# Self-Optimization Evaluation Model about the Ship Suppliers Based on Improved Particle Swarm Optimization

Authors: Xiangran Du; Min Zhang; Jiayue Li
Journal: Mobile Information Systems
 (2022)

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## Abstract

Shipbuilding is a complex process and needs plentiful suppliers. Knowing how to select ship suppliers according to the customer requirements is a pivotal task. A dynamic self-optimization evaluation model for ship suppliers is presented in this paper, which is accomplished by an improved particle swarm optimization. The experiment shows that the novel method can not only accomplish the intelligent evaluation of ship suppliers and avoid redundant experts’ dependence but also adjust the evaluation function dynamically according to the annual situations and maintain the practicability of the evaluation model.


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## Body

## 1. Introduction

Shipbuilding is a complex process. It is difficult for shipping factories to accomplish shipbuilding according to the demands of customers because of the long production period, high construction cost, many kinds of equipment and accessories, higher quality demand, and so on. The purchase volumes are enormous and the procurement costs account for 70 percent of the total construction cost. The management of the supply chain is necessary to coordinate some processes, such as purchase, storage, product, and so on, with the advanced information technology and management philosophy in shipbuilding. The selection of the shipbuilding suppliers in the supply chain becomes a crux and a decisive factor to build the higher-level system of the ship supply [1]. There are some shortcomings in the current estimation methods about ship suppliers. The first is the establishment of the estimation model needs redundant help from estimation experts. Another is the accuracy decrease without enough maintenance and support from experts by degree. In this paper, a new mathematical evaluation model is presented first considering more attributes to estimate the actual strength of ship suppliers. The second attribution is the improved particle swarm optimization avoiding falling into the local best value. The last is a self-optimization evaluation algorithm for ship suppliers based on the improved particle swarm optimization that is presented to solve the problem of shipping suppliers (short for SOSSESIPSO).This paper is organized as follows. In Section2, a brief review of the research of the supplier chain is given and the following section provides the component of the evaluation function in the ship-suppliers evaluation system. Section 3 presents the mathematical model of the evaluation function of the shipping suppliers. Two experiments are shown in Section 4, one is to select the best parameters with the best performance, and another is to testify to the optimization effects of the self-optimization evaluation system for ship suppliers. Section 5 discusses a summary of the paper and points out the direction of future research.


## 2. Correlational Studies

The research on suppliers’ evaluation began in 1966. Dickson GW first analyzed the vendor selection system [2]. Vahdani and Zandieh established a linear programming model with a target on the cost in 1989 [3]. Bakeshlou et al. found that the mathematical programming model was superior to the evaluation model and the single model was better than the multidimensional model through studying the past articles in 2000 [4]. Carter and Kaufmann proposed the hybrid and round nonlinear programming model to solve the huge demands under the support limit of the suppliers [5]. Guo et al. began to study vendor evaluation by the analytic hierarchy process [6]. Guo-Qing et al. presented the evaluation of the ship suppliers model based on the analytic hierarchy process and the triangular fuzzy number [7]. Wen et al. proposed an evaluation model for the comprehensive evaluation method of the ship equipment suppliers in 2011 [8, 9]. Fang used the artificial neural network to evaluate every ship supplier and Hao Deng designed an evaluation of marine diesel engine manufacturers based on the GA-BP neural network separately. Fang designed the RBF neural network evaluation model to evaluate the shipbuilding suppliers [10].From the abovementioned analysis, some researchers have selected operations analysis or statistics to solve the problems before 2011. These methods need redundant help from experts and the actual results are influenced by the experts’ experiences. Since 2013, many scholars have attempted to employ artificial intelligent algorithms to promote the intelligence of the ship-suppliers estimation model. The effects are unsatisfactory, although artificial intelligent methods avoid the ship-suppliers estimation model from the plethoric participation of the experts.


