Intelligent Evaluation of Innovative Enterprise Performance -
Construction of BPNN Model based on Improved WOA Optimization
HUAYING CAO
Lyceum of the Philippines University,
Manila 1002,
PHILIPPINES
Abstract: -With the economic progress, the environment in which enterprises operation is becoming
increasingly complex. Intelligent performance evaluation of innovative enterprises is of great significance for
their own development. The traditional performance evaluation indicators of enterprises rely too much on their
financial indicators, leading producers and operators to pay more attention to the short-term financial
performance growth of the enterprise. The long-term development of enterprises is neglected, resulting in weak
core competitiveness. Therefore, to better achieve the scientific evaluation of innovative enterprise
performance, based on the innovative enterprise performance evaluation index system, an innovative enterprise
performance intelligent evaluation model with the whale optimization algorithm optimized backpropagation
neural network is constructed. For the shortcomings of the whale optimization algorithm in the operation, the
wolf swarm algorithm isintroduced to optimize it. The experimental results show that the evaluation model
based on the improved whale optimization backpropagation neural network proposed in the study has very
small errors in the evaluation results of different samples, with no more than 3%. This indicates that the
performance evaluation index system for innovative enterprises can objectively reflect enterprise performance.
This evaluation model can offer a reasonable analysis of enterprise performance, providing reference for
intelligent evaluation of innovative enterprise performance.
Key-Words: -Innovative companies; performance evaluation; improving WOA; BPNN; WPA
Received: October 15, 2022. Revised: August 27, 2023. Accepted: September 25, 2023. Published: October 12, 2023.
1 Introduction
As the continuous growth of the knowledge
economy, enterprises are facing increasingly
complex environments and fierce competition. Only
by continuously improving their innovation level
can enterprises catch up with the growth of the
market economy for a long time and not be
eliminated by society, [1], [2]. Therefore, innovative
enterprises have emerged. Innovative enterprises
refer to measures such as enhancing cultural
innovation, encouraging communication, clarifying
organizational structure responsibilities, and
incentive policies to enhance the adaptability of
enterprises to flexible markets. By reducing costs
and improving product quality, they promote the
vigorous development of the social economy. As the
foundation and key component of the national
innovation system, innovative companies have great
impact on globalization. Within the development of
innovative enterprises, the scientific evaluation of
the economic benefits brought by innovation
capabilities is a hot topic for scholars, [3], [4]. The
existing performance evaluation of enterprises is
mainly based on the enterprise capital turnover and
enterprise management. From the perspective of
enterprise resource turnover, Protsenko proposed
that the financing limit is the main criterion for the
sustainable development of each enterprise when
evaluating the performance. The financial situation
of industrial energy enterprises largely depends on
the rationality of the innovation potential structure,
[5]. From the perspective of corporate management,
[6] found a positive correlation between board size
and corporate performance when evaluating
corporate performance. The impact of independent
director ratio and CEO duality on corporate
performance was not significant. Research has
shown that optimizing the structure of the board of
directors can improve corporate performance. [7]
studied the role of corporate social responsibility in
driving corporate performance. Green process
innovation plays a positive mediating role between
corporate social responsibility and corporate
performance,. However, unlike traditional enterprise
performance evaluation, the evaluation methods of
innovative enterprises must adapt to the
characteristics of the enterprise and the needs of the
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times. Therefore, establishing a scientific and
innovative function assessment system for
companies is of great significance for their own
development, as well as for the government and the
country. The existing performance evaluation
methods for enterprises are applicable to traditional
enterprises. Meanwhile, these performance
evaluation methods mostly rely on financial
indicators to achieve performance evaluation, which
cannot objectively reflect the level of enterprise
performance. Therefore, to better assess the
effectiveness of innovative enterprises, a
backpropagation neural network (BPNN)
performance evaluation model with the improved
Whale Optimization Algorithm (WOA) is
constructed on the basis of the designed
performance evaluation indicators for innovative
enterprises. It is expected to achieve intelligent
evaluation of innovative enterprise performance,
scientifically layout the resources of innovative
enterprises, ensure orderly production and
operation, and achieve steady improvement of
enterprise performance. The primary structure of the
study contains five parts. The first part is
introduction. The second part is to analyze the
current research on enterprise performance
evaluation and BPNN. The third part is to construct
an intelligent performance evaluation model for
innovative enterprises based on improved WOA-
BPNN. The fourth part is to validate the
effectiveness of the improved WOA-BPNN
intelligent evaluation model. The last part is a
summary of the research content.
