in each trial.
This is because GRN-based individuals can search around thesolution of requirement A more widely than SGA by multibit phenotype mutations from single-bit genotype mutation.
Another reason is the characteristic of GRN that generates a
new phenotype from memorized phenotypes by the network
structure. A phenotype shown in Fig. 4 is generated by GRN
and it is similar to the solution of requirements A and C.
The phenotype shows high fitness in requirement A. GRN cansearch around such a new phenotype.
In Fig. 3(a), the unavailable time is 149 s for GRN and

382 s for SGA; the average power consumption is 288 W in
GRN and 366 W in SGA. Power consumption is reduced andthe service is provided stably.
In the case of requirement B, there are 371 cases where
the fitness of GRN, where N2 = 50, after 10 s from networkchanges is higher than SGA, 89 cases where SGA is higher
than GRN, and 40 cases where they achieve the same fitness
out of 500 cases. Thus, the proposed method has higher
adaptability than SGA in the same environment. SGA tends
to fall into local solutions in the case of requirement B. For
example, the SGA in Fig. 3(b) finds it in the 26 th environment.
This happened in 9 out of 10 trials. On the other hand, GRN
does not fall into the local solution and it leads to findinga higher fitness solution than SGA. GRN can escape fromthe local solution by multi-bit phenotype mutation caused bysingle-bit genotype mutation.
In some cases, GRN takes longer to satisfy the requirements.
The number of times requirements are satisfied after 10 sfrom the environmental change is 408 out of 500 cases for
GRN and 467 for SGA, and after 180 s, it is 446 for GRN
and 492 for SGA. One reason is that the local solution foundby SGA was the common solution to satisfy the requirement.
Another reason is that the solution memorized by GRN was
not adaptable to the bandwidth changes. We have to selectan adaptable solution to be memorized in different network
bandwidths, which is our future work. In a comparison of
power consumption, the average power consumption of GRN
and SGA is 389 W and 455 W respectively in Fig. 3(b).
However, the unavailable time of GRN is 1, 294 s which islonger than SGA, 296 s. This is a case in which GRN could
not achieve more adaptability than SGA.
In the case of requirement C, GRN achieves higher adaptability than SGA. In 500 simulations, GRN is superior in
the number of times that requirements are satisfied after 10 sfrom environmental changes: 500 times for the GRN and 461
times for the SGA. Also in Fig. 3(c), the unavailable time is
246 s for GRN and 257 s for SGA, which indicates GRN
can provide stable service. The average power consumption
is 392 W for GRN and 421 W for SGA, we can find thatpower consumption is reduced. The memorized solution has
a high fitness even if the bandwidth changes. SGA alsoachieves high fitness by using the same solution as the previous
environment. Therefore, GRN recalls memories stably, while
the SGA temporarily falls into a local solution, which causesa small difference.
Overall, we can verify that GRN is more adaptive than SGA
in the same environment. GRN can improve service stability
as long as selecting the adaptable solution in other bandwidth
to store in GRN.
The N2 is a trade-off between the ability to recall thememory and to search around the memory. This environment
settings requires phenotypic mutations around the optimal
solution. Thus, after recalling the memorized solution, GRN,
where N2 = 85, has better fitness because many individuals
are generated by the phenotypic mutation to search around.

and 257 s for SGA. GRN slightly reduces power consumption
and improves stability due to the difference in early stage.

TABLE VR ANDOMLY DEFINED REQUIREMENTS .
App. requirement
for each session
D1
D2
D3
D4

Latency:Tsmax
0.14406 s
0.06332 s
0.07354 s
0.12460 s

Accuracy:Amins (mAP)
57.585 %23.988 %54.967 %40.494 %V. C ONCLUSION

0500

fitness

1000
1500
GRN N2=15
GRN N2=50
GRN N2=85
SGA

2000
2500

0

2000

4000

time[s]

6000

8000

Fig. 5. The fitness of the proposed method (GRN) and SGA when theapplication requirement is in Table V with 50 patterns of bandwidth.