### 2.1. Ship-Supplier Evaluation Mathematical Model

The demands for the evaluation of ship suppliers are quite different in the whole lifecycle of the ship from production to extinction, due to the demand subjects in each stage being various. In view of the characteristics of the shipbuilding industry and the demand for marine equipment suppliers, six attributes influencing the selection of the ship supplier are obtained through in-depth interviews with experts, research results, data search, and expert review in this study [11–13]. The assessment of ship suppliers can be accomplished from six attributes, including enterprise strength, financial status, enterprise reputation, product quality, service quality, and cost control [14]. The estimation of every attribute can be carried out by different sub-attributes.The mathematical model to access the ship suppliers from six parts is shown in Table1. The mathematical expression is shown in formula (1), which is an objective function in the ship supplier evaluation mathematical model.(1)Fx=∑i=16wi⋅fix=∑i=16wi⋅∑j=1nwij⋅fijx.Table 1
The component of the attributes in SOSSESIPSO.
AttributesEnterprise Strength (f1)Financial Status (f2)Enterprise Reputation (f3)Sub-attributesHandheld Orders Number (f11)Order Delivery Timely Rate (f12)Order Lead Time(f13)Delivery Rate within Delivery Period(f14)Number of Patents(f15)Quantity of Qualification Certifications(f16)Asset liability Ratio(f21)Return On net Assets(f22)Asset Turnover ratio(f23)Number of Enterprise Awards(f31)Business Risks(f32)Legal Risks(f33)AttributesProduct Quality (f4)Service Quality (f5)Cost Control(f6)Sub-attributesProduct Qualification Rate(f41)Product Premium Rate(f42)Product Quality Certification System(f43)Product Warranty Period(f44)Average Product Life Cycle(f45)Service Satisfaction(f 51)Service Improvement Capability(f 52)Product Development Service Capability(f 53)Product Price(f 61)Order Cost(f62)Transportation Cost(f63)Storage Cost(f 64)The six attributes should be represented by the six parametersf1∼f6, respectively. These parameters wii=1∼6 express the significant degree of about six parts in the evaluation function and the values are in proportion to the significant degree. The values of six parameters are between 0 and 1 under the condition of the sum of six parameters wii=1∼6 equal to 1 shown in formula (2).(2)w1+w2+w3+w4+w5+w6=1.These sub-parameterswij add together are 1 in every attribute fix, the formula representation is shown below.(3)∑j=1nwij=1.Thewifii=1∼6 should satisfy the relationship shown below. In other words, the more value, the more importance.(4)w4f4≥w1f1≥w6f6≥w2f2≥w5f5≥w3f3.


### 2.2. Enterprise Strength

In the ship supply chain, failure to deliver goods within the lead time (delivery date of ship products) or failure to meet customer order quantity will bring obstacles to the effective operation of the ship supply chain. In the ship supply chain, the delivery rate, order satisfaction rate, and order lead time can reflect the delivery situation. Handheld orders, order delivery time rate, order advance time, delivery rate within the delivery period, number of patents, and quantity of qualification certification reflect the enterprise’s strength.Handheld orders refer to the number of orders announced by the shipbuilder in the previous year, which can be obtained from data.Guaranteeing full ordering is the minimum requirement for shipping companies to suppliers, but for some sparsely supplied items, the order satisfaction rate is difficult to maintain, so it is more necessary to put forward requirements for suppliers. Order delivery time rate reflects the possibility of the delivery of the ship suppliers on time.The shorter the order lead time, the stronger the supply chain’s ability to respond to customer needs and the fewer inventories need to be held. Using order advance time as the evaluation criterion, the percentage of delivery times less than this lead time in the total delivery times are measured.Delivery period is the delivery period specified in the shipping industry, mainly reflecting the delivery capacity of suppliers from the perspective of time.The number of patents of an enterprise is composed of the number of software copyrights, utility models, appearance patents, and invention patents. The number of patents is directly proportional to the strength of the enterprise.Qualification certification refers to conformity assessment activities in which a state-recognized certification body certifies that an organization’s products, services, and management system comply with relevant standards, technical specifications, or mandatory requirements. The more qualifications an enterprise obtains for related products, the more standardized the enterprise and the stronger its strength. The formula of the enterprise strength is shown in formula (5).(5)f1=w11f11+w12f12+w13f13+w14f14+w15f15+w16f16.Thew14f14 is more significant than the w12f12, although the delivery rate within the delivery period is less than the order delivery timely rate. The qualification is represented by formula (6).(6)w14f14≥w12f12.


### 2.3. Financial Status

The amount of capital required for ship material procurement is usually large, and good financial and reputation status is an important guarantee for the smooth progress of the procurement. Asset-liability ratio, returns on net assets, and asset turnover ratio are the reflection of the financial situation.The asset-liability ratio is used to measure the long-term solvency of suppliers and reflects whether the enterprise has the ability for sustainable development. This is a very important evaluation indicator for long-term cooperation.Returning on net assets reflects the profitability of the supplier’s net assets and embodies its operating performance and profitability, which is more expressive than sales margin and other indicators.The asset turnover ratio reflects the supplier’s capital turnover capacity to a certain extent, so it is a core indicator that reflects the company’s operational capabilities.The restriction relationship among these attributes is shown in formula (7).(7)f22⋅1−f21f23≥0.


### 2.4. Enterprise Reputation

Good enterprise reputation is the premise of cooperation. Only a good reputation can win the trust of partners, and a good enterprise reputation also reflects the economic strength of the enterprise to a certain extent. The enterprise credibility of the business can be judged from three aspects including the judicial risks, the business risks of the company, and the award number obtained by the enterprise. The number of business risks of an enterprise includes administrative penalties, environmental penalties, abnormal operations, abnormal taxation, and serious violation of laws and promises. The number of judicial risks includes the number of court announcements, the number of legal proceedings, the number of court announcements, and the number of executed persons.