The specific research contributions are as
follows. Firstly, based on the characteristics of
innovative enterprises, a performance evaluation
index system is constructed that reasonably reflects
the performance level of innovative enterprises.
Secondly, based on the indicator system, an
intelligent evaluation model WOA-BPNN suitable
for performance evaluation of innovative enterprises
is constructed. Finally, in response to the
shortcomings of the intelligent evaluation model in
the application process, the Wolf pack algorithm
(WPA) algorithm is applied to optimize it. An
innovative enterprise performance intelligent
evaluation model based on WPA-WOA-BPNN is
designed, providing effective support for
performance evaluation of such enterprise.
This paper is important for the research of
innovative companies. The specific reasons are as
follows. Firstly, taking the path of innovative
development has been a key method for enterprises
to enhance their competitiveness in recent years. As
many enterprises gradually implement innovative
development strategies, how to measure the
innovation level and enterprises development has
become an urgent problem to be solved. This study
constructs corresponding solutions to this problem.
Secondly, based on the performance evaluation
methods of ordinary enterprises and the
characteristics of innovative enterprises, a more
suitable performance evaluation method for
innovative enterprises is constructed in the
manuscript. It provides direct and effective support
for various innovative enterprises to evaluate their
own innovation capabilities in the future.
2 Related Works
In terms of enterprise performance evaluation,
relatively rich research results have been obtained
through long-term research and accumulation,
which provide a basis for the performance
evaluation of innovative enterprises. [8], designed a
scientific and effective assessment index system to
assess the performance of international enterprises.
The study focused on the influence of financial and
structural ratios on performance under the review of
the influencing factors of internationalization
performance. Adaptive training was accomplished
using artificial neural networks. The findings denote
that the method is reasonable. In the context of
sustainable development, paper companies need to
pay more attention to low-carbon strategies.
Accordingly, [9], constructed a carbon performance
assessment system including carbon input, transfer
and output indicators. The indicator weights were
determined by hierarchical analysis. The results
show that the function assessment system provides a
useful reference for enterprises to identify important
reasons influencing carbon emissions and carbon
performance assessment, [10]. [11], took an
innovative leading enterprise as an exampleto
establish an evaluation index system from two
aspects: innovation capability and enterprise
performance. In enterprise innovation ability
evaluation, six secondary indicators were selected
from three views of innovation input and output and
economic benefit to establish the company creative
ability assessment index system. In enterprise
performance evaluation, 11 secondary indicators
were selected from the three perspectives of
profitability, operation capability and development
capability. Then an enterprise performance
evaluation index system was established. The
findings indicate that the metric assessment system
can evaluate the innovation capability of enterprises,
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[12]. [13], used the necessary conditions analysis to
explore the influence of six antecedent conditions at
the "technology-organization-environment" level on
enterprise innovation performance. The study
denotes that innovation performance is influenced
by several factors. The findings of the study can
provide useful insights for enterprises to carry out
green innovation practices. [14], used the triple
performance approach to construct a effectiveness
assessment metric system for corporate green
governance. Based on the hierarchical analysis
(AHP) and Matlab programming, the weights of
each index in the enterprise green management
performance evaluation index system were
determined.The fuzzy integrated assessment manner
was applied to assess the green management
effectiveness assessment of industrial enterprises.
The findings express that the green management
effectiveness assessment metrics system constructed
by the "triple performance method" has crucial
theoretical significance and utilization value for the
evaluation.
The BPNN can be used to learn and train the
input sample data to obtain the implicit law of the
data samples. According to the law, data prediction
is achieved. Liu developed a local utility
management performance prediction model
according to BPNN model. The local utility
management performance was predicted with a
sample of 11 regions in the east, middle and west of
China. The index system can better achieve the
function assessment of local utility management,
[15]. [16], analyzed the integration performance
statistics of green suppliers based on BPNN. The
outcomes denote that it is adoptable to assess the
integration effectiveness of green logistics
enterprises. With proper calculation methods and
models, useful assessment outcomes can be got,
which can assess the important aspects of company
management and correctly distribute resources. [17],
utilized genetic algorithm (GA) to optimize the
BPNN method in the evaluation of rivers. GA-BP
was developed to determine the weights of these
indicators. The water environment index of the river
was given the greatest weight, followed by the river
hydrology, river aquatic life, river morphology and
river social service function indexes. [18], proposed
a metal surface defect classification method based
on an improved BPNN.The features were extracted
from 6 types of fault images such as inclusions,
patches, cracks, pitting, rolling and scratches using
the local binary pattern (LBP) algorithm. The
extracted feature values were used to establish a
feature sample library. The BPNN optimized with
this method has high accuracy. [19], used BPNN to
optimize the DCF model to accomplish the financial
data prediction of a company. The research
outcomes illustrated that the method can achieve the
prediction of the company's financial data,
providing data support for corporate investment.