GRN, where N2 = 15, recalled many memorized ones, so
it has less searching ability. Dynamically setting N2 would
improve these adaptations.
D. Simulation of dynamic bandwidth with a new application
We set new application requirements and dynamic network
bandwidth to evaluate adaptability in non-similar environments
where the optimal solution structure is different from the one
memorized by GRN. Variants in requirements tend to change
the optimal solution structure more significantly than changes
in network bandwidth. We evaluate the adaptability of the
proposed method in cases where the solution structure changes
to the not-trained ones and changes in some parts due to
network variations. The application requirements are set asshown in Table V. In simulations, dynamic network bandwidth
uses the same protocols as in Section IV-C1.
We describe the fitness transitions in Fig. 5. GRN, where
N2 = 50, shows higher adaptability than SGA in early stage,
up to the seventh environment. It is considered that GRN captures certain features of optimization problems by memorizing
multiple solutions, even if the solution structure differs fromthe stored ones. For example, particular bits of phenotypes ofgood solutions are often “0” in any case. In other words, GRN
avoids solutions considered to be less adaptive. We need moreevaluations of whether similar results can be obtained in othercases. After SGA found an adaptive solution, GRN showedslightly lower adaptability than SGA. SGA can search mainly
around the discovered solution, while GRN searches aroundthe memorized solution when the genotype mutation occurs.
Adaptation speed of GRN, where N2 = 15, is slower. Since
optimal solution are not memorized, it has to search for a newone by phenotypic mutation. However, GRN, where N2 = 15,
generates few individuals by phenotypic mutations and many
ones by recalling other solution structure’s memory.
The proposed method consumes 392 W on average, while
421 W for SGA. Also, the unavailable time is 246 s for GRN

We proposed an optimization method to improve the adaptability of GA by GRN to distribute tasks for edge computing.
We confirmed that our method could improve the adaptability to the switching of known environments by recallingthe memorized solutions. Also in similar environments tothe memorized cases, our method improved the adaptability.
GRN escaped from local solutions by the multi-bit change ofphenotype from single-bit genotypic mutation and the newly
generated solutions by GRN. Our method is also effective ina non-similar environment because GRN captures certain features of optimization problems by storing multiple solutions.
It avoided solutions that are considered to be less adaptive.
Thus, the proposed method improved the adaptability of GA
and achieved reductions in power consumption.
The matrix structure of GRN poses challenges in terms ofscalability and computational complexity. The number of phenotypes that GRN can memorize depends on the mathematicalmodel. It is necessary to confirm whether GRN can represent
dynamic and complex systems even with increased scale. We
also evaluate in more complex environments, such as moresessions, and compare with other optimization methods. To
improve adaptability, dynamical adjusting of parameters is also
our future work.
R EFERENCES[1] M. Singh, E. Fuenmayor, E. P. Hinchy, Y. Qiao, N. Murray, and
D. Devine, “Digital twin: Origin to future,” Appl. Syst. Innov., vol. 4(2), no. 36, pp. 1–19, May 2021.
[2] J. Redmon, S. Divvala, R. Girshick, and A. Farhadi, “You only lookonce: Unified, real-time object detection,” in Proc. of IEEE Conf.
Comput. Vis. and Pattern Recog. (CVPR), Jun. 2016, pp. 779–788.
[3] J. Gubbi, R. Buyya, S. Marusic, and M. Palaniswami, “Internet of Things(IoT): A vision, architectural elements, and future directions,” Future
Gener. Comput. Syst., vol. 29, no. 7, pp. 1645–1660, Sep. 2013.
[4] V. K. Quy, A. Chehri, N. M. Quy, N. D. Han, and N. T. Ban,
“Innovative trends in the 6g era: A comprehensive survey of architecture,applications, technologies, and challenges,” IEEE Access, vol. 11, pp.
39 824–39 844, 2023.
[5] W. Shi, J. Cao, Q. Zhang, Y. Li, and L. Xu, “Edge computing: Visionand challenges,” IEEE Internet of Things J., vol. 3, no. 5, pp. 637–646,
Oct. 2016.
[6] C. Caiazza, S. Giordano, V. Luconi, and A. Vecchio, “Edge computing
vs centralized cloud: Impact of communication latency on the energy
consumption of LTE terminal nodes,” Comput. Commun., vol. 194, pp.
213–225, Oct. 2022.
[7] D. Whitley, “A genetic algorithm tutorial,” Statistics and Comput., vol. 4,
pp. 65–85, Oct. 1998.
[8] H. Shimonishi, M. Murata, G. Hasegawa, and N. Techasarntikul, “Energy optimization of distributed video processing system using genetic
algorithm with bayesian attractor model,” in Proc. of IEEE 9th Int. Conf.
Netw. Softwarization, Jun. 2023, pp. 35–43.
[9] P. A. Dnyane, S. S. Puntambekar, and C. J. Gadgil, “Method for identification of sensitive nodes in boolean models of biological networks,”
IET Syst. Biol., vol. 12, no. 1, pp. 1–6, Feb. 2018.
[10] R. A. Watson, G. P. Wagner, M. Pavlicev, D. M. Weinreich, and
R. Mills, “The evolution of phenotypic correlations and “developmental
memory”,” Evolution, vol. 68, no. 4, pp. 1124–1138, Dec. 2014.
[11] A. Wagner, “Does evolutionary plasticity evolve?” Evolution, vol. 50,
no. 3, pp. 1008–1023, Jun. 1996.
[12] Online:https://github.com/AlexeyAB/darknet. Accessed 8 August 2023.