### 2.5. Product Qualification Rate

The product qualification rate refers to the percentage of qualified products in the total purchase amount within a certain period. A higher product pass rate can not only effectively reduce the repair and return but also, more importantly, help to improve the satisfaction of ship owners.The product premium rate refers to the ratio between the number of premium products and the total quantity of products in a certain period. Some precision instruments need not only qualified products but also quality products. Therefore, the premium rate can reflect the high level of the supplier’s products, which is less than the product qualification rate shown in formula (8).(8)w42f42−w41f41≥0.Product quality certification systems can refer to relevant quality certification standards and directly adopt the certification results of authoritative departments to give a certain rating level. The higher the level, the more perfect the certification system will be.The product warranty is a manufacturer’s warranty service for a certain number of years in order to protect the interests of buyers. In general, the longer the product warranty period, the more the manufacturer will recognize the quality of its products.The life cycle of the ship is the whole process of the ship from its usage in the market to the substitution or vanishment from the market. The average life cycle is an average of the life cycle of the ships, which is the economic life in the market movement.


### 2.6. Service Quality

The characteristics of many varieties and long cycles of ship products require ship-supporting enterprises to have a high level of service to maintain the normal operation of the ship. The indicators reflecting the service level of ship suppliers include historical delivery records, after-sales service satisfaction rate, and service improvement capabilities.The after-sales service satisfaction rate is an important indicator for most companies to measure the service level of suppliers, which is designed to reflect the quality management capabilities of suppliers after transactions.Service improvement capability: After-sales service satisfaction rate is an evaluation of the supplier’s “past,” while service improvement capability is a prediction of the supplier’s future service level. As a long-term partner, the future development of suppliers is even more important.Product development service capability is to modify or improve related products to meet the requirements of the enterprise in response to the special needs of shipbuilding enterprises or customers.


### 2.7. Cost Control

Price competition is the focus of shipbuilding competition, and the high cost of materials has become an aporia that needs to be solved in the shipbuilding industry around the world. Competitive suppliers should have competitive advantages in terms of price, ordering cost, transportation cost, and storage cost.Product price refers to the cost that an enterprise needs to pay for each unit of product, and it is the key indicator that most directly reflects the enterprise’s procurement cost.The order cost has a linear relationship with the shipping volume, which is the actual cost that can be calculated according to the relevant standards.The transportation cost is linearly related to the volume, distance, and mode of transportation. If the supplier can provide transportation service by itself, a large amount of cost can be saved for the shipping enterprise.The raw materials and spare parts of ship products, such as steel, are large items that require a large amount of space and sufficient manpower to store. Therefore, storage cost is an important factor in the evaluation process of ship suppliers. These attributes in the cost control satisfy formula (9); in other words, the order cost is determined by the product price and the transportation cost and the storage cost at least.(9)f62≥f61+f63+f64.


### 2.8. Data Collection and Initialization

Some data are obtained from the Internet easily, such as business management risk, order numbers, and so on [15]. The amassment of these data employed in the ship-suppliers evaluation experiment is accomplished by the data crawler. Some information lack an appropriate information source assigned by experts in ship-supplier chain management initially. These data are classified into 5° including very good, good, middle, bad, and very bad according to the evaluation results. These assessments should be standardized in order to compare with each other in the process of optimization and evaluation because evaluations from experts are fuzzy. The valid value is shown in Table 2.Table 2
Evaluation degree.
LevelVery goodGoodMiddleBadVery badRange81–10061–8041–6021–400–20Validation value9070503010


## 2.1. Ship-Supplier Evaluation Mathematical Model

The demands for the evaluation of ship suppliers are quite different in the whole lifecycle of the ship from production to extinction, due to the demand subjects in each stage being various. In view of the characteristics of the shipbuilding industry and the demand for marine equipment suppliers, six attributes influencing the selection of the ship supplier are obtained through in-depth interviews with experts, research results, data search, and expert review in this study [11–13]. The assessment of ship suppliers can be accomplished from six attributes, including enterprise strength, financial status, enterprise reputation, product quality, service quality, and cost control [14]. The estimation of every attribute can be carried out by different sub-attributes.The mathematical model to access the ship suppliers from six parts is shown in Table1. The mathematical expression is shown in formula (1), which is an objective function in the ship supplier evaluation mathematical model.(1)Fx=∑i=16wi⋅fix=∑i=16wi⋅∑j=1nwij⋅fijx.Table 1
The component of the attributes in SOSSESIPSO.
AttributesEnterprise Strength (f1)Financial Status (f2)Enterprise Reputation (f3)Sub-attributesHandheld Orders Number (f11)Order Delivery Timely Rate (f12)Order Lead Time(f13)Delivery Rate within Delivery Period(f14)Number of Patents(f15)Quantity of Qualification Certifications(f16)Asset liability Ratio(f21)Return On net Assets(f22)Asset Turnover ratio(f23)Number of Enterprise Awards(f31)Business Risks(f32)Legal Risks(f33)AttributesProduct Quality (f4)Service Quality (f5)Cost Control(f6)Sub-attributesProduct Qualification Rate(f41)Product Premium Rate(f42)Product Quality Certification System(f43)Product Warranty Period(f44)Average Product Life Cycle(f45)Service Satisfaction(f 51)Service Improvement Capability(f 52)Product Development Service Capability(f 53)Product Price(f 61)Order Cost(f62)Transportation Cost(f63)Storage Cost(f 64)The six attributes should be represented by the six parametersf1∼f6, respectively. These parameters wii=1∼6 express the significant degree of about six parts in the evaluation function and the values are in proportion to the significant degree. The values of six parameters are between 0 and 1 under the condition of the sum of six parameters wii=1∼6 equal to 1 shown in formula (2).(2)w1+w2+w3+w4+w5+w6=1.These sub-parameterswij add together are 1 in every attribute fix, the formula representation is shown below.(3)∑j=1nwij=1.Thewifii=1∼6 should satisfy the relationship shown below. In other words, the more value, the more importance.(4)w4f4≥w1f1≥w6f6≥w2f2≥w5f5≥w3f3.