From the above research results, the system of
corporate performance evaluation indexes and
evaluation methods are abundant. These methods
can achieve a relatively reasonable assessment of
enterprise performance. However, for the
performance evaluation of innovative enterprises,
the existing evaluation indexes are not applicable to
them, whichcannot accurately evaluate the
innovation ability and level of enterprises.
Accordingly, depending on the advantages of BPNN
in data prediction, the WOA is used to optimize it.
Then, an innovative enterprise performance
intelligent evaluation method based on WOA
optimized BPNN is constructed. It is expected that
the evaluation method can better evaluate the
creative performance of companies and improve the
creativity of innovative enterprises.
3 Construction of an Intelligent
Enterprise Performance Evaluation
Model based on Improved WOA-
BPNN
Innovative companies improve their profit levels
and enhance their core competitiveness by
continuously innovating their brand concepts,
business models, management systems, cultural
concepts, and technologies. This chapter constructs
an intelligent evaluation model of enterprise
performance based on improved WOA-BPNN from
the characteristics of innovative enterprises
themselves.
3.1 Innovative Enterprise Performance
Evaluation Index Construction
Generally speaking, the performance of innovative
enterprises is mainly reflected in the economic
activities of the enterprise. The organizational
structure, departments, and production factors in
each industrial chain in the production are
associated with the performance of the enterprise.
Specifically, every functional department of the
company should ensure the close association of
performance and establish an effective performance
evaluation mechanism. Performance evaluation is a
process of continuous development and
improvement. In the existing performance
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evaluation index system, financial indicators occupy
a large proportion, which is not suitable to the
function assessment of innovative companies, [20].
Table 1. Innovative Enterprise Performance Evaluation Indicator System
Primary
indicators
Secondary indicators
Primary indicators
Economic
benefits
Innovative product sales rate
Social benefit
Operating revenue growth rate
Asset liability ratio
Rate of circulating fund turnover
Innovation
Innovation investment capacity
Innovation output capacity
Ability to innovate management
systems
Talent benefits
Employee innovation motivation
level
Marketing
management
Employee learning and growth
Employee satisfaction level
To more accurately analyze the effectiveness of
innovative enterprises, taking enterprise M as an
example, the performance of this enterpriseare
evaluated. In constructing the performance
evaluation indexes of this enterprise, the evaluation
indexes should be designed strictly according to the
principles of operability, scientificity,
systematization, simplicity and consensus. Based on
the existing information of company performance
indicators and the characteristics of innovative
enterprises, an innovative enterprise performance
evaluation system is established, including five
main indicators and related secondary indicators,
[21]. The specific index composition is presented in
Table 1.
The ultimate purpose of economic behaviour is
still to obtain economic benefits. Therefore,
financial indicators under the economic return index
still have relatively important impact on the above
index system. Based on the specific characteristics
of innovative enterprises, the innovation ability of
enterprises is also used as one of the performance
evaluation indexes. In addition, Social benefits are
also considered as one of the performance
evaluation indicators. The reasons are as follows.
Firstly, with the rapid development of the economy,
the quality of enterprise development has received
more attention. The social benefits created by
enterprise development have become an important
indicator of the healthy development of the
enterprise itself. Secondly, with the rapid
development of China's economy, it has become
particularly important to pay attention to the quality
and prospects of enterprise development. It
promotes the healthy and orderly development of
the national economy. In addition, the social
benefits of enterprises are of great significance for
social stability, coordination, and healthy
development. Therefore, incorporating social
benefits into the evaluation and assessment system
can comprehensively reflect the effectiveness of
enterprises in terms of social benefits, including
environmental protection, social security work,
population quality, and quality of life. In addition,
talents are the key to enterprise operation, which can
directly reflect the overall culture level of the
enterprise. Especially for innovative enterprises,
talents are the core competitiveness to improve their
innovation capabilities. Finally, marketing is also
used as one of the performance evaluation indicators
of innovative enterprises. Enterprise development
not only needs to rely on the functions and attributes
of the products themselves, but also needs to
continuously develop the sales market. Based on the
above evaluation indexes, the index weights are
analyzed using the hierarchical analysis method.
According to the intrinsic relationship between the
indicators, a comparison matrix is constructed as
shown in Equation (1).
()
ij mn
Rr
(1)
In equation (1),
ij
r
is the importance of the
element
j
relative to the element
i
.
R
is the
reciprocal inverse matrix. Then the indicators are
tested for consistency. The indicator weights are
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determined by the judgment matrix, as shown in
Equation (2).
11 12 1
21 22 2
12
...
...
... ... ... ...
...
n
n
m m mn
r r r
r r r
R
r r r






(2)
Based on the judgment matrix
R
, the feature
vector
12
, ,...,
A A A
n
W W W W


of
R
is calculated as
the weight of the corresponding second-level index.
For the total target weight, it can be calculated by
evaluating the weight of the first and the second
level indexes, as shown in Equation (3).
12
W W W
(3)
In Equation (3),
W
indicates the total target
weight, i.e., the weight of secondary evaluation
indicators in the whole evaluation system.
1
W
indicates the indicator weight of each secondary
indicator under the target factor dimension.
2
W
is
the weights of various target factors. The weight
coefficients of secondary indicators in the system
can be calculated.
3.2 Improving WOA-BPNN Enterprise
Performance Intelligence Evaluation Model
Construction
In the BPNN model, gradient search technology is
used to reduce the error between the actual output
and expected output of the network. BPNN mainly
contains forward transmission signal and reverse
feedback error. When forward transmission is
performed, the signal is analyzed and transmitted
through the topology of the BPNN. When the output
does not match the expected result, the error value is
analyzed and fed back to reverse feedback, [22]. In
the reverse feedback, the error is reduced by
continuously adjusting the weights and thresholds
among the neurons in each layer to make the output
match the expected value. The computational flow
of BPNN is shown in Figure 1 (Appendix).
In the BPNN model, the amount of nodes in the
output layer relies on the dimensionality of the
target variable in the practical problem.The more
commonly used nonlinear transfer function,
Equation (4), is used to represent the Hyperbolic
functions.
1
1x
fx e
(4)
In BPNN, the neuron is the most basic unit.The
output signal can be expressed as Equation (5).
y f wx

(5)
In Equation (5),
f
is a transfer function.
y
is the output value of the neuron.
denotes the
threshold value.
w
is the weight coefficient of the
network nodes.
x
is the input signal in the BPNN.
A three-layer BPNN structure is used in the
research, containing an input, an implicit and an
output layer. The input layer receives external data.
The input layer generally applies a linear function.
The trial-and-error method is used to determine the
amount of nodes in the hidden layer, as can be seen
in Equation (6).
, [1,10]k m n a a
(6)
In Equation (6),
k
,
m
and
n
are respectively
the amount of nodes in the hidden, input and output
layers.
a
is a constant between 1 and 10. In BPNN,
the structure concluding a hidden layer can solve
any closed interval continuous function. The 3-layer
BPNN can be mapped to any dimension, which has
the merits of simple structure, simple operation and
short running time. Nevertheless, the convergence
speed of BPNN is not quick, which has influence on
the accuracy of performance assessment results.
Therefore, WOA is applied to optimize the BPNN.
The WOA mainly solves the optimal solution by
simulating whale predation, [23]. The WOA is
mainly divided into three phases. The position of
any whale in the
D
space is represented as
12
, ,..., D
X x x x x
. The first is the encirclement
phase, where the whale moves to the optimal
position when encircling the prey. The whale
position is updated as shown in Equation (7).
1t t t t
i best best i
X X A C X X
(7)
In Equation (7),
best
X
is the current optimal
position. Each dimension of
A
means a uniformly
distributed random number of
,aa
.The initial
value of
a
takes the value of 2, which gradually
decreases to 0 as the amount of iterations increases.