## 2.2. Enterprise Strength

In the ship supply chain, failure to deliver goods within the lead time (delivery date of ship products) or failure to meet customer order quantity will bring obstacles to the effective operation of the ship supply chain. In the ship supply chain, the delivery rate, order satisfaction rate, and order lead time can reflect the delivery situation. Handheld orders, order delivery time rate, order advance time, delivery rate within the delivery period, number of patents, and quantity of qualification certification reflect the enterprise’s strength.Handheld orders refer to the number of orders announced by the shipbuilder in the previous year, which can be obtained from data.Guaranteeing full ordering is the minimum requirement for shipping companies to suppliers, but for some sparsely supplied items, the order satisfaction rate is difficult to maintain, so it is more necessary to put forward requirements for suppliers. Order delivery time rate reflects the possibility of the delivery of the ship suppliers on time.The shorter the order lead time, the stronger the supply chain’s ability to respond to customer needs and the fewer inventories need to be held. Using order advance time as the evaluation criterion, the percentage of delivery times less than this lead time in the total delivery times are measured.Delivery period is the delivery period specified in the shipping industry, mainly reflecting the delivery capacity of suppliers from the perspective of time.The number of patents of an enterprise is composed of the number of software copyrights, utility models, appearance patents, and invention patents. The number of patents is directly proportional to the strength of the enterprise.Qualification certification refers to conformity assessment activities in which a state-recognized certification body certifies that an organization’s products, services, and management system comply with relevant standards, technical specifications, or mandatory requirements. The more qualifications an enterprise obtains for related products, the more standardized the enterprise and the stronger its strength. The formula of the enterprise strength is shown in formula (5).(5)f1=w11f11+w12f12+w13f13+w14f14+w15f15+w16f16.Thew14f14 is more significant than the w12f12, although the delivery rate within the delivery period is less than the order delivery timely rate. The qualification is represented by formula (6).(6)w14f14≥w12f12.


## 2.3. Financial Status

The amount of capital required for ship material procurement is usually large, and good financial and reputation status is an important guarantee for the smooth progress of the procurement. Asset-liability ratio, returns on net assets, and asset turnover ratio are the reflection of the financial situation.The asset-liability ratio is used to measure the long-term solvency of suppliers and reflects whether the enterprise has the ability for sustainable development. This is a very important evaluation indicator for long-term cooperation.Returning on net assets reflects the profitability of the supplier’s net assets and embodies its operating performance and profitability, which is more expressive than sales margin and other indicators.The asset turnover ratio reflects the supplier’s capital turnover capacity to a certain extent, so it is a core indicator that reflects the company’s operational capabilities.The restriction relationship among these attributes is shown in formula (7).(7)f22⋅1−f21f23≥0.


## 2.4. Enterprise Reputation

Good enterprise reputation is the premise of cooperation. Only a good reputation can win the trust of partners, and a good enterprise reputation also reflects the economic strength of the enterprise to a certain extent. The enterprise credibility of the business can be judged from three aspects including the judicial risks, the business risks of the company, and the award number obtained by the enterprise. The number of business risks of an enterprise includes administrative penalties, environmental penalties, abnormal operations, abnormal taxation, and serious violation of laws and promises. The number of judicial risks includes the number of court announcements, the number of legal proceedings, the number of court announcements, and the number of executed persons.


## 2.5. Product Qualification Rate

The product qualification rate refers to the percentage of qualified products in the total purchase amount within a certain period. A higher product pass rate can not only effectively reduce the repair and return but also, more importantly, help to improve the satisfaction of ship owners.The product premium rate refers to the ratio between the number of premium products and the total quantity of products in a certain period. Some precision instruments need not only qualified products but also quality products. Therefore, the premium rate can reflect the high level of the supplier’s products, which is less than the product qualification rate shown in formula (8).(8)w42f42−w41f41≥0.Product quality certification systems can refer to relevant quality certification standards and directly adopt the certification results of authoritative departments to give a certain rating level. The higher the level, the more perfect the certification system will be.The product warranty is a manufacturer’s warranty service for a certain number of years in order to protect the interests of buyers. In general, the longer the product warranty period, the more the manufacturer will recognize the quality of its products.The life cycle of the ship is the whole process of the ship from its usage in the market to the substitution or vanishment from the market. The average life cycle is an average of the life cycle of the ships, which is the economic life in the market movement.


## 2.6. Service Quality

The characteristics of many varieties and long cycles of ship products require ship-supporting enterprises to have a high level of service to maintain the normal operation of the ship. The indicators reflecting the service level of ship suppliers include historical delivery records, after-sales service satisfaction rate, and service improvement capabilities.The after-sales service satisfaction rate is an important indicator for most companies to measure the service level of suppliers, which is designed to reflect the quality management capabilities of suppliers after transactions.Service improvement capability: After-sales service satisfaction rate is an evaluation of the supplier’s “past,” while service improvement capability is a prediction of the supplier’s future service level. As a long-term partner, the future development of suppliers is even more important.Product development service capability is to modify or improve related products to meet the requirements of the enterprise in response to the special needs of shipbuilding enterprises or customers.


## 2.7. Cost Control

Price competition is the focus of shipbuilding competition, and the high cost of materials has become an aporia that needs to be solved in the shipbuilding industry around the world. Competitive suppliers should have competitive advantages in terms of price, ordering cost, transportation cost, and storage cost.Product price refers to the cost that an enterprise needs to pay for each unit of product, and it is the key indicator that most directly reflects the enterprise’s procurement cost.The order cost has a linear relationship with the shipping volume, which is the actual cost that can be calculated according to the relevant standards.The transportation cost is linearly related to the volume, distance, and mode of transportation. If the supplier can provide transportation service by itself, a large amount of cost can be saved for the shipping enterprise.The raw materials and spare parts of ship products, such as steel, are large items that require a large amount of space and sufficient manpower to store. Therefore, storage cost is an important factor in the evaluation process of ship suppliers. These attributes in the cost control satisfy formula (9); in other words, the order cost is determined by the product price and the transportation cost and the storage cost at least.(9)f62≥f61+f63+f64.


## 2.8. Data Collection and Initialization

Some data are obtained from the Internet easily, such as business management risk, order numbers, and so on [15]. The amassment of these data employed in the ship-suppliers evaluation experiment is accomplished by the data crawler. Some information lack an appropriate information source assigned by experts in ship-supplier chain management initially. These data are classified into 5° including very good, good, middle, bad, and very bad according to the evaluation results. These assessments should be standardized in order to compare with each other in the process of optimization and evaluation because evaluations from experts are fuzzy. The valid value is shown in Table 2.Table 2
Evaluation degree.
LevelVery goodGoodMiddleBadVery badRange81–10061–8041–6021–400–20Validation value9070503010


## 3. Intelligent Evaluation Model on Ship Suppliers

### 3.1. Particle Swarm Optimization

Particle swarm optimization (PSO) algorithm is a successful case that evolved from biosimulation and is a significant application to solve the optimization problem. In 1995, Professor Eberhart and Shi designed the PSO algorithm by simulating the searching activity of birds [16]. Some near-optimal solutions may solve some problems or phenomena that cannot be solved in real society through the PSO algorithm. The PSO’s advantages include the higher speed in optimization and easier realization in application mainly in comparison with the genetic algorithm, which is a successful optimization algorithm. The main disadvantage is the difficulty in the selection of the study parameters, which makes the results fall into local optimization easily. Some researchers have made massive innovations to optimize the PSO according to the variety of application areas. Zhang presented an adaptive BBPSO by adding an adaptive disturbance variable to elevate the variety of swarms [17]. Song et al. reported that cost-based feature selection problems can be solved by a multiobjective PSO [18]. A variable-size cooperative coevolutionary particle swarm optimization algorithm is proposed by Song to solve multitarget optimization [19]. These particle swarm optimizations optimized by different methods have been applied in many fields successfully and achieved many significant results.


### 3.2. Self-Optimization Ship-Suppliers Evaluation Algorithm

A self-optimization evaluation algorithm for ship suppliers based on the improved particle swarm optimization (SOSSESIPSO) is presented to elevate the evaluation quality of the ship suppliers efficiently and avoid excessive dependence on some experts.The assessment of ship suppliers can be accomplished from six attributes and every attribute includes diverse sub-attributes. Formula (10) shows the evaluation process in every attribute according to the variety of the attributes.(10)fix=∑j=1nwij⋅fijx.Parameterwij expresses the significant degree of the j th sub-attribute in the i th attribute. The values of these parameters are between 0 and 1 under the condition of the sum of these parameters wijj=1∼n equals to 1 in the evaluation of every attribute. The formula representation is shown as formula (11).(11)∑j=1nwij=1.Parametern is the number of sub-attributes in every attribute. The target function in the training process is to min the difference between the evaluation value and the real value in SOSSESIPSO, which indicates the optimization direction in the study process. The formula is shown below.(12)MINTx=Fx−Rx.TheR(x) expresses the real evaluation value of the enterprise x in the formula (12). The calculation of the R(x) is accomplished by the analysis of the investigative results and the confirmation about the R(x) is finished by the experts.The whole optimization process of the ship-suppliers evaluation algorithm is shown in Figure1.Figure 1
The optimization process of the SOSSESPSO.