C
denotes a uniformly distributed random number
between
0,2
. The second stage is the bubble
attack. When the whales besiege the prey, they will
spew bubbles to narrow the target range and update
the position to achieve the local optimum. When the
whale is performing bubble attack, the whale
position update method is shown in Equation (8).
1cos(2 )
t t bl t
i best best
X X A e l X
(8)
In Equation (8),
b
is a constant.
l
presents a
random number with a uniform distribution of
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1,1
. The third stage is the search for physical
objects stage. At this time, the food location is
determined by changing the
A
vector. When
1A
,
the individual whale converges to the reference
whale. The position is updated by randomly
selecting the reference whale according to the
individual, as shown in Equation (9).
()
( 1)
rand
rand
D C X X t
X t X A D
(9)
In Equation (9),
D
denotes the distance
between the whale and the prey.
C
refers to the
coefficient vector.
rand
X
is the random reference
whale's position vector. Based on the above process,
the specific flow of the obtained WOA is shown in
Figure 2.
However, the basic WOA has the demerits of
low accuracy, slow convergence speed and easy to
fall into local optimal solutions when analyzing
enterprise performance index data. Therefore, the
Wolf pack algorithm (WPA) algorithm is adopted to
optimize it. The WPA algorithm is a top-down
collaborative search path structure based on
artificial wolf (AW) themes and responsibility
division, [24]. The social division of labor in the
WPA algorithm includes the head wolf, the probe
wolf and the fierce wolf. In solving the target data,
the wolf activities are classified into 3 smart
behaviours, namely wandering, calling and siege
behaviours.
In a hunting space, the number of artificial
wolves in a wolf pack is
N
. The number of
individuals of the variable to be searched for
superiority is
M
. The state of any AW is denoted by
12
, ,...,
a a an
Q q q q q
.
an
q
means that the
a
-th
AW is searching for the optimal spatial position in
the
d
space. The target concentration captured by
the AW is
()Y f X
.
Y
denotes the solution of the
objective function. The distance between any two
artificial wolves
u
and
v
is shown in Equation (10).
1
( , ) D
ud vd
i
L u v x x

(10)
In the wandering behaviour, the wolf with the
best fitness value among the remaining wolves
except the head wolf is selected as the probe wolf to
search for the optimal solution. After advancing
along the direction of
( 1,2,..., )p p h
, the position
of the probe wolf
i
in the
d
dimensional space is
shown in Equation (11).
sin(2 / )
pd
id id a
x x p h step
(11)
In Equation (11),
a
is the probe wolf scaling
factor. The step length of the probe wolf forward in
the direction of
h
is
d
a
step
.
id
x
is the initial
position where the probe wolf is located. The WPA
algorithm takes the optimal solution as the head
wolf when it is updated. After each iteration
calculation, the obtained value is bigger than the
previous value. Then the previous generation of
head wolves is replaced with the new head wolf.
This method iterates continuously until the optimal
solution is obtained. The implementation flow of the
WPA algorithm is shown in Figure 3.
Start Input
samples Compute
Input Layer Calculate
sample error
Reverse
modification
threshold
End Y
N
Does the error meet the
requirements
Fig. 1: The structure of BPNN
Start Population
initialization
Obtain the whale with the best
fitness and update the
correlation coefficient
Determine the random
generation of disturbance
values A and P in place of
whales
P<0.5 ?
A≥1
Bubble attack
Termination
conditions
End
Search for
prey
N
Y
Besiege
N
Y
Fig. 2: WOA algorithm process
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Start
Initialization
Wandering behavior of greedy
wolves
Get a better solution
Y
N
Update the information of the head
wolf
Fierce wolf attack behavior
Get a better position
Wolf pack siege behavior
Update the position of the head
wolf
Update wolf pack location
Whether the termination
conditions are met
Output the position of the head
wolf, that is, the optimal solution
End
Y
N
N
Y
Fig. 3: WPA algorithm process
Start
Initialize whale and wolf pack
positions
Whale Location Code
Determine the optimal whale
Whale position movement
Restrict wolf pack location
Calculate the objective function of
a wolf pack
Update wolf pack location
wandering
Evaluate Whales
Evaluate Whales
Produce a head wolf, a probe wolf,
and a fierce wolf
siege
End
call
The best wolf replaces the worst
whale
Training network
Training error
Calculate objective function
Iteration completed ?