## 3.1. Particle Swarm Optimization

Particle swarm optimization (PSO) algorithm is a successful case that evolved from biosimulation and is a significant application to solve the optimization problem. In 1995, Professor Eberhart and Shi designed the PSO algorithm by simulating the searching activity of birds [16]. Some near-optimal solutions may solve some problems or phenomena that cannot be solved in real society through the PSO algorithm. The PSO’s advantages include the higher speed in optimization and easier realization in application mainly in comparison with the genetic algorithm, which is a successful optimization algorithm. The main disadvantage is the difficulty in the selection of the study parameters, which makes the results fall into local optimization easily. Some researchers have made massive innovations to optimize the PSO according to the variety of application areas. Zhang presented an adaptive BBPSO by adding an adaptive disturbance variable to elevate the variety of swarms [17]. Song et al. reported that cost-based feature selection problems can be solved by a multiobjective PSO [18]. A variable-size cooperative coevolutionary particle swarm optimization algorithm is proposed by Song to solve multitarget optimization [19]. These particle swarm optimizations optimized by different methods have been applied in many fields successfully and achieved many significant results.


## 3.2. Self-Optimization Ship-Suppliers Evaluation Algorithm

A self-optimization evaluation algorithm for ship suppliers based on the improved particle swarm optimization (SOSSESIPSO) is presented to elevate the evaluation quality of the ship suppliers efficiently and avoid excessive dependence on some experts.The assessment of ship suppliers can be accomplished from six attributes and every attribute includes diverse sub-attributes. Formula (10) shows the evaluation process in every attribute according to the variety of the attributes.(10)fix=∑j=1nwij⋅fijx.Parameterwij expresses the significant degree of the j th sub-attribute in the i th attribute. The values of these parameters are between 0 and 1 under the condition of the sum of these parameters wijj=1∼n equals to 1 in the evaluation of every attribute. The formula representation is shown as formula (11).(11)∑j=1nwij=1.Parametern is the number of sub-attributes in every attribute. The target function in the training process is to min the difference between the evaluation value and the real value in SOSSESIPSO, which indicates the optimization direction in the study process. The formula is shown below.(12)MINTx=Fx−Rx.TheR(x) expresses the real evaluation value of the enterprise x in the formula (12). The calculation of the R(x) is accomplished by the analysis of the investigative results and the confirmation about the R(x) is finished by the experts.The whole optimization process of the ship-suppliers evaluation algorithm is shown in Figure1.Figure 1
The optimization process of the SOSSESPSO.


## 4. Global Optimum and Local Optimum

There are two significant elements, global optimum and local optimum, in the particle swarm optimization algorithm. The global optimum is the best value in the particle swarm during the optimum process and the local optimums are the highest value in the optimization process for every particle. The comparation scopes are different, although both values are optimum. The global optimum is only one in the whole particle swarm but the number of the local optimum is different and equal to the number of particles in the swarm. The functions of these two elements play an important role in the optimization quality and speed and determine the optimization result.The research about the improvement of the particle swarm optimization algorithm concentrates on the local optimums usually, because they focus on the individual optimum excessively, making the optimization result falls into local pitfalls easily. A modified particle swarm optimization based on the dynamic k-means algorithm is presented in order to surmount the defect in the local optimum of the particle swarm optimization. These rules deciding thek are various, although some researchers have applied the k-means to improve the particle swarm optimization in the past. In this paper, the concrete method of computing the local optimum is to average the local optimums of k particles that are nearest to the target particle, and the k is a dynamic value rather than a stationary value. The concrete value of the k is resolved by the different rates among local particles, which can be calculated by formula (13).(13)DifferenceRatei=LocalBesttarget−LocalBestjLocalBesttarget.The different rates between the target particle and every particle in the nearestk particles should be calculated. If the difference rate is less than a concrete percent that is ascertained by the experiment, the particle will be considered in the average range to compute the local optimum of the target particle shown at (14). The concrete percent is dynamic instead of static. In this experiment, the concrete percent is 10 percent. The value of the k is 10 percent of the total amount of the particle swarm and should be rounded off.(14)LocalBestj=∑i=1kLocalBestik.The global best value in the SOSSESIPSO is the minimum value in the absolute difference in the enterprise strength, financial status, enterprise reputation, product quality, service quality, and cost control.


## 5. Algorithm Initialization

Some attributes employed in the ship-suppliers evaluation system are designed by the analysis of the commerce data about ship-supplier companies on the Internet or the information distributed by the factories about ship suppliers. The other attributes are assigned by some experts about ship-supplier chains according to their working experiences or research results.These attributes should be initialized first in order to make these attributes compare with each other easily. The accomplishment of the initialization method for the ship-suppliers data is to employ the mean value and variance. From formula (15) to formula (17),DSLU shows the initialization process.(15)xij=xij−xi¯si,(16)xi¯=∑j=1nxijn¯,(17)si=1n−1∑i=1nxij−xi¯.Parameterxij represents the value of the j th sub-attribute in the i th attribute. si is the standard deviation of the i th attribute and xi is the mean value of the i th attribute.


## 6. Experiment and Discussion

The evaluation process of the ship suppliers has been presented explicitly, and in the following section, the experiments on the SOSSESIPSO will be elaborated clearly. One experiment is to select parameters with the best performances, and another is to confirm the performance of the improved particle swarm optimization is better than the unimproved one.


### 6.1. Training Performance

Two experiments will be designed to verify the optimization results of the self-optimization evaluation algorithm for the ship suppliers. The first experiment is to compare the performances with different parameter combinations (C1 = C2 = 2, C1 = C2 = 1.5 with rand = 0.3 or rand = 0.5) and select the optimal attributes with the best performance before 500 generations. The second experiment validates that the performance of the improved particle swarm optimization is better than the unimproved one in the evaluation of optimization results about the ship suppliers.These parameterswiji=1∼6andj=1∼n at the beginning of the evaluation optimization about the ship suppliers are assigned randomly from 0 to 1 without the help from experts and 20 particles are included in the particle swarm. The experiment platform is some personal computers with an Inter(R) Core™ i5-3230M CPU, 2.60 GHz, and 16 GB RAM. The accomplishment of the programs employed in the experiments is achieved with the help of Python.For the analysis of the optimizing performance through the training process, 25 global optimums with the best fitness in particle swarm are selected every 20 generations from 1 to 500 generations for every parameter combination shown in Figure2.Figure 2
The performances of the SOSSESIPSO with different parameters. (a) Performances by C1 = C2 = 1.5 rand = 0.3. (b) Performances by C1 = C2 = 1.5 rand = 0.5. (c) Performances by C1 = C2 = 2 rand = 0.3. (d). Performances by C1 = C2 = 2 rand = 0.5.
(a)(b)(c)(d)Figures2(a) and 2(b) show the performance of the evaluation optimization in the ship suppliers when the parameter C1 = C2 = 1.5 and rand = 0.3 or rand = 0.5. The evaluation value clearly decreased from 37 to about 23 before about 380 generations which are shown in Figure 2(a). As the optimization continues, the evaluation result is around 23 means the study power is in a stable situation without further decline. When the C1 = C2 = 1.5 and rand = 0.5, the evaluation value is in the decline situation before 340 generations; however, some rebound phenomena are clear in the decline process. The optimization results are not clear decline after 340 generations and the study result is around 24.The optimizing condition of the SOSSESIPSO when the C1 = C2 = 2 is shown in Figures2(c) and 2(d). Before 230 generations, the learning effect of the SOSSESIPSO is no evident difference between the rand = 0.5 and rand = 0.3, and the best fitness of the evaluation function averages at about 25. When the rand equals 0.3, the study efficiency accelerated from the 230 generations to the 500 generations, in which unusual phenomenon is limited and out of consideration, and the evaluation value decreased from around 26 to 12. The study efficiency of the rand = 0.5 is slower than the rand = 0.3 after 230 generations and the evaluation value reaches 19 with some little zigzag phenomenon.Because the optimization velocity of the best fitness when the parameter rand is initially assigned to 0.3 is higher than the rand which is initialized to 0.5 in the optimization process without considering C1 and C2 and the range of the oscillation of the former is smaller than the latter, the rand assigned to 0.5 is eliminated from consideration. From the abovementioned analysis and Figure2 from (a) to (d), we can conclude that the SOSSESIPSO whether the C1 = C2 = 1.5 or C1 = C2 = 2 can optimize the evaluation of the ship suppliers to some extent and the optimization speed of the C1 = C2 = 2 is faster than the C1 = C2 = 1.5. Therefore, these parameter combinations (C1 = C2 = 2 and rand = 0.3) are selected for further optimization.The performances of the SOSSESIPSO are not satisfactory when parameter C1 is not equal to C2 compared with the C1 equivalent of C2 from the analysis of the experiments above. These parameters C1 = C2 = 2 and rand = 0.3 will be selected for consideration in the next experiment because the training results are superior to the other parameters combination when the C1 is equal to the C2.