Output results
Y
N
Fig. 4: WOA-WPA-BPNN process
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Based on the WPA algorithm, the WOA
optimization method is constructed. Depending on
the function assessment index system of the
innovative company constructed in the above
research, the constructed indicators are used as input
layer nodes. The output value is the performance
evaluation result of this innovative company. The
initial values of the BPNN are optimized by
improving the WOA algorithm through WPA. That
is, the optimal value of WPA is used to replace the
worst value of WOA. The optimal value of the
output replaces the initial weights and thresholds of
the BPNN. The flow of the innovative enterprise
performance assessment model based on WOA-
WPA-BPNN is shown in Figure 4.
4 Performance Analysis based on the
Improved WOA-BPNN Model
To investigate the performance of the improved
WOA-BPNN innovative enterprise performance
evaluation model, this chapter will test the improved
performance evaluation model and the original
model. Data related to innovative enterprises are
selected to evaluate the performance of the
improved model.
4.1 Analysis of Enterprise Performance
Evaluation Indicators
Based on the innovative enterprise performance
evaluation index system constructed by the research,
a corresponding questionnaire is developed and the
relevant professionals are invited to rate it. The
questionnaire is based on a percentage system. After
the evaluation is completed, the valid questionnaires
are reasonably collected to obtain the experimental
data. According to the analysis method mentioned in
the above section, the weights of the performance
evaluation indexes for innovative enterprises are
finally obtained, as denoted in Table 2. From the
relevant weight values, the highest weight of 0.08 is
given to the asset-liability ratio, which is the key
indicator for the performance evaluation. In
addition, the growth rate of business income and
innovation management system also has a weight of
0.07. Therefore, to improve the economic efficiency
and innovation ability of innovative enterprises,
enterprise managers must focus on the enterprise
innovation.
Table 2. Evaluation Index Weights
Primary
indicators
Secondary indicators
Weight
value
Primary
indicators
Secondary indicators
Weight
value
Economic
benefits
Innovative product sales
rate
0.05
Social benefit
Energy saving consumption
0.06
Operating revenue
growth rate
0.07
Elimination of outdated
production capacity
0.06
Asset liability ratio
0.08
Environmental protection
technology investment
0.05
Rate of circulating fund
turnover
0.05
Financial security
0.05
Innovation
Innovation investment
capacity
0.06
Technical support
0.05
Innovation output
capacity
0.06
Employment opportunities
0.04
Ability to innovate
management systems
0.07
Social services
0.06
Talent
benefits
Employee innovation
motivation level
0.05
Marketing
management
Market share of innovative
products
0.05
Employee learning and
growth
0.05
Ratio of market researchers
0.06
Employee satisfaction
level
0.04
Sales expenses to operating
income ratio
0.06
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4.2 Effect Analysis of the Improved WOA-
BPNN Performance Evaluation Model
The improved intelligent performance evaluation
model based on WOA-BPNN was comprehensively
and scientifically analyzed by constructing an
innovative enterprise performance evaluation
indicator system and calculating indicator weights.
In Matlab2013b, the improved WOA-BPNN
innovative enterprise performance evaluation model
is simulated. The error threshold of the BPNN is 0
and the learning rate is 0.01. The training results of
the BPNN model are illustrated in Figure 5. From
Figure 5(a), the mean square error of WOA-BP
decreases more rapidly in the first 28 iterations,
slows down in the 29th to 81st iterations, and
reaches convergence after 85 iterations. From Figure
5(b), the WPA-WOA-BP is fast in the first 2
iterations, slows down in the 3rd to 8th iterations,
and reaches convergence in the 19th iteration. It
raises the convergence speed of the BPNN to some
extent. In Figure 6, the convergence speed of WPA-
WOA-BP is increased by 79.41% and the
convergence accuracy is nearly doubled. The results
confirmed that WPA has good optimization effects.
WPA-WOA-BP can not only accelerate the
convergence speed, but also improve the
convergence accuracy to a certain extent.
To verify the convergence of the WPA-WOA-
BP, several methods are run in three different
functions to calculate the effectiveness of the
method. The WSOA, IWOA algorithm and PSO
algorithm are used as comparative method. The
research findings of the WOA and the improved
WOA in the multi-peaked function are shown in
Figure 6. From Figure 6, the WPA-WOA method
requires the smallest number of iterations in all three
different functions, which are 40, 100 and 90,
respectively. From this data, the efficiency and
speed of the algorithm are significantly higher than
other comparison methods. That is, this method is
significantly superior to other optimization methods.
The comparison of the fitness values between
the WOA-BP and WPA-WOA-BP is displayed in
Figure 7. In Figure 7(a), the average and best fitness
converge rapidly until the 18th generation, slow
down from 30 to 60 generations, and level off after
65 iterations, with the fitness value stabilizing at
0.82. In Figure 7(b), the WPA-WOA-BP fitness
converges at the 19th. The fitness value stabilizes at
1.33. From the comparative analysis in Figure 7, the
improved model has strong adaptability and faster
convergence speed. The optimal and average fitness
values of the improved method are better than those
of WOA-BP, indicating that the method has strong
problem-solving ability in the optimization process.
030
10-15
105
10-10
10-5
100
10-20
10 20 40 50 7060 80
Epochs
The best value is 8.61e-18 at epoch 86
06
10-15
10-5
105
2 4 8 10 14
12 16
Train
Best
Goal
Epochs
The best value is 3.39e-20 at epoch 18
18
(a) WOA-BP (b) WPA-WOA-BP
Train
Best
Goal
90
1015
MSE
MSE
Fig. 5: Mean square error of BP under two algorithms
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DOI: 10.37394/232018.2023.11.42
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0
100
30
50
40 Iterations
80 120 160 200
40
20
10
WPA-WOA
IWOA
0
80
20 60 100 140 180
Fitness value
WOA
PSO
60
90
70
0
30
15
40 Iterations
80 120 160 200
20
10
5
WPA-WOA
IWOA
020 60 100 140 180
Fitness value
WOA
PSO
25
0
100
30
50
40 Iterations
80 120 160 200
40
20
10
WPA-WOA
IWOA
0
80
20 60 100 140 180
Fitness value
WOA
PSO
60
90
70
(a) f1 function (b) f 2 function
(d) f3 function
Fig. 6: Comparison of Convergence in Different Functions
0
0.2
0.9
0.4
0.6
0.8
0.1
20
Fitness
Genetic algebra
40 60 80 100
0.7
0.5
0.3
Optimal fitness
Average fitness
(a) WOA-BP
0
1.4
1.2
0.2
20
Fitness
Genetic algebra
40 60 80 100
1.0
(b) WPA-WOA-BP
0.4
0.8
0.6
Optimal fitness
Average fitness
Fig. 7: BP fitness in the two algorithms
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Volume 11, 2023
Table 3. Performance Comparison of Models
Algorithm
R2
MSE
RMSE
MPAE
MAE
WPA-WOA-BP
0.9649
0.0177
0.0213
1.1460
0.0091
WOA-BP
0.9653
0.1546
0.0674
3.5097
0.0422
BP
0.8867
1.0643
0.1906
6.4508
0.0766
The R2 values, MSE, RMSE, MPAE, and
MAE values of this intelligent evaluation algorithm
are compared separately. The nearer the value of R2
is to 1, the better the performance of the model. The
performance comparison of this performance
evaluation method is shown in Table 3. From Table
3, the MSE, RMSE, MPAE and MAE of WPA-
WOA-BP are 0.0177, 0.0213, 1.1460 and 0.0091,
respectively, which is significantly lower than the
remaining methods. Different error evaluation
indicators are used to measure the performance of
the constructed methods, resulting in relatively low
error levels. The error level of the performance
evaluation method for innovative enterprises
constructed through research is relatively low. It can
be applied to evaluate the performance of innovative
enterprises.
To verify the consistency and stability of the
innovative enterprise performance intelligence
evaluation method proposed by the research, 20
companies are selected for testing. 10 samples are
utilized to train the network and the other 10
samples are evaluated. The optimized BPNN and
traditional BPNN models are applied to the same
dataset for training and testing. The obtained
evaluation results with expected values are shown in
Figure 8. From Figure 8, the basic change trends of
the performance evaluation results for innovative
enterprises obtained under the three different
performance evaluation methods are consistent.