## 6.1. Training Performance

Two experiments will be designed to verify the optimization results of the self-optimization evaluation algorithm for the ship suppliers. The first experiment is to compare the performances with different parameter combinations (C1 = C2 = 2, C1 = C2 = 1.5 with rand = 0.3 or rand = 0.5) and select the optimal attributes with the best performance before 500 generations. The second experiment validates that the performance of the improved particle swarm optimization is better than the unimproved one in the evaluation of optimization results about the ship suppliers.These parameterswiji=1∼6andj=1∼n at the beginning of the evaluation optimization about the ship suppliers are assigned randomly from 0 to 1 without the help from experts and 20 particles are included in the particle swarm. The experiment platform is some personal computers with an Inter(R) Core™ i5-3230M CPU, 2.60 GHz, and 16 GB RAM. The accomplishment of the programs employed in the experiments is achieved with the help of Python.For the analysis of the optimizing performance through the training process, 25 global optimums with the best fitness in particle swarm are selected every 20 generations from 1 to 500 generations for every parameter combination shown in Figure2.Figure 2
The performances of the SOSSESIPSO with different parameters. (a) Performances by C1 = C2 = 1.5 rand = 0.3. (b) Performances by C1 = C2 = 1.5 rand = 0.5. (c) Performances by C1 = C2 = 2 rand = 0.3. (d). Performances by C1 = C2 = 2 rand = 0.5.
(a)(b)(c)(d)Figures2(a) and 2(b) show the performance of the evaluation optimization in the ship suppliers when the parameter C1 = C2 = 1.5 and rand = 0.3 or rand = 0.5. The evaluation value clearly decreased from 37 to about 23 before about 380 generations which are shown in Figure 2(a). As the optimization continues, the evaluation result is around 23 means the study power is in a stable situation without further decline. When the C1 = C2 = 1.5 and rand = 0.5, the evaluation value is in the decline situation before 340 generations; however, some rebound phenomena are clear in the decline process. The optimization results are not clear decline after 340 generations and the study result is around 24.The optimizing condition of the SOSSESIPSO when the C1 = C2 = 2 is shown in Figures2(c) and 2(d). Before 230 generations, the learning effect of the SOSSESIPSO is no evident difference between the rand = 0.5 and rand = 0.3, and the best fitness of the evaluation function averages at about 25. When the rand equals 0.3, the study efficiency accelerated from the 230 generations to the 500 generations, in which unusual phenomenon is limited and out of consideration, and the evaluation value decreased from around 26 to 12. The study efficiency of the rand = 0.5 is slower than the rand = 0.3 after 230 generations and the evaluation value reaches 19 with some little zigzag phenomenon.Because the optimization velocity of the best fitness when the parameter rand is initially assigned to 0.3 is higher than the rand which is initialized to 0.5 in the optimization process without considering C1 and C2 and the range of the oscillation of the former is smaller than the latter, the rand assigned to 0.5 is eliminated from consideration. From the abovementioned analysis and Figure2 from (a) to (d), we can conclude that the SOSSESIPSO whether the C1 = C2 = 1.5 or C1 = C2 = 2 can optimize the evaluation of the ship suppliers to some extent and the optimization speed of the C1 = C2 = 2 is faster than the C1 = C2 = 1.5. Therefore, these parameter combinations (C1 = C2 = 2 and rand = 0.3) are selected for further optimization.The performances of the SOSSESIPSO are not satisfactory when parameter C1 is not equal to C2 compared with the C1 equivalent of C2 from the analysis of the experiments above. These parameters C1 = C2 = 2 and rand = 0.3 will be selected for consideration in the next experiment because the training results are superior to the other parameters combination when the C1 is equal to the C2.


## 7. Optimizing Comparison

The next experiment is to retestify the performance of the improved PSO. The comparative performances of the self-optimization evaluation system about ship suppliers based on unimproved particle swarm optimization and improved particle swarm optimization with the parameters C1 = C2 = 2 and rand = 0.3 before 1000 generations are shown in Figure3.Figure 3
The performances of the SOSSESIPSO with different parameters.The performances of these self-optimization evaluation systems are not different clearly before 220 generations in which the optimal results are not obvious and these best values rebound around 30. The optimization speed with improved particle swarm optimization is faster than the unimproved PSO from 220 generations. At the same time, the performance of the latter is not stable and the fluctuation is great, although the changing tendency of the best value is declining. The global optimums of two self-optimization evaluation systems based on different PSOs are 7 and 15, respectively, when the training reaches the 1000 generation.From the abovementioned analysis, the particle swarm optimization based on the dynamic k-means can effectively improve the capability of the evaluation function of the ship suppliers and the optimization effect and speed are superior to the unimproved PSO. The particle swarm optimization based on the dynamic k-means algorithm makes the ship-suppliers evaluation system have the self-optimization ability without the experts’ help.


## 8. Conclusions

The new particle swarm optimization accomplishes the self-optimization evaluation of ship suppliers, which avoids the plethoric experts’ help. The experiment shows that the improved particle swarm optimization can arrive at the best optimum easily and the application performance is superior to the unimproved particle swarm optimization in optimization.The limitation of the proposed approach is the improvement of the standard particle swarm optimization instead of the up-to-date PSO, which has been improved by different methods. In the future, we will apply many excellent PSO algorithms to perfect the SOSSESIPSO algorithm and analyze the optimization results. The final purpose is to realize the intelligent ship-suppliers evaluation.



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*Source: 9092390-2022-09-30.xml*