Specifically, the differences between the
effectiveness assessment manners based on BPNNs
and the expected values are significant. Among
them, the differences between data sample 1, data
sample 4 and data sample 6 and the expected
performance are the largest. The differences
between the performance evaluation results obtained
based on the WOA-BP and the expected
performance are also relatively significant, with
large deviations in samples 2, 4, and 5. The
difference between the results obtained by the
WPA-WOA-BP performance evaluation model and
the expected performance is the smallest, and the fit
between the two is the highest. The evaluation is
relatively stable for each sample. When the
enterprise performance evaluation method is applied
to actual enterprise performance evaluation, it can
better reflect the innovation and development
situation of the enterprise. The intelligent
performance evaluation method proposed in the
research has good performance evaluation results
for innovative enterprises.
0
1.00
0.75
0.85
2Number of samples
46810
0.80
0.70
0.65
Desired value
WPA-WOA-BP
0.60
0.95
1 3 5 7 9
Performance value
WOA-BP
BP
0.90
Fig. 8: Comparison of evaluation performance and
expected performance
The evaluation results of the performance for
10 different innovative companies based on the
improved WPA-WOA-BPNN are expressed in
Table 4. From the above evaluation results, the
performance evaluation ranking of innovative
companies obtained from the training and testing
results has not changed. It indicates that the
improved WPA-WOA-BPNN model for intelligent
performance evaluation has better stability. In the
tests of different samples, the errors of the
evaluation results are very small. All results do not
exceed 3%, which indicates that the intelligent
evaluation method has relatively ideal accuracy. The
constructed innovative enterprise performance
intelligent evaluation method can accurately reflect
the innovation ability the enterprise, while
measuring the shortcomings of the enterprise in the
innovation development.
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DOI: 10.37394/232018.2023.11.42
Huaying Cao
E-ISSN: 2415-1521
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Volume 11, 2023
Table 4. Performance evaluation of different
companies
Order
number
Evaluate
results
Actual
results
Error
1
0.8633
0.8621
0.140%
2
0.7564
0.7412
2.010%
3
0.6135
0.6086
0.799%
4
0.8795
0.8822
0.307%
5
0.5536
0.5671
2.439%
6
0.7623
0.7502
1.587%
7
0.8921
0.8882
0.437%
8
0.5406
0.5319
1.609%
9
0.4789
0.4852
1.317%
10
0.6573
0.6625
0.791%
5 Conclusion
By analyzing the existing enterprise performance
evaluation indexes, a performance assessment
metrics system for innovative companies is
constructed. By calculating the index weights, an
optimized BPNN intelligent evaluation model with
the improved WOA is designed to assess the
innovative enterprises performance. The research
outcomes demonstrated that among the index
systems constructed by the research, the weight
value of the asset-liability ratio index is 0.08, which
has the greatest influence on the performance level
of innovative enterprises. The WPA-WOA-BP
fitness reaches convergence at the 19th. It stabilizes
at 1.33. The MSE, RMSE, MPAE and MAE of
WPA-WOA-BP are 0.0177, 0.0213, 1.1460 and
0.0091, which are significantly lower than the rest
of the methods. The performance evaluation index
system for innovative enterprises constructed
through research can better reflect the influencing
factors of the performance. The performance
intelligent evaluation model constructed based on
this indicator system exhibits higher convergence
effects and lower error value performance. The
accuracy obtained by applying the proposed method
to the performance evaluation for innovative
enterprises is superior to other commonly used
methods. In summary, this indicates that the
proposed intelligent performance evaluation method
for innovative enterprises based on improved WOA-
BPNN has better performance, which can be utilized
the performance assessment of innovative
enterprises. However, there are still shortcomings in
the manuscript. First, when constructing the
performance assessment indicators system of
innovative enterprises, the influencing factors
analysis is not comprehensive enough. The
performance influencing indexes may be different
for different types of innovative enterprises.
Secondly, there is no professional standard for
selecting the structure of BPNN in the manuscript.
The optimal structure is verified through multiple
experiments, which may have some errors.
Additionally, the number of test samples selected
for the intelligent evaluation of the performance for
innovative enterprises is limited. Therefore, in the
subsequent research, a more integrated analysis of
the performance assessment indicators for
innovative enterprises should be conducted to
ensure full coverage of the indicators. At the same
time, more sample data should be collected to verify
the performance of the model.
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The author independently completed the work from
the first draft to the final draft, including revisions.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for this study.
Conflict of Interest
The author declares that there has no conflict of
interest.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
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DOI: 10.37394/232018.2023.11.42
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Volume 11, 